3 squares in a number?

Find a three-digit number containing three different non-zero digits, such that
1) the first digit plus the number formed by the second and third digits,
2) the first digit multiplied by the number formed by the second and third digits, and
3) the sum of the three digits
are all perfect squares.


The answer is 916.

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1 solution

Dan OBrien
Jun 6, 2015

The answer is 916.

1) 9+16 = 25, which is 5^2.

2) 9 x 16 = 144, which is 12^2.

3) 9 + 1 + 6 = 16, which is 4^2.

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