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by Brian Gladman on June 7, 2020

New Scientist Enigma 957 – Open The Box!

by Susan Denham

From Issue #2112, 13th December 1997

Ten executives each rented two of the 20 safe-deposit boxes shown:

Each of the 10 had the same number of gold coins to share out between her two boxes. The first executive put 1 coin in one of her boxes and the rest in her other box. The second executive put 2 coins in one of her boxes and the rest in her other box. The third executive put 3 coins in one of her boxes and the rest in her other box. And so on, up to the tenth executive, who put 10 coins in one of her boxes and the rest in her other box. The overall effect of this was that each of the four rows of boxes contained in total an equal number of the gold coins. Also each of the five columns of boxes contained in total an equal number of coins.

One night a burglar broke into and emptied four of the boxes, three of them being in the same row. His total haul of coins was a three-figure number with no zeros.

How many coins did each executive have in the first place?

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