Louie won’t tell you his age, but it happens that if you square his age this year, and you square his age next year, the difference between those two perfect squares is 75. So how old is he?
This can be done by guessing. It can also be done with a spreadsheet.
And there’s always algebra:
x2 + 2x + 1 – x2 = 75
2x + 1 = 75
x = 37