The New Sudoku Players' Forum

[Mathimagics]

Thanks blue!

The time I gave was correct, but I must have been running an LCT catalog update at the time - when this goes to dump an updated band to the slow disk, some peculiarity of the IO system means that other processes get locked out, even if they aren't doing IO, and this can be for up to (and clearly sometimes over) a minute ...

The automorphic grid table is interesting ...

We still don't have a "no-668" grid, that only has the non-trivial automorphism.

BlueMagic will hopefully find one, it's not on active duty just yet ...

[Mathimagics]

Here's a new entry for blue's table:

Code: Select all

123456789456789123789123465215937648634218957897564312361872594542391876978645231

Code: Select all

> BlueMagic Test20C.txt
no puzzle: 123456789456789123789123465215937648634218957897564312361872594542391876978645231
1 grids, 0 puzzles, 78.125 ms/g

> NotMagic Test20C.txt 999
05:58:16: [Find 20C] Processing Test20C.txt (bailout = 999s)
1....6....5...9..3....2.4......3...8..4...9....75......6.8.......23...7.9.....2.. #     43.415s


The grid has automorph count of 2, sadly. It did take a very long time to find the 20C, so perhaps it has a low total 20C puzzle count?

Also of possible interest is that this grid is the only grid with MCN = 16 (of 222,278 known cases) that failed the 668 check.

[Mathimagics]

I have fixed the post above which had the wrong grid quoted ...

But now I see it's NOT new at all ... 4th from the end in the table ... oh, good grief, I give up!

The observation about MCN=16 grids is, on the other hand, 100% kosher ...

[Mathimagics]

It is just come to my attention that the 4 known grids which have no 20C puzzle are all automorphic. The automorphism class is shown for each grid below.

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123456789456789123789123456214897365365214897897365214541632978632978541978541632 # 18
123456789456789123789132465218967534564213978937548216391875642645321897872694351 #  6
123456789457189326689327154216534897745891632938672541361245978574918263892763415 #  6
123456789457189326689327154216534897745891632938672541392765418574918263861243975 #  2


Also, for the 268,296 grids with a 20C but no 19C puzzle, the automorphism rate is still quite high. There are 4815 automorphic grids, which is ~1.8%.

The background level is around 1 automorphic grid in 11,000 ...