Sudoku Difficulty Analysis: number of clues: 34 number of tidbits: 566 number of steps required: 5 number of eliminations from... ...hidden singles : 29 ...naked singles : 18 ...hidden pairs : 0 ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 0 ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 0 ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
5 steps Step 1 Step 2 Step 3 Step 4 Step 5 ||/,,,,5,,,,,,,3,,,,,,,1,2,,4,,,,,,,2,,,,6,,,,,,,,,,7,,,,2,,4,,6,,8,,1,,,4,,,,8,9,1,2,,4,,,,,9,,2,,,,,,8,,,,,,,6,,,,,2,,4,,,7,,,,2,,4,,,7,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,4,,,7,8,,,2,,4,,,,,,,2,,,,,7,8,,1,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,2,3,,,,,,,,,3,4,,,,,,,2,,4,,,,,,1,,3,4,5,,7,,,,,,,,6,,,,,2,,,,,7,,,,,,,,,,8,,1,2,,,5,,,,,1,2,,,5,,,,9,,,,,,,7,,9,,,,,,6,,,,1,,,4,,,,,,,,,4,5,,7,,9,,2,,4,5,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,2,,,,6,,,9,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,9,,2,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,1,,3,,5,,,,9,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,4,5,,,8,9,,,,4,5,,,,9,,,,,,6,,,,1,,3,,,,,,9,,,,,,6,,,,1,,3,,5,,,,9,,,3,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,2,,,,,7,8,,,2,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,1,2,3,,,,,,,1,2,,4,5,,,,,1,2,3,4,5,,,,,,2,3,,5,6,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,6,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,2,,4,,,,,,,2,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,4,,,7,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,4,,,,,,,2,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,2,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,7,,,,,,,,,,8,,1,,,,5,,,,,1,,,,5,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,4,,,,,,,,,4,,,,,9,,2,,4,5,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,4,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,5,,,,,,,,4,5,,,,,,2,,,5,6,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,1,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,4,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,4,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,5,,,,,,,,4,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9
Sudoku Difficulty Analysis: number of clues: 27 number of tidbits: 509 number of steps required: 16 number of eliminations from... ...hidden singles : 34 ...naked singles : 20 ...hidden pairs : 0 ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 0 ...naked tuples : 1(step 6) ...naked quads : 0 ...locked candidates : 2(step 4) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
14 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 ||/,,,,,,,,9,1,,3,4,,,,,,1,,3,,,,,8,,,2,,,,,,,,1,,3,,,6,7,,,1,,3,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,1,2,,,,,,,9,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,1,2,,,5,,,8,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,2,,,,6,7,8,9,1,2,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,8,,,,,,,6,,,,,,3,,5,,7,8,9,1,,,,,,,,,,2,3,,5,,7,8,,,2,3,,,,7,,,,2,3,,,,,8,9,,2,,,,,,8,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,3,,5,,,8,9,,,3,,5,,,,,,,3,4,5,,,8,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,1,2,,,,6,7,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,1,,,,5,6,7,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,6,7,,9,1,,,4,,6,7,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,1,,3,,,,,8,,,2,,,,,,,,1,,3,,,6,7,,,1,,3,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,8,9,1,,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,8,,,,,,,6,,,,,,3,,5,,7,8,9,1,,,,,,,,,,,3,,5,,7,8,,,2,3,,,,7,,,,,3,,,,,8,9,,2,,,,,,8,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,3,,5,,,8,9,,,3,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,1,,,,5,6,7,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,6,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,8,9,1,,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,7,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,,,5,,,8,9,,,3,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,7,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,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Sudoku Difficulty Analysis: number of clues: 28 number of tidbits: 522 number of steps required: 27 number of eliminations from... ...hidden singles : 33 ...naked singles : 20 ...hidden pairs : 2(step 11) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 0 ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 10(step 4) ...X-wings : 1(step 18) ...swordfish : 1(step 18) ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
26 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 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,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,8,,,,,,,6,,,,,,,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,8,,1,,,,,,,,,,,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,4,,,,,,,,3,,,,,8,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,6,7,,,,,,,,6,7,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,8,,,,,,,6,,,,,,,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,8,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9
Sudoku Difficulty Analysis: number of clues: 40 number of tidbits: 568 number of steps required: 14 number of eliminations from... ...hidden singles : 21 ...naked singles : 20 ...hidden pairs : 0 ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 0 ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 4(step 1) ...X-wings : 0 ...swordfish : 1(step 5) ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
13 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 ||/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,3,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,6,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,6,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,7,,9,,,,,,6,,,,,,,4,,,,,,,,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,7,,9,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,,6,,,9,,,3,,,6,,,9,,,,,,,,8,,,,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,9,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,5,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,8,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,,,,7,,,,,,4,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2
Sudoku Difficulty Analysis: number of clues: 32 number of tidbits: 528 number of steps required: 33 number of eliminations from... ...hidden singles : 24 ...naked singles : 25 ...hidden pairs : 3(step 5) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 4(step 4) ...naked tuples : 1(step 20) ...naked quads : 0 ...locked candidates : 9(step 1) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 2(step 10) ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
31 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 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6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,6,7,,,,2,,,5,6,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,2,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,2,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,8,,,2,,,,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,8,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,8,9,,,,,,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,8,,,,,,,6,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,9,,2,,,,,,,,,,,,,,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,8,,,,,,,6,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5
Sudoku Difficulty Analysis: number of clues: 47 number of tidbits: 583 number of steps required: 24 number of eliminations from... ...hidden singles : 5 ...naked singles : 29 ...hidden pairs : 0 ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 1(step 15) ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 11(step 1) ...X-wings : 1(step 9) ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 4(step 10) ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
23 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 ||/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,6,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,7,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,7,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,5,,,,,,,3,,,,,8,9,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,9,,,,,,,,8,,,,3,,,,,,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,9,,,,,,,,8,,,,,,,,,,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8||6b
Sudoku Difficulty Analysis: number of clues: 17 number of tidbits: 409 number of steps required: 63 number of eliminations from... ...hidden singles : 35 ...naked singles : 29 ...hidden pairs : 6(step 22) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 1(step 52) ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 32(step 2) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 1(step 53) ...weak Medusa cycles : 0 ...hypothesis and proof : 0 ||
62 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 Step 32 Step 33 Step 34 Step 35 Step 36 Step 37 Step 38 Step 39 Step 40 Step 41 Step 42 Step 43 Step 44 Step 45 Step 46 Step 47 Step 48 Step 49 Step 50 Step 51 Step 52 Step 53 Step 54 Step 55 Step 56 Step 57 Step 58 Step 59 Step 60 Step 61 Step 62 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,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,4,,,,,,,,,,5,,,,,,,,,,,,8,9,,,3,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,3,4,,6,,,9,,,3,4,,,,,9,,2,,,,,,,,1,,3,4,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,4,,,,,,,,,,5,,7,,,,2,,,,,,8,,1,,3,4,,6,,,,,2,,,,,,8,,,,,,5,,7,,,1,,3,4,,6,,,,1,,,4,5,,7,,,,,,,5,,7,,,,,3,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,4,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,2,,,,,,,,1,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,3,,5,,,,9,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,4,,,,,,,,,,5,,,,,,,,,,,,8,9,,,3,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,3,4,,6,,,9,,,3,4,,,,,9,,2,,,,,,,,1,,3,4,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,4,,,,,,,,,,5,,7,,,,2,,,,,,8,,1,,3,4,,6,,,,,2,,,,,,8,,,,,,5,,7,,,1,,3,4,,6,,,,1,,,4,,,,,,,,,,5,,7,,,,,3,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,4,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,2,,,,,,,,1,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,3,,5,,,,9,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,4,,,,,,,,,,5,,,,,,,,,,,,8,9,,,3,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,3,4,,6,,,9,,,3,4,,,,,9,,2,,,,,,,,1,,3,4,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,4,,,,,,,,,,5,,7,,,,2,,,,,,8,,1,,3,4,,6,,,,,2,,,,,,8,,,,,,5,,7,,,1,,3,4,,6,,,,1,,,4,,,,,,,,,,5,,7,,,,,3,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,2,,,,,,,,1,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,3,,5,,,,9,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,3,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,3,,,6,,,9,,,,4,,,,,,,2,,,,,,,,1,,3,,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,2,,,,,,8,,1,,3,,,6,,,,,2,,,,,,8,,,,,,5,,7,,,1,,3,4,,6,,,,1,,,4,,,,,,,,,,5,,7,,,,,3,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,2,,,,,,,,1,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,,,5,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,,,,6,,,9,,,,4,,,,,,,2,,,,,,,,1,,,,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,2,,,,,,8,,1,,,,,6,,,,,2,,,,,,8,,,,,,5,,7,,,1,,3,,,6,,,,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,2,,,,,,,,,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,,,5,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,9,1,,,,,6,,,9,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,,,,8,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,2,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,6,7,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,,,,9,,,,,5,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,,,,8,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,8,,,,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,,,,2,,,,6,,,9,,,,4,,,7,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,6,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,5,,,,,,,,,5,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,,,,8,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,,,,,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,,,,4,,,,,9,,2,,,,,,,9,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,7,,,,,,,,,,,9,,,,,5,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,9,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,4,5,,,,,1,,,,,,,,,,,,4,,,,8,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,8,9,1,,,,,,,,,,2,,,,,,,,,,,,,,,8,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,,,,4,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,8,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,4,,,,8,,,,,4,,,,8,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,,,,,,8/,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,4,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,,,,,9,,2,,,,,,,,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,,,,,,8||6a
Sudoku Difficulty Analysis: number of clues: 42 number of tidbits: 583 number of steps required: 18 number of eliminations from... ...hidden singles : 17 ...naked singles : 22 ...hidden pairs : 3(step 6) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 1(step 13) ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 9(step 1) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 1(step 14) ...hypothesis and proof : 0 ||
17 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 ||/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,4,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,4,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,3,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,1,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,1,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,4,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,3,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,1,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,1,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,3,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,1,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,1,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,1,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,1,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,1,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,5,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,8,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,8,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,5,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,9,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,8,9,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,1,,3,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,,,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,,,,4,5,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,,,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,,,,4,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,1,,,,,,7,8,9,1,,,,,6,,,,,,,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,3,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,,,,3,,,6,,,9,,,3,,,,,,9,,,,,,,7,,,,,,4,5,,,,,,,,4,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,7,8,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,,6,,,,,,,4,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,,,,,,,7,8,9,1,,,,,6,,,,,,,,,,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,9,1,,,,,6,,,,,,3,,,6,,,9,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,8,,1,,3,4,,,,,,1,,3,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,3,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,,,,,,,7,8,9,1,,,,,6,,,,,,,,,,7,8,9,,,,,,,7,8,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,9,,,,,,,7,8,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,9,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,1,,,4,,,,,,,,3,,,,,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,9,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,1,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,6,,,,,,,,,,7,,9,,,,,,,7,,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,7,,,,,3,,,,,,,,,,,5,6,7,,,,,,,5,,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1/,,,4,,,,,,,,,,,,,8,,,,,,,,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,9,1,,,,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,2,,,,,,8,,1,,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,8,,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,9,,,,4,,,,,,1,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,6,,,,,,,,5,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,,,,,,,7,,,1||y-cycles
Sudoku Difficulty Analysis: number of clues: 23 number of tidbits: 453 number of steps required: 38 number of eliminations from... ...hidden singles : 37 ...naked singles : 21 ...hidden pairs : 3(step 15) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 2(step 13) ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 13(step 3) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 0 ...weak Medusa cycles : 0 ...hypothesis and proof : 1(step 18) ||
37 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 Step 32 Step 33 Step 34 Step 35 Step 36 Step 37 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,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,6,,,,1,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,5,6,,,,,,,,5,6,,8,,1,,3,,5,,,8,,,,,4,,,,,,1,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,1,,,,5,,,8,,,,3,,,,,,,1,,,,5,,,,,,,,,,,7,,,1,,,,5,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,1,,,,5,,,8,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,1,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,6,,,,1,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,5,6,,,,,,,,5,6,,8,,1,,3,,5,,,8,,,,,4,,,,,,1,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,5,,,8,,,,3,,,,,,,1,,,,5,,,,,,,,,,,7,,,1,,,,5,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,1,,,,5,,,8,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,1,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,6,,,,1,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,5,6,,,,,,,,5,6,,8,,1,,3,,5,,,8,,,,,4,,,,,,1,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,5,,,8,,,,3,,,,,,,1,,,,5,,,,,,,,,,,7,,,1,,,,5,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,1,,,,5,,,8,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,6,,,,,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,5,6,,,,,,,,5,6,,8,,,,3,,5,,,8,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,5,,,8,,,,3,,,,,,,1,,,,5,,,,,,,,,,,7,,,,,,,5,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,5,6,,,,,,,,5,6,,,,,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,5,6,,8,,,,3,,5,,,8,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,5,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,5,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,5,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,,,,,3,,,,,8,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,3,,5,,,8,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,5,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,8,,1,,,4,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,8,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,,,1,,,4,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,8,,1,,,,,6,,8,,1,,,,,6,,8,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,8,,,,,4,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,1,,3,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,,,1,,,4,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,1,,,,,6,,,,1,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,3,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,1,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,4,,,,,,1,,,4,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,1,,,,,6,,,,1,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,,,,4/1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,1,,,,,6,,,,1,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,,,,4||proof
Sudoku Difficulty Analysis: number of clues: 18 number of tidbits: 427 number of steps required: 63 number of eliminations from... ...hidden singles : 24 ...naked singles : 39 ...hidden pairs : 7(step 12) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 13(step 20) ...naked tuples : 1(step 53) ...naked quads : 0 ...locked candidates : 22(step 2) ...X-wings : 0 ...swordfish : 1(step 55) ...4x4 grids : 0 ...strong Medusa cycles : 2(step 31) ...weak Medusa cycles : 0 ...hypothesis and proof : 6(step 16) ||
62 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 Step 32 Step 33 Step 34 Step 35 Step 36 Step 37 Step 38 Step 39 Step 40 Step 41 Step 42 Step 43 Step 44 Step 45 Step 46 Step 47 Step 48 Step 49 Step 50 Step 51 Step 52 Step 53 Step 54 Step 55 Step 56 Step 57 Step 58 Step 59 Step 60 Step 61 Step 62 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,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,4,,6,,,,,,,4,,6,,,,,,3,,,,,,,1,,,,,,,,,,2,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,1,,,,,6,,,,,2,,,,6,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,9,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,,,2,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,5,,7,,,,,,,,,,8,,,,,,5,,,,,,2,,,,6,,,,1,,,,,,,,,,2,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,9,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,9,,,,,,6,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,8,,,2,,4,,,,,,,,,4,,,,,9,,2,,,,,,,9,,,3,,,,,,,1/,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,4,,6,,,,,,,4,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,2,,,,6,,,,1,,,,,,,,,,2,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,9,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,8,,,2,,4,,,,,,,,,4,,,,,9,,2,,,,,,,9,,,3,,,,,,,1/,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,4,,6,,,,,,,4,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,8,,,2,,4,,,,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,1/,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,3,,,,,,,1||+depth
Sudoku Difficulty Analysis: number of clues: 25 number of tidbits: 490 number of steps required: 49 number of eliminations from... ...hidden singles : 30 ...naked singles : 26 ...hidden pairs : 5(step 10) ...hidden tuples : 0 ...hidden quads : 0 ...naked pairs : 33(step 5) ...naked tuples : 0 ...naked quads : 0 ...locked candidates : 7(step 1) ...X-wings : 0 ...swordfish : 0 ...4x4 grids : 0 ...strong Medusa cycles : 1(step 38) ...weak Medusa cycles : 1(step 33) ...hypothesis and proof : 21(step 4) ||
48 steps Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 Step 32 Step 33 Step 34 Step 35 Step 36 Step 37 Step 38 Step 39 Step 40 Step 41 Step 42 Step 43 Step 44 Step 45 Step 46 Step 47 Step 48 ||/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,5,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,4,5,6,,,9,1,,,,5,6,,,,,,,,,,,8,,1,,3,,,,,,,1,,,4,5,6,,,,1,,,4,5,,,,,,,3,,,,,,,1,2,,4,,6,,,,1,,,,5,6,,,,,,,,,,,8,,1,2,,,5,6,7,,,1,2,,,5,,7,,,,,,,,,,,9,,2,,4,,,,8,9,,,,4,,,7,8,9,,2,,4,,,7,8,,,,,,5,,,,,1,,,,,6,,8,9,,,,4,,6,,,9,,,3,,,,,,,1,2,,4,,,7,,,1,2,,4,,,7,8,,,,3,4,5,,,8,,,,,,,6,,,,,,,4,5,,7,8,,1,,,4,,,,8,,,2,,,,,,,,,,3,4,,,,,,1,,,,5,,7,8,,,,,,,,,,9,1,,,4,,,7,8,,,2,3,4,5,,,8,9,,,,4,5,,,8,9,1,,,,,,,,,,,,4,,,,8,9,,,3,,,,,8,9,,,,,,,7,,,,2,,,5,,,8,,,2,,4,5,,,,,,,,,,6,,,,1,2,,4,5,6,,8,,1,,,4,5,,7,8,,,2,,4,5,6,7,8,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,6,,,,,,,,,,,,9,1,2,,4,,,7,,,1,2,,4,,,7,8,,1,2,,,5,,,8,,,,3,,,,,,,,2,,,5,,7,8,,,2,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,4,,6,,8,,,,,4,,,7,8,,,,,,,,,,9,,2,,,,6,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,5,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,4,5,6,,,9,1,,,,5,6,,,,,,,,,,,8,,1,,3,,,,,,,1,,,4,5,6,,,,1,,,4,5,,,,,,,3,,,,,,,1,2,,4,,6,,,,1,,,,5,6,,,,,,,,,,,8,,1,2,,,5,6,7,,,1,2,,,5,,7,,,,,,,,,,,9,,2,,4,,,,8,9,,,,4,,,7,8,9,,2,,4,,,7,8,,,,,,5,,,,,1,,,,,6,,8,9,,,,4,,6,,,9,,,3,,,,,,,1,2,,4,,,7,,,1,2,,4,,,7,8,,,,3,4,5,,,8,,,,,,,6,,,,,,,4,5,,7,8,,1,,,4,,,,8,,,2,,,,,,,,,,3,4,,,,,,1,,,,5,,7,8,,,,,,,,,,9,1,,,4,,,7,8,,,2,3,4,5,,,8,9,,,,4,5,,,8,9,1,,,,,,,,,,,,4,,,,8,9,,,3,,,,,8,9,,,,,,,7,,,,2,,,5,,,8,,,2,,4,5,,,,,,,,,,6,,,,1,2,,,5,6,,8,,1,,,4,5,,7,8,,,2,,4,5,6,7,8,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,6,,,,,,,,,,,,9,1,2,,4,,,7,,,1,2,,4,,,7,8,,1,2,,,5,,,8,,,,3,,,,,,,,2,,,5,,7,8,,,2,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,4,,6,,8,,,,,4,,,7,8,,,,,,,,,,9,,2,,,,6,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,5,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,4,5,6,,,9,1,,,,5,6,,,,,,,,,,,8,,1,,3,,,,,,,1,,,4,5,6,,,,1,,,4,5,,,,,,,3,,,,,,,1,2,,4,,6,,,,1,,,,5,6,,,,,,,,,,,8,,1,2,,,5,6,7,,,1,2,,,5,,7,,,,,,,,,,,9,,2,,4,,,,8,9,,,,4,,,7,8,9,,2,,4,,,7,8,,,,,,5,,,,,1,,,,,6,,8,9,,,,4,,6,,,9,,,3,,,,,,,1,2,,4,,,7,,,1,2,,4,,,7,8,,,,3,4,5,,,8,,,,,,,6,,,,,,,4,5,,7,8,,1,,,4,,,,8,,,2,,,,,,,,,,3,4,,,,,,1,,,,5,,7,8,,,,,,,,,,9,1,,,4,,,7,8,,,2,3,4,5,,,8,9,,,,4,5,,,8,9,1,,,,,,,,,,,,4,,,,8,9,,,3,,,,,8,9,,,,,,,7,,,,2,,,5,,,8,,,2,,4,5,,,,,,,,,,6,,,,1,2,,,5,6,,8,,1,,,,5,,7,8,,,2,,4,5,6,7,8,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,6,,,,,,,,,,,,9,1,2,,4,,,7,,,1,2,,4,,,7,8,,1,2,,,5,,,8,,,,3,,,,,,,,2,,,5,,7,8,,,2,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,4,,6,,8,,,,,4,,,7,8,,,,,,,,,,9,,2,,,,6,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,5,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,4,5,6,,,9,1,,,,5,6,,,,,,,,,,,8,,1,,3,,,,,,,1,,,4,5,6,,,,1,,,4,5,,,,,,,3,,,,,,,1,2,,4,,6,,,,1,,,,5,6,,,,,,,,,,,8,,1,2,,,5,6,7,,,1,2,,,5,,7,,,,,,,,,,,9,,2,,4,,,,8,9,,,,4,,,7,8,9,,2,,4,,,7,8,,,,,,5,,,,,1,,,,,6,,8,9,,,,4,,6,,,9,,,3,,,,,,,1,2,,4,,,7,,,1,2,,4,,,7,8,,,,3,4,5,,,8,,,,,,,6,,,,,,,4,5,,7,8,,1,,,4,,,,8,,,2,,,,,,,,,,3,4,,,,,,1,,,,5,,7,8,,,,,,,,,,9,1,,,4,,,7,8,,,2,3,4,5,,,8,9,,,,4,5,,,8,9,1,,,,,,,,,,,,4,,,,8,9,,,3,,,,,8,9,,,,,,,7,,,,2,,,5,,,8,,,2,,4,5,,,,,,,,,,6,,,,1,2,,,5,6,,8,,1,,,,5,,7,8,,,2,,,5,6,7,8,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,6,,,,,,,,,,,,9,1,2,,4,,,7,,,1,2,,4,,,7,8,,1,2,,,5,,,8,,,,3,,,,,,,,2,,,5,,7,8,,,2,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,4,,6,,8,,,,,4,,,7,8,,,,,,,,,,9,,2,,,,6,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,5,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,4,5,6,,,9,1,,,,5,6,,,,,,,,,,,8,,1,,3,,,,,,,1,,,4,5,6,,,,1,,,4,5,,,,,,,3,,,,,,,1,2,,4,,6,,,,1,,,,5,6,,,,,,,,,,,8,,1,2,,,5,6,7,,,1,2,,,5,,7,,,,,,,,,,,9,,2,,4,,,,8,9,,,,4,,,7,8,9,,2,,4,,,7,8,,,,,,5,,,,,1,,,,,6,,8,9,,,,4,,6,,,9,,,3,,,,,,,1,2,,4,,,7,,,1,2,,4,,,7,8,,,,3,,5,,,8,,,,,,,6,,,,,,,4,5,,7,8,,1,,,4,,,,8,,,2,,,,,,,,,,3,4,,,,,,1,,,,5,,7,8,,,,,,,,,,9,1,,,4,,,7,8,,,2,3,4,5,,,8,9,,,,4,5,,,8,9,1,,,,,,,,,,,,4,,,,8,9,,,3,,,,,8,9,,,,,,,7,,,,2,,,5,,,8,,,2,,4,5,,,,,,,,,,6,,,,1,2,,,5,6,,8,,1,,,,5,,7,8,,,2,,,5,6,7,8,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,6,,,,,,,,,,,,9,1,2,,4,,,7,,,1,2,,4,,,7,8,,1,2,,,5,,,8,,,,3,,,,,,,,2,,,5,,7,8,,,2,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,4,,6,,8,,,,,4,,,7,8,,,,,,,,,,9,,2,,,,6,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,1,,,,5,,,8,9,,,,,5,6,,8,,1,2,,,,6,,,9,1,,3,,,6,,,9,,2,3,,5,6,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,3,,,,,,,1,,,4,5,6,,,9,,2,,,,,,,,,,,4,5,6,,,,1,,,4,,6,,,9,,,,,,,7,,,,,3,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4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,5,,,,,,2,,,5,,,,,,,,,,6,,,,1,2,,,,6,,8,,1,,,,5,,7,,,,2,,,5,6,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,2,,,,,,8,,,,3,,,,,,,,2,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,6,,8,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,5,,,,,1,2,,,,,,,,1,,,,,6,,,9,,2,,,,,,,,,,,,5,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,1,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,9,,,,,,,7,,9,,2,,,,,7,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,5,,,,,,2,,,5,,,,,,,,,,6,,,,1,2,,,,6,,8,,1,,,,5,,7,,,,2,,,5,6,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,2,,,,,,8,,,,3,,,,,,,,2,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,6,,8,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,6,,,9,,2,,,,,,,,,,,,5,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,1,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,9,,,,,,,7,,9,,2,,,,,7,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,5,,,,,,2,,,5,,,,,,,,,,6,,,,1,2,,,,6,,8,,1,,,,5,,7,,,,2,,,5,6,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,2,,,,,,8,,,,3,,,,,,,,2,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,6,,8,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,6,,,9,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,9,,,,,,,7,,9,,2,,,,,7,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,1,2,,,,6,,8,,1,,,,5,,7,,,,2,,,5,6,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,2,,,,,,8,,,,3,,,,,,,,2,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,2,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,6,,8,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,2,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,,,,9,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,9,,,,,,,7,,9,,2,,,,,7,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,1,2,,,,6,,8,,1,,,,5,,7,,,,2,,,5,,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,2,,,,,,8,,,,3,,,,,,,,2,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,6,,8,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,,,,9,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,9,,2,,,,,7,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,6,,8,,1,,,,5,,7,,,,,,,5,,7,,,,,3,,,,,,,,,,,5,6,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,8,,1,,,,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,5,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,9,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,1,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,1,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,1,,,,5,,7,,,,,,,5,,7,,,,,3,,,,,,,,,,,5,,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,1,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,,,7,8,9,,,,4,,,,,,,2,,,5,,,,9,1,,,,,,7,8,,,,,,,6,,,,1,2,,,,,7,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,1,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,1,,,,,,7,8,,,,,,,,,,9,1,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,1,,,,5,,,,,,,,,5,,7,,,,,3,,,,,,,,,,,5,,,8,,,2,,,5,,,,,,,,,,,,,9,1,2,,4,,,,,,1,2,,4,,,7,8,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,5,,,,9,1,,,,,,7,,,,,,,,6,,,,1,2,,,,,7,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,1,2,,,,,,,,1,2,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,1,,,,,,,,,,,,,5,,7,,,,,3,,,,,,,,,,,5,,,8,,,2,,,,,,,,,,,,,,,,9,,2,,4,,,,,,,2,,4,,,7,8,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,6,,,,1,2,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,,/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,1,2,,,,,,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,4,,,,,,1,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,8,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,,4,,,,8,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,,2,,,,,,,,1,,,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,,,,7,,,,,,,,,,,9,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,1,,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,,,,,,8,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5||hard
You can enter a Sudoku in just about any way you can think of --
as a straight line of digits, a block of digits containing periods, question marks, dashes, or underlines,
even as tables showing all possibilities.
Spaces are ignored.
clear entry area
load this puzzle