Who wants to find a new 17 given sudoku? And maybe a 16?

coloin · Posted: Thu Aug 27, 2009 5:51 am Post subject:

Nice work on exploring those gaps - the two normalizations are indeed confusing - and the gaps are not straightforward at all !
: 1. minlexpuzzle
: 2. puzzle from the minlex grid of the puzzle solution

I agree that a puzzle found in the gap between either of these normlizations is probably unlikely to be new.

Changing back to minlexpuzzles,,,,,,,,,

It would be interesting to know just how many possible minlex 17-templates are in the "gap" between two 17-templates from the minlexpuzzles.

These min lex templates....there are 36137 different templates in my collection of Gordon's 48072.

How many possible templates are there with 17 clues ?

81! /[64! x 17!] = 128447994798305325

These will be subject to the 6^8 *2 reductions = 38237309836.9

But many of these will be invalid.
eg
must have at least 1 clue in every double row of 18 clues
must have at least 3 clues in a band of 27 clues ?
must have at least 8 clues in 2 bands [2 x 27 clues]
must have no more than 9 clues in a band
there are also many other patterns which dont have minimal puzzles.

This is based on the fact that there isnt a 17 puzzle with 2 clues in a band. [2,8,9]
There isnt a puzzle with 3 clues in band 1, 4 clues in band 2 and 27 clues in band 3. [3,4,27][to my knowledge]