## Minimum number of clues for exactly N solutions?

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Red Ed wrote:While I'm here, an update on the minimum unattainable number of solutions. Having given up on the 3x3 case, I looked at 3x2 and 4x2. The answer for 3x2 appears to be just over 1000: I'm stuck at 1019 at the moment (any takers?).

For these puzzles with around 1000 solutions, what is the range of numbers of clues?

What is the minimum number of clues for 3x2 sudoku?
Moschopulus

Posts: 256
Joined: 16 July 2005

Moschopulus wrote:For these puzzles with around 1000 solutions, what is the range of numbers of clues?
Some 6, many 7, some 8 clues. I wouldn't bank on this being representative of "random" grids with 1000ish solutions, though: the search makes no attempt to be unbiased.

What is the minimum number of clues for 3x2 sudoku?
The minimum is 8 (here).

The first few believed-to-be-unattainable nrs of solutions for 3x2 were: 1019, 1145, 1149, 1165. 1167, 1197. Are these genuinely unattainable? Can anyone find counterexample grids? A comprehensive search shouldn't be out of the question.

btw, I got everything from 1 to 150942 solutions for 4x2 before giving up on that case.

Ed.
Red Ed

Posts: 633
Joined: 06 June 2005

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