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9x9 grid of digits with an ambiguous solution is not a Sudoku. It is part of the definition.

Within the set of initial grids that have unambiguous solutions there are ones which require guessing or backtracking, these are generally not considered proper Sudokus and are not presented to humans to solve.

A Sudoku is not a destination, it is a journey.



If a Sudoku has one and only one solution, then it is always solvable without guessing or backtracking. It just might not be within the scope of the human brain. There exist (many) configurations where every cell is influenced by every other, so to solve any one cell essentially requires a simultaneous solve of the entire puzzle. There's no theoretical reason a human couldn't do that too; it's a problem simply of computational capacity not fundamental approach.


How would you structure a program to solve such a puzzle without having it generate and test potential solutions along the way?




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