Nine square numbers, split into three matching progressions
Nine boxes, A through I, each hold a square number of coins. A, B and C form an arithmetic progression; so do D, E and F; and so do G, H and I — and all three progressions share exactly the same common difference. Box A holds fewer than a dozen coins. How many coins are in each of the nine boxes?
Reveal the answer
A=4, B=3,364, C=6,724, D=2,116, E=5,476, F=8,836, G=9,409, H=12,769, I=16,129 — nine perfect squares (roots 2, 58, 82, 46, 74, 94, 97, 113, 127), where each of the three progressions shares a common difference of 3,360. Henry Dudeney set this as 'The Nine Treasure Boxes,' puzzle no. 132 in Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — 1917, puzzle no. 132
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