```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
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cases, one type of weak-link analysis (3D Medusa) has been
replaced by another (almost-locked set analysis).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
```