Latin Square Generator

A Sudoku grid IS a 9×9 Latin square (each digit 1-9 once per row and column) with the added constraint that each 3×3 box also contains all digits. So Sudoku is a special case of Latin square.

Two n×n Latin squares are orthogonal if, when superimposed, every ordered pair of symbols appears exactly once. Euler conjectured none exist for n≡2 (mod 4), but this was disproven for all n>6. Only n=2 and n=6 have no orthogonal pairs.

Cyclic construction: row i has symbols (i, i+1, i+2, ..., i+n-1) mod n. This always works! For n=4: row 0 = [0,1,2,3], row 1 = [1,2,3,0], row 2 = [2,3,0,1], row 3 = [3,0,1,2].