**From New Scientist #2601, 28th April 2007**

I asked Tom, Dick and Harry how many “Enigma” puzzles each had entered last year. None of them had submitted more than one entry to any puzzle! The number of entries that each had submitted was triangular (a triangular numbers fits the formula n(n+1)/2, like 1, 3, 6, 10, 15).

The number of incorrect entries that each had submitted was a perfect square — the same square for each of them. The number of correct entries that each had submitted was prime — a different prime for each of them. The total number of correct entries that they had between them submitted was a multiple of the total number of incorrect entries that they had between them submitted.

What was that total number of correct entries?

[enigma1440]

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Solution:The total number of correct entries is 60.