If x+y=100, x is a square number and y is a prime number, find the values of x and y.

Firstly we know that both x and y are positive, so we can make a list of possibilities for x by listing square numbers up to 100: 1,4,9,16,25,36,49,64,81 (We do not consider x=100 as y cannot be 0) Then, we try subtracting each of these from 100 to see if we get a prime number: 100-1=99 (not prime), 100-4=96 (not prime), ..... Eventually we find 100-81=19 (PRIME). So we have x=81, y=19.