Henry Ernest Dudeney/Puzzles and Curious Problems/86 - Digits and Cubes/Solution

by : $86$

 * Digits and Cubes

Solution
There are $3$ solutions:


 * $237^2 = 56 \, 169$, where $56 + 69 = 125 = 5^3$
 * $251^2 = 63 \, 001$, where $63 + 01 = 64 = 4^3$
 * $152^2 = 23 \, 104$, where $23 + 04 = 27 = 3^3$

Proof
A computer program can be used to perform an exhaustive search.