Problem #7

In French, the first ten counting numbers are: un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix. In a cryptarithm, numbers are represented by replacing their digits by letters; a given letter consistently represents the same digit and different letters represent different digits. Leading zeroes are not permitted. This month's problem is to solve the French cryptarithm:

TROIS is a triangular number,
QUATRE is a perfect square, and
SEPT is not the sum of three squares.

[Recall that a triangular number is the sum of the the first n positive integers, e.g. 6 = 1 + 2 + 3 is triangular.]

The solution will be posted shortly.

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