The New Sudoku Players' Forum

[Mathimagics]

Some recent LCT-18 developments:

• I now have an SSD drive for JILL (i7700K, 4-core x 2-threads PC), so the old problem of slow access to the catalog is eliminated. In fact, it turns out that JILL now has even faster access times than JACK (the 16x2 AMD Ryzen PC).

• I have a new "random morph walker" 18C search function, that employs colin's "subpuzzle solution counts" idea to find 18C puzzles. This can find new 18C's much faster than any previous method, and is not restricted to puzzles in the immediate {+2,-2} vicinity.

• Much of the grunt work involves canonicalising grids/puzzles, and I have found Michael Deverin (holdout)'s Minlex Form via Chaining method is 8x faster than the existing function. If I can get it to transform a puzzle alongside the solution grid, then all things related to LCT-18 will be faster.

[coloin]

Very good again..presumably you are adding 3 clues .... what inspired it was this .. from What is most solved cells with "n" clues?

Code: Select all

+---+---+---+
|...|3.1|...|
|2.4|...|...|
|...|...|...|
+---+---+---+
|8..|52.|...|
|...|...|9.1|
|...|...|3..|
+---+---+---+
|...|.4.|.5.|
|91.|...|...|
|.3.|...|...|
+---+---+---+   this 15C found by G Royle has only 576 sol 

solves to

+---+---+---+
|5.9|3.1|...|
|2.4|.95|13.|
|1.3|...|59.|
+---+---+---+
|891|523|...|
|35.|...|9.1|
|.4.|91.|3.5|
+---+---+---+
|.2.|149|.53|
|915|.3.|...|
|43.|.5.|.19|
+---+---+---+    which has 29 more solved clues !  [still 576 sol]

Adding 2 clues does not give a 17C
Adding 3 clues gives us 1093 minimal 18C - although many from the same grid solution

1093.txt

(87.53 KiB) Downloaded 6 times

and this 15 clue [one clue different] has 2715 grid solutions

Code: Select all

+---+---+---+
|...|3.1|...|
|2.4|...|...|
|...|...|...|
+---+---+---+
|8..|52.|...|
|...|...|9.1|
|...|...|3..|
+---+---+---+
|...|.4.|.5.|
|71.|...|...|
|.3.|...|...|
+---+---+---+


Adding 2 clues gives one 17C [ thats how Gordon found it, I suppose]
Adding 3 clues gives us 1150 minimal 18C - which are different but again probably many from the same grid solution

I admit that it is highly likely that all these solution grids are known, and presumably remote 18C wont necessarily have a 15C subpuzzle with a low sol count / extra solved clues ....