SudoRules has finally completed its analysis of mith's collection of 158,276 min-expand puzzles in T&E(3) and of eleven's list of 630 3-digit impossible patterns in two bands (or two stacks).
As expected, the full calculations don't bring results significantly different from those obtained before with the partial lists of puzzles:
- there are four natural selections of Subsets of the 630 patterns (defined by how "useful" they are in solving the puzzles);
- Select1 is unchanged, apart from the last two patterns being permuted (but internal changes are not really relevant);
- there is more internal change in the other 3 subsets (but internal changes are not really relevant);
- 2 patterns are downgraded from Select3 to Select4 (but anyway, no calculations were done with Select3 or Select4);
- 2 new patterns are added to Select4.
The final result is:
Select1 = {EL13c290, EL14c30, EL14c159, EL14c1, EL14c13}
Select2 = Select1 + {EL10c28, EL13c179, EL13c30, EL13c171, EL13c234, EL13c176, EL10c6}
Select3 = Select2 + {EL13c259, EL10c8, EL13c172, EL14c19, EL10c4}
Select4 = Select3 + {EL13c175, EL13c136, EL15c97, EL13c187, EL14c93, EL12c2, EL14c154, EL13c19, EL13c170, EL13c168, EL10c10}
and these are the four subsets of patterns that can be collectively selected in SudoRules.
Remember that "usefulness" of a pattern is defined by the number of puzzles in which it leads to at least one elimination when the rules of (Trid+Imp630)+W8+OR5W8 are activated.
The final "usefulness" numbers are as follows. I give them here to show that the four subsets appear quite naturally.
- Code: Select all
Trid = 152446 (in some puzzles, the tridagon pattern doesn't imply any elimination)
Total IMP630-EL<xxx>c<yyy> = 128584 (percentages below are wrt to this number)
Imp630-Select1 (total 86164, 67.01%):
EL13c290 = 29764
EL14c30 = 22989
EL14c159 = 14111
EL14c1 = 10027
EL14c13 = 9240
Imp630-Select2 (total +23789, +18.50% = 85.51%):
EL10c28 = 5486
EL13c179 = 4834
EL13c30 = 3200
EL13c171 = 2768
EL13c234 = 2598
EL13c176 = 2475
EL10c6 = 2428
Imp630-Select3 (total +7427, +5.78% = 91.29):
EL13c259 = 2108
EL10c8 = 1804
EL13c172 = 1462
EL14c19 = 1040
EL10c4 = 1013
Imp630-Select4 (total +5309, +4.13% = 95.42%):
EL13c175 = 726
EL13c136 = 656
EL15c97 = 623
EL13c187 = 581
EL14c93 = 578
EL12c2 = 448
EL14c154 = 396
EL13c19 = 389
EL13c170 = 316
EL13c168 = 307
EL10c10 = 289
SudoRules has been updated to reflect these minor changes (to be published soon).
The User Manual is also being updated and will be published soon. It will contain detailed additional results on the classification of puzzles that allow to draw stronger conclusions than the existence of the above sets of patterns.
As a personal side note:
After the discovery of the tridagon impossible pattern and of Loki by mith (http://forum.enjoysudoku.com/loki-ser-11-9-t39840.html?hilit=Loki)
and following my surprise to find it was in T&E(3) (http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1048.html),
I've been working on how to define generic resolution rules (ORk-chains) able to use application-specific impossible patterns (applied in particular to T&E(3) puzzles). More specifically, my recent work has been on selecting a small set of impossible patterns from the full set, with almost the same resolution power.
The above results make me feel my approach has reached its goals and I can now switch to other topics.
As a result, I don't plan to propose more T&E(3) puzzles from mith's collection in the "Puzzles" section (those I've proposed illustrate the different cases of interest I've found). However, I plan to publish my detailed classification results on GitHub, together with some explanation of how to use them to find more interesting puzzles. It may take some time to prepare all this.
Alternatively, you can use the "puzzles" section in a new way, to ask questions such as: is there a T&E(3) puzzle such that.... I can probably not answer all such questions, but let's see.
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