This is basically due to the fact that the cardinality of the union set of the possible values within uncertain cells in any block, row or column of the puzzle equals the number of uncertain cells put into the union.
Original puzzle is hard because the setter has taken care that none of the easy solving tricks work. Probably could be done much quicker even in javascript. Javascript - 461ms using 4 layers of heuristics derived from easier sudoku and then depth first search with back tracking if an inconsistent node was reached. Performing an exhaustive search at that depth would take an inconceivable amount of time.Īs this is the furthest depth we know of, and the only puzzle of this depth known, it currently takes top spot as the computationally hardest Sudoku. The solver on SudokuWiki can't get it because it would simply take too long to do in Javascript, and it's not programmed to look to a depth of nine. That is what makes this puzzle difficult: the number of steps one has to look ahead in order to reduce away clues. "Normal sudoku puzzle logic eliminates the possibilities for each box in two or three steps, but this one requires puzzlers to think ahead eight or nine steps at a time - making very long deductions to eliminate the possible candidates for each box." ( source)
There is nothing to suggest that this is the singular hardest puzzle in existence, however, it's still a pretty dern difficult puzzle. The claim that this is the world's hardest sudoku puzzle was actually made by the author, and popularized by the media.
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