Consecutive Sudoku is a variant with the extra rule that orthogonally adjoining numbers are consecutive if and provided that there’s a dot between them. A Nonconsecutive Sudoku is one with no dots; no orthogonally adjoining numbers are consecutive. I’ve been making an attempt to make one not too long ago and my regular technique of checking with a solver to see whether or not I’ve made the puzzle not possible is not working, because the “options” it spits out all fail the consecutiveness check.

This makes me marvel what share of Sudoku options are additionally legitimate for Nonconsecutive Sudoku. I do know that there are 6.67 × 10²¹ legitimate Sudoku boards, ignoring symmetries/transformations. How a lot of these are nonconsecutive, once more ignoring symmetries? (Computer assist is clearly allowed for computation)