ORk-FW classification results for mith's 63137 min-expand puzzles in T&E(3):

Puzzles solved in SFin+Trid+Wn+ORkFWn

- Code: Select all
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n=3 n=5 n=7 n=8

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8 ,196 puzzles solved by SFin+Trid (among 63 137 min-expands)

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k=0 8,137 17,532 21,160 22,332

16,333 9,395 25,728 3,628 29,356 1,172 30,528

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k=2 3,350 8,713 11,231 12,068

19,683 14,758 34,441 6,146 40,587 2,009 42,596

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k=3 428 2,255 3,471

20,111 16,585 36,696 7,362 44,058

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k=4 67 365 540

20,178 16,883 37,061 7,537 44,598

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k=5 2 28 99

20,180 16,909 37,089 7,608 44,697

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k=6 0 4

20,180 16,913 37,093

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Lines are separated by dashes, columns are separated by large white spaces.

Each (k, n) cell has three values in it:

- the main one, in the lower right corner, is the total number of puzzles solved by SFin + Trid + Wn + ORkFWn;

- the value above it is the difference with the previous line; it shows what’s gained by increasing k by 1;

- the value on the left of the main number is the difference with the previous cell; it shows what’s gained by increasing n.

Some general conclusions can be drawn from this table:

• for fixed n, as k increases, the difference between two lines decreases quite fast; this shouldn’t be too surprising, as larger k means more chains have to converge to the same candidate;

• for fixed k, as n increases, the difference between two columns decreases quite fast; this shouldn’t be too surprising either, as it already happens with all the “classical” chains (whips…);

• starting from k=2 and n=3, at any point in the table, it is much more fruitful to increase n than to increase k;

I'll give a similar table for ORk-Contrad-Whips, but the calculations are still running.

[Edit]:added case (k=2, n=8)