clue 1: i am a two digit number
clue 2: my second digit is the square of the first
clue 3: the product of my digits is a cube
Looking at clue 2:
The only digits whose squares are also digits are 0,1,2, and 3 and their
squares are 0,1,4, and 9, respectively. So the only possibilities are
00, 11, 24, and 39.
Looking at clue 1:
We rule out 00 as being a two-digit number.
So the only candidates are 11, 24, and 39.
Looking at clue 3:
They must be so that their product is a cube.
It's true of 11 because 1×1 = 1 = 1³
It's true of 24 because 2×4 = 8 = 2³
It's true of 39 because 3×9 = 27 = 3³
So there are three possible different answers 11, 24, and 39.
Edwin
