In Pursuit of the Impossible Equation

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Imagine that a typical 9-by-9 Sudoku puzzle (in which the numbers 1 through 9 must appear exactly once in each row, column, and square) has been transformed into a 25-by-25 grid. The number of possibilities increases drastically, but while difficult, the puzzle remains solvable. Now imagine that the game has become a 1,000-by-1,000 behemoth. The chances of finding a solution plummet—in fact, this game can prove too complex for our fastest computers and most-advanced