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The First Solutions
Chessboard size 53×53

1, 3, 5, 2, 4, 9, 11, 13, 15, 6, 8, 19, 7, 22, 10, 25, 27, 29, 31, 33, 41, 43, 45, 42, 49, 52, 50, 53, 44, 46, 48, 51, 47, 12, 14, 24, 17, 21, 28, 30, 34, 16, 18, 20, 26, 23, 38, 40, 35, 32, 36, 39, 37

Diagram of the first possible solution to the 53 Queens on a 53x53 chessboard problem