Following Paquita's publication of a new collection of hard puzzles (https://drive.google.com/file/d/1_vC06xr0bWLWqJ8hROcs3zusiuYB0fEb/view?usp=sharing), I've applied the (1+BRT)-expansion technique to it
As usual, there are some preliminary preparations:
- eliminate 4 non-valid puzzles (==> 62,355 puzzles);
- replace a few non-minimal puzzles by their minimals (==> 63,128 minimals);
- split the collection according to T&E-depth (==> 45,274 minimals in T&E(2) and 17,854 minimals in T&E(3))
This post is about the T&E(2) part (45,274 minimals), more precisely about the subpart with BxB ≥ 7 (i.e. 7,249 minimals, corresponding to 1,099 different solution grids).
My purpose was to see if any meaningful differences appeared wrt the previous T&E(2) collections, namely the Mastermins 1 to 15 collected by coloin.
First thing to notice: in Paquita's collection, the minimals and min-expands are not cross-saturated in T&E(2). My first step was therefore to cross-saturate them:
- compute the min-expands;
- find all their minimals (10,840 minimals, guaranteed to be in T&E(≥2);
- split them according to T&E-depth: 10,812 minimals in T&E(2), guaranteed to have BxB ≥ 7; and 28 minimals in T&E(3);
- keep only those in T&E(2) (and therefore with BxB≥7);
- compute their min-expands (3,437 min-expands).
At this point, cross-saturation is guaranteed.
(Note: I didn't check whether some puzzles were already in the Mastermins).
Now, the full (1+BRT)-expansion procedure can be applied in a totally automated way - using SudoRules command "(SGS-script-compute-TE2-expansion-phases-upto-k 15)". It doesn't seem to produce anything new wrt Mastermins. Here are the basic stats:
- 9.84 minimals per solution grid (9.36 in Mastermins);
- 3.13 min-expands per solution grid (3.22 in Mastermins);
- 3.15 minimals per min-expand (2.91 in Mastermins);
- 49.41 T&E(2)-expand per solution grid (53.60 in Mastermins).
Note that I didn't cross-saturate the minimals wrt the T&E(2)-expands - nor was it done systematically in the Mastermins (though the last figure suggests some cross-saturation beyond min-expands may have been done). The reason is, whereas this is possible in T&E(3), this would lead to extremely long calculations in T&E(2).
One can also check the detailed expansion profiles, with the same peak at phase 4, and with the same reasons why combinatorial explosion is contained.
The longest expansion path has length 11, close to the 13 for the larger Mastermins collection (in which very few paths have length 12 or 13).
- Code: Select all
T&E(2) expansion phase p0
10812 mins puzzles
10812 ME puzzles
3437 MEU puzzles
T&E(2) expansion phase p1
168272 p1 puzzles
167468 p1U puzzles
126070 p1U-d2 puzzles
104404 p1EU-d2 puzzles
T&E(2) expansion phase p2
4953195 p1EU-d2-p2 puzzles
4206766 p1EU-d2-p2U puzzles
654173 p1EU-d2-p2U-d2 puzzles
273609 p1EU-d2--p2EU-d2 puzzles
T&E(2) expansion phase p3
12677562 p1EU-d2--p2EU-d2-p3 puzzles
11259918 p1EU-d2--p2EU-d2-p3U puzzles
1081062 p1EU-d2--p2EU-d2-p3U-d2 puzzles
319628 p1EU-d2--p3EU-d2 puzzles
T&E(2) expansion phase p4
14542692 p1EU-d2--p3EU-d2-p4 puzzles
13251971 p1EU-d2--p3EU-d2-p4U puzzles
961529 p1EU-d2--p3EU-d2-p4U-d2 puzzles
239989 p1EU-d2--p4EU-d2 puzzles
T&E(2) expansion phase p5
10728259 p1EU-d2--p4EU-d2-p5 puzzles
9949464 p1EU-d2--p4EU-d2-p5U puzzles
576475 p1EU-d2--p4EU-d2-p5U-d2 puzzles
134194 p1EU-d2--p5EU-d2 puzzles
T&E(2) expansion phase p6
5888449 p1EU-d2--p5EU-d2-p6 puzzles
5535379 p1EU-d2--p5EU-d2-p6U puzzles
257180 p1EU-d2--p5EU-d2-p6U-d2 puzzles
58188 p1EU-d2--p6EU-d2 puzzles
T&E(2) expansion phase p7
2502134 p1EU-d2--p6EU-d2-p7 puzzles
2381658 p1EU-d2--p6EU-d2-p7U puzzles
88218 p1EU-d2--p6EU-d2-p7U-d2 puzzles
19710 p1EU-d2--p7EU-d2 puzzles
T&E(2) expansion phase p8
828755 p1EU-d2--p7EU-d2-p8 puzzles
799267 p1EU-d2--p7EU-d2-p8U puzzles
23021 p1EU-d2--p7EU-d2-p8U-d2 puzzles
5065 p1EU-d2--p8EU-d2 puzzles
T&E(2) expansion phase p9
207694 p1EU-d2--p8EU-d2-p9 puzzles
202882 p1EU-d2--p8EU-d2-p9U puzzles
4461 p1EU-d2--p8EU-d2-p9U-d2 puzzles
967 p1EU-d2--p9EU-d2 puzzles
T&E(2) expansion phase p10
38572 p1EU-d2--p9EU-d2-p10 puzzles
38105 p1EU-d2--p9EU-d2-p10U puzzles
511 p1EU-d2--p9EU-d2-p10U-d2 puzzles
133 p1EU-d2--p10EU-d2 puzzles
T&E(2) expansion phase p11
5174 p1EU-d2--p10EU-d2-p11 puzzles
5149 p1EU-d2--p10EU-d2-p11U puzzles
11 p1EU-d2--p10EU-d2-p11U-d2 puzzles
5 p1EU-d2--p11EU-d2 puzzles
T&E(2) expansion phase p12
199 p1EU-d2--p11EU-d2-p12 puzzles
199 p1EU-d2--p11EU-d2-p12U puzzles
0 p1EU-d2--p11EU-d2-p12U-d2 puzzles
0 p1EU-d2--p12EU-d2 puzzles
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