Math Puzzle - THE FORTY-NINE COUNTERS.

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THE FORTY-NINE COUNTERS.

(Chessboard Problems)
Can you rearrange the above forty-nine counters in a square so that no
letter, and also no number, shall be in line with a similar one,
vertically, horizontally, or diagonally? Here I, of course, mean in the
lines parallel with the diagonals, in the chessboard sense.

Answer:

The counters may be arranged in this order:--
A1, B2, C3, D4, E5, F6, G7.
F4, G5, A6, B7, C1, D2, E3.
D7, E1, F2, G3, A4, B5, C6.
B3, C4, D5, E6, F7, G1, A2.
G6, A7, B1, C2, D3, E4, F5.
E2, F3, G4, A5, B6, C7, D1.
C5, D6, E7, F1, G2, A3, B4.