Mike Barker wrote:Here are the results (number of times a technique is used based only on successfully solved puzzles (9725 out of 10000)1) Naked Single (322048)

2) Hidden Single (92521)

3) Naked Pair (42327)

4) Empty Rectangle (13916)

5) Locked Candidate (12185)

6) ALS-xz rule with >=2 cells per ALS (2378)

7) Two Strong Links (2030)

8) Generalized WXYZ-wing (1968)

9) Naked Triple (1964)

10) XY-wing (1403)

11) Generalized VWXYZ-wing (962)

12) ALS-xy rule with A=1 cell ALS (685)

13) Hidden Pair (649)

14) ALS-xz rule with >=3 cells per ALS (571)

15) Generalized XYZ-wing (494)

16) Finned X-wing (468)

17) Three Strong Links (441)

18) ALS-xy rule with A=2 cell ALS (413)

19) 4-node XY-chain (253)

20) Finned Swordfish (174)

21) ALS-xy rule with A=3 cell ALS (135)

22) Hidden Triple (128)

23) ALS-xz rule with >=4 cells per ALS (91)

24) Type 1 Unique Rectangles (79)

25) Type 4/4B Unique Rectangles (66)

26) ALS-xy rule with A=4 cell ALS (64)

27) 5-node XY-chain (58)

28) 4-node XY-ring (45)

31) Type 3/3B Unique Rectangles (26)

32) Swordfish (23)

33) Type 2/2B Unique Rectangles (22)

34) Naked Quadruple (21)

35) 5-node XY-ring (18)

36) SueDeCoq (16)

37) Grouped 6-node X-cycle (9)

38) Four Strong Links (5)

39) Grouped Broken Wing (5)

40) Hidden Quadruple (1)

41) Finned Jellyfish (1)

42) Grouped 7-node Broken Wing (1)

43) Unused (0)

44) X-wing (0)

45) Jellyfish (0)

46) Squirmbag (0)

47) Finned Squirmbag (0)

48) ALS-xz rule with >=1 cells per ALS = XY-wing, etc (0)

49) 4-node X-cycle = X-wing (0)

50) Turbot Fish (0)

51) 6-node X-cycle (0)

52) 7-node Turbot Chain (0)

53) Grouped 4-node X-cycle = Locked box/box (0)

54) Broken Wing (0)

55) 7-node Broken Wing (0)

56) Simple Colouring Type 1 = X-cycle (0)

57) Simple Colouring Type 2 = X-cycle (0)

58) Simple Colouring Type 3 = X-cycle (0)

59) Grouped Simple Colouring Type 1 = X-cycles (0)

60) Grouped Simple Colouring Type 2 = X-cycles (0)

61) Grouped Simple Colouring Type 3 = X-cycles (0)

Hi Mike!

Wow, thanks for your speedy reply with such interesting results! Great work!

First of all, was this solved with the order of techniques that I proposed in the previous post? I'll just assume that and make the comments thereafter...

First of all, there is a healthy sign that your solver did not find any x-wings or Turbot Fish. That just means that your "two-strong-links" algorithm is doing its job! It is also a healthy sign that the number of jellyfish-squirmbags etc (finned and not) also has decreased as a result of three and four strong links. It only makes me more interested to see that one Finned Jellyfish... Can that be arranged? However, how is it that your solver finds 23 swordfish? If your "three-strong-links" routine is indeed before the swordfish, there should really be 0 swordfish (unless you also pick up on some of the more unusual swordfish-patterns) Can you check this?

The biggest surprise was the number of Empty Rectangles... Are you sure the two-strong-links are checked before the ER? The fact that he found more of them than locked candidates just seems a bit crazy... It is not that I am unhappy with this result (it would indeed make the ER quite useful), but it almost seems too good to be true!

The increase in number of techniques used is no big surprise to me. The two strong links can pick up on all eliminations done by a Turbot Fish, but while a Turbot Fish that have more than two strong sides can place numbers directly, the two strong links leaves them for the single (locked) candidate to pick up on. Hence you get a "easier" but longer solution since it needs more steps. I think this is really good, and I would love to see these:

29) Grouped Turbot Fish (38)

being reduced as well...

would it be possible for you to post them (maybe in the hierarchy thread) so they can be closely examined for easier reductions?

anyway, thanks for your effort! Good stuff!

havard