Effect of Adding Almost-Locked Set Analysis
---------------------------------------------
solver:      Sudoku Assistant
data source: http://magictour.free.fr/top1465

synopsis:

All told, in the solutions of the 1465 puzzles in this
collection, 2115 marks were eliminated using almost-
locked set analysis.

The 40 puzzles listed showed improved solution when basic 
almost-locked set analysis was included. In each case, the
first line is without almost-locked set analysis; the
second line is with.

(This basic analysis includes checking to see if there are 
marks that are common to two almost-locked sets that are
already weakly linked, allowing for the elimination of
those marks.) 

For 14 of these puzzles, adding almost-locked set 
analysis allowed solution without resort to basic
"trial and error" (P). These cases probably have something
like an XYZ-Wing that the almost-locked set analysis found.
3D Medusa cannot find that sort of configuration. In all other 
cases, one type of weak-link analysis (3D Medusa) has been 
replaced by another (almost-locked set analysis).

To load a puzzle into Sudoku Assistant:

1. go to http://www.stolaf.edu/people/hansonr/sudoku
2. click on "Number Block Input"
3. click on "load all 1465" 
4. select the puzzle from the selection box that appears

Methods used (in order of necessity):

  cross-hatch scanning (looking for singles; required) 
  range checking (locked candidates) 
  row/cell/block subset elimination 
A: almost-locked sets analysis (basic only)
W: grid (weak cycle) analysis (X-wings, Swordfish, etc.) 
M: 3D Medusa chain analysis -- strong+weak
P: hypothesis and disproof (trial and error)

puzzle #clues #tidbits methods    #W   #M   #P  #steps
------------------------------------------------------
   12     18      423      MP           3    3     53
   12     18      423  A   M            3          48

   16     18      422      MP           4    2     51
   16     18      422  A   M            2          45

   44     18      417      M            1          52
   44     18      417  A                           52

   47     18      420      M            2          53
   47     18      420  A                           52

   64     18      421      M            3          45
   64     18      421  A                           47

   73     18      420      M            1          48
   73     18      420  A                           48

   75     18      420      M            3          50
   75     18      420  A                           51

   83     18      419      M            2          50
   83     18      419  A                           49

   86     18      420      M            1          45
   86     18      420  A                           44

   94     22      468      M            1          32
   94     22      468  A                           33

   97     18      419      M            3          55
   97     18      419  A                           52

  129     18      422    W2MP      2    6    1     46
  129     18      422  A W4M       2    5          47

  150     18      422      M            1          51
  150     18      422  A                           51

  155     18      420      M            3          50
  155     18      420  A                           49

  163     18      416      M            2          52
  163     18      416  A                           51

  206     18      415      M            1          50
  206     18      415  A                           50

  226     18      424      M            1          45
  226     18      424  A                           44

  300     19      449      M            2          46
  300     19      449  A                           42

  307     19      449      M            1          42
  307     19      449  A                           42

  405     17      405    W2MP      2    5    1     47
  405     17      405  A W2M       1    1          46

  512     21      460      MP           8    2     48
  512     21      460  A   M           11          52

  533     22      463    W2M       1    1          32
  533     22      463  A W2        1               37

  598     24      480    W2 P      2         1     34
  598     24      480  A W5        2               33

  613     24      487    W2MP      1    4    1     38
  613     24      487  A W4M       1    6          41

  701     23      473      M            2          32
  701     23      473  A                           32

  848     23      476    W3MP      1    2    1     42
  848     23      476  A W3M       2    2          51

  906     23      474    W2MP      1    2    1     45
  906     23      474  A W5M       2    2          48

 1080     21      462      M            1          32
 1080     21      462  A                           37

 1136     23      479      MP          15    1     42
 1136     23      479  A   M           20          47

 1245     24      480      MP          14    2     44
 1245     24      480  A   M            3          32

 1249     23      471      MP           2    2     31
 1249     23      471  A   M            2          32

 1257     24      491    W2M       1    3          32
 1257     24      491  A W2        1               31

 1306     21      456      M            1          42
 1306     21      456  A                           41

 1321     23      472    W2M       2    1          28
 1321     23      472  A W2        2               30

 1358     22      472    W2M       1    1          29
 1358     22      472  A                           31

 1365     24      480       P                2     30
 1365     24      480  A                           28

 1386     23      468    W2MP      1    3    1     31
 1386     23      468  A W5M       1    3          31

 1407     17      408      M            1          42
 1407     17      408  A                           42

 1454     24      472      M            1          22
 1454     24      472  A                           24

 1464     24      475      M            1          30
 1464     24      475  A                           29

Disclaimer