The Number Game

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!
 
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And 25 is the smallest integer which is both a square and the sum of two square integers (as in Pythagoras).
 
Whereas 27 is the first odd perfect cube (apart from 1 which is trivial).
 
On August 29, 1988, Sarah Palin eloped with her high school sweetheart, Todd Palin.
 
38 is the magical constant in the only possible magic hexagon which uses the numbers 1 to 19:

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