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.]