53x15
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I offer no proof, but some evidence: An 87-clue Pencilmark Sudoku: +=====+=====+=====+=====+=====+=====+=====+=====+=====+ | 1.. | 123 | 123 | 123 | 123 | 123 | 123 | 123 | ..3 | | ..6 | 4.6 | .56 | ...

Have a look at the thread below which catalogs the most clueful puzzles discovered at each Sudoku Explainer difficulty rating: http://forum.enjoysudoku.com/maximum-number-of-clues-for-a-given-se-...

When designed for speed rather than adherence to human solving process, and with the notable exception of those based on exact cover, most of the Sudoku solving algorithms I've seen are functionally ...

As tehtmi mentioned in a comment above, you can confirm using Andrew Stewart's solver that these techniques do not suffice for most difficult Sudoku. But more generally, if your main goal is to write ...

The players ante a sequence of odd numbers, so if a round ends after $x$ pairs of cards are drawn then a player's payoff is $\pm x^2$. Since the players break even after three rounds we must have \$x^...