Question

Find the unique two-digit number such that the square of the sum of digits equals the number obtained
by reversing its digits.

Answer 1

Let the number be ab, where a and b are digits. This number is equal to 10a+b.

This means we need (a+b)² = 10b+a.

After some trial and error, we get a=1 and b=8, and thus the number is 18.