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## Saturday, March 7, 2009

### More Fun with Dates!

Birth dates, actually. Ages, to be exact.

So, here's the thing. When people have a birthday I often tell them why their new age is a cool number. (I know, I know, the nerditude. It consumes.) I'm already planning a 33 1/3 birthday party. For myself. Also, when kids ask me how old I am, I just give them a mathematical clue. They find this very annoying.

My favorite is students turning 16, because we sing them a special little song (originally written in honor of my friend Denisse) -

Happy birthday to you!
You're a power of two!
The next time that happens,
You'll be 32!

I've lately been trying to compile a list. I left out all the primes - they're more interesting as people get older. Can you fill in any holes? And no cheating - everyone older than 3 is the sum of two primes!

If your age is _____, you are a(n) ________

6 - a perfect number
7 - the only single digit number spoken with two syllables
8 - a perfect cube
9 - a perfect square
10 - a triangular number
11 - the first three-syllable counting number
12 - an abundant number
15 - a triangular number
16 - a power of two, and a perfect square
24 - a factorial
25 - a perfect square
27 - a perfect cube
28 - a perfect number
32 - a power of two

Anything else I come up with is either "prime" or a big stretch! I could really use good ones for 17 and 18.

update: 13, 19, 23 and 31 are happy numbers.
17 is a hungry number.
17 is also a Fermat Prime.
65 is the least number that can be written as the sum of two squares in more than one way.