| 10x10 - 1s and 2s |
Slithy
Kwon-Tom Addict
Puzzles: 102
Best Total: 8h 37m 59s | Posted - 2022.01.06 23:18:37
> My SAT solver assures me the solution is unique but I cannot make any meaningful progress.
> Solvers: 9
Wow.
Any comments on what magic was involved, and how long the incantation took? |
Darklady
Kwon-Tom Obsessive
Puzzles: 5133
Best Total: 9m 37s | Posted - 2022.01.07 06:22:04
My time was 9:26. I don't remember precisely what sequence I did, but it was something like this:
This was as far as I could get easily, and it involved a highlander deduction (green) and a slightly non-obvious lookahead (blue). From there, the 2 I circled in orange stood out, because if you put an X below its lower-right corner it becomes another potential location for highlander deductions.
(In general, highlander deductionsー"there can be only one [solution]", therefore any path that would produce multiple solutions must be wrongーare very powerful when dealing with difficult puzzles. They require knowing that there is in fact a unique solution, of course.)
Two explorations starting from the points circled in blue both quickly lead to dead ends. The second created a new potential highlander location over on the left edge of the puzzle, so I started focusing there:
Again, potential highlander circled in orange, starting point of explorations circled in blue.
This one didn't turn out to be a great spot to start an exploration, but enough of the puzzle had been solved that it went pretty quickly.
And done. 
Thanks for the puzzle, it was fun! |
Slithy
Kwon-Tom Addict
Puzzles: 102
Best Total: 8h 37m 59s | Posted - 2022.01.09 10:15:03
Quote: Originally Posted by Darklady ... something like this... |
Thank you for your many pointers. So far I have only 11 of the crosses on your first board, so still some way to go 
Also glad you enjoyed it. I intend to produce more, but while generation only take a second or so, testing them takes much longer and their quality and difficulty seem quite unpredictable. |
foilman
Kwon-Tom Admin
Puzzles: 2799
Best Total: 24m 6s | Posted - 2022.01.18 12:44:17
I've just solved your other hard 1s & 2s puzzle - #544 - that was a big challenge! |
Slithy
Kwon-Tom Addict
Puzzles: 102
Best Total: 8h 37m 59s | Posted - 2022.01.18 14:17:52
I'm glad to hear someone else finds them difficult as they are frankly too hard for me. Even with DarkLady's pointers the first took me a couple of hours and I've only managed one of the others. Below I attach a beast (go on, I'll be right behind you  and if anyone is interested I can now easily upload more of the smaller ones.
My approach so far has been based on trying to spread information as evenly and diffusely as possible, leading to the predominance on 1s and 2s. As it doesn't look interesting to head any further in that direction I'm going to try to introduce some structure or lumpiness in a way that will make them more approachable and hopefully more interesting.
40x30:2b1a2b2a211b1a2d2a22e1a2c112a2a2a1121b2a2a2a2a1e22112a211c2b1b01d2c11a21a221a221a22a1b1a11a1b1g122a1a212b1d1a2b1b11b1211222a2222a2f12a11a12a221a12a1c1e2a1a22b21a2a1a2a1222a1211e2a22a22a1b2b2b1211b1122d2a2121a2f211a11a2a212d11b2112112a21b21a12a122d2b12a22a1212a2a21i11222a1221g2a1b2a2c2a221d2b2a221b21a112222b2a11b1b22a1a2b1a2112a122d1a22a2a221a22a2d1a11c2a1b2a1a1a2a1b12a211a2c21a22b2c21a2a1a21a12b12121111d2a2a1c1a22c2b22a22b1b1a1c2c22a12b22c122b121a212e112a1b121b21a1d1a2a12a2a2c2112a2111a12a11121e2b2a2122b2122b212f1b222b11222a2b2f22a2b2a1b2a12a11e2b1b2221222c21a2b121a21a2b111a121112b2b2c1122a21d2a22b1a222b2a2b121212a12a22222d11c1c211c12a12g11a1c11a2221c1a212a1b1c2b222a2b22111a111a22a2a11212a2a22b1a1211b2211b1a2a11a12a12a22b2c1c11b1b221222a2a12c2b112b21a11221a2b212b212c12a12a2a222c221c21a212122c121a1a121d12b111a1122b12b2a212221b1222b22a2d1a22a22b12c2b222b2b1d2a2c1111a11a1b1c1111b2b1a12b1b111a1a1a222d212a22a2c11a232b
2 1 2 2 211 1 2 2 22 1 2 112
2 2 1121 2 2 2 2 1 22112 211 2
1 01 2 11 21 221 221 22 1 1 11 1
1 122 1 212 1 1 2 1 11 121
1222 2222 2 12 11 12 221 12 1 1
2 1 22 21 2 1 2 1222 1211 2 22 2
2 1 2 2 1211 1122 2 2121 2 2
11 11 2 212 11 2112112 21 21 12 122
2 12 22 1212 2 21 11222 122
1 2 1 2 2 2 221 2 2 221 21
112222 2 11 1 22 1 2 1 2112 122
1 22 2 221 22 2 1 11 2 1 2 1 1 2 1
12 211 2 21 22 2 21 2 1 21 12 12
121111 2 2 1 1 22 2 22 22 1 1
1 2 22 12 22 122 121 212 112
1 121 21 1 1 2 12 2 2 2112 2111
12 11121 2 2 2122 2122 212 1
222 11222 2 2 22 2 2 1 2 12 1
1 2 1 2221222 21 2 121 21 2 11
1 121112 2 2 1122 21 2 22 1 222
2 2 121212 12 22222 11 1 211
12 12 11 1 11 2221 1 212 1 1
2 222 2 22111 111 22 2 11212 2 22 1
1211 2211 1 2 11 12 12 22 2 1 11
1 221222 2 12 2 112 21 11221 2 2
12 212 12 12 2 222 221 21 212122
121 1 121 12 111 1122 12 2 21222
1 1222 22 2 1 22 22 12 2 222 2
1 2 2 1111 11 1 1 1111 2 1 1 |
