champagne wrote:JPF wrote:On the other hand, gridchecker is the only one that efficiently determines MinLex from any sequence of digits.

...what do you mean precisely?

Mathimagics wrote:I think he means the minlexing of Puzzle-only (Pattern only) forms (ie. without reference to a solution grid)

Yes,

Mathimagics is right.

In a more formal way:

For any sequence of 81 digits SQ=(x1,x2,...,x81) with 0≤xi≤9, gridchecker is able to find MinLex(SQ) which is defined by

the sequence (f(x1),f(x2),...,f(xn)) such that f(x1).10^80 + f(x2).10^79 + ... + f(x81) is the minimum for all f of the group

S9x

GS9 is the symmetric group

S9 ; |

S9|=9!

G is the group of geometric transformations (VPT) ; |

G|=2 x 6^8=3359232

Then, gridchecker can be used for different purposes, like minlexing patterns (xi=0 or xi=1), minlexing solution grids, minlexing valid or invalid puzzles...

Here are some examples:

- Code: Select all
`003195329531437918877070817926625631136964997876804980377882615741485757087268715`

268261042050737255219334240066880947143419936281503711125758373130829310325633378

723817951694116970628976526980432981379045310795598334875127824724030567308657391

101001111000100010011101110010100000011100111000100000000011010001110000100000010

101111111010111110100000101010101111110100111101001001101100110011110010100110110

010001110110001011110000110010111010100000000000101100010011001111010110001010001

MinLex

- Code: Select all
`001112123345060567816634253272116493729210413842831114280192052589693155947795396`

001112334256072474289270269099375808268663140647945756412834944604064852612434381

001234256256107891283726437278231869588594029592537536341970879604129081769296411

000000001000001001111011001000010011001000110001100000001000001011011101111110100

000001011111010101111101111001011111010101010011010111001101101101001101101110100

000000001001011000010111010011000011011001010110001011011100111100100100100101010

JPF