Would you believe that 21 is the smallest number of distinct squares into which a square can be dissected?

Did you know that if there are 24 people in a room then the odds are greater then evens that two of them share a birthday? It's true - honest!

And 25 is the smallest integer which is both a square and the sum of two square integers (as in Pythagoras).

38 is the magical constant in the only possible magic hexagon which uses the numbers 1 to 19: http://www.mathematische-basteleien.de/magichexagon.htm