Problem #1

In German, the first ten counting numbers are eins, zwei, drei, vier, fünf, sechs, sieben, acht, neun, and zehn. 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 German cryptarithm:

If VIER is a perfect square,
SECHS is a triangular number, and
NEUN is a perfect square,
what is DREI?

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

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