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I consider, what happens if there is no solution, or is imposible, For instance appliying Cramer's Rule if Determinant is zero don't have solutions ... something alike is "available" for a Sudoku, or maybe ir recursions got over a fix number or by...
You can try with lists functions Max or Min or Position... lna = RandomInteger[999, 600]; mlna = Max[lna] Out[2]= 994 Position[lna, mlna] mxpo[lst_] := {Max[lst],...