## 08 July 2008

### On today's New York Times crossword

Today's New York Times crossword is by Tim Wescott. There is someone who's commented at Secret Blogging Seminar with that name.

Anyway, here are some of the answers:

4 down: EVEN TENOR
6 down: PERFECT GAME
11 down: ODD MEN OUT
25 down: SQUARE KNOTS
33 down: REAL MCCOY
37 down: PRIME TIME

There was one more clue saying that the first word of each of those answers (which had a star before the clue) described the number of its clue. So 4 is even, 6 is perfect, 11 is odd, 25 is square, 33 is real, and 37 is prime.

33 down seems like a bit of a cop-out to me. But I'm not saying I could do better at making a crossword. Crosswords (especially American-style ones) are hard to make; read the information-theoretic argument in MacKay's book for some justification why.

For the non-mathematicians who may have stumbled in (and the mathematicians who don't remember this particular bit of trivia), I feel like I should point out what a perfect number is. A number is perfect if it's equal to the sum of all the numbers it's divisible by. So 6 is divisible by 1, 2, and 3, and 1 + 2 + 3 = 6. 28 is the next perfect number; it's divisible by 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28. But 12 isn't perfect; it's divisible by 1, 2, 3, 4, and 6, and 1 + 2 + 3 + 4 + 6 = 16, which isn't 12. We call 12 "abundant" because 16 (the sum of its divisors) is more than 12. Just under one quarter of integers are abundant, which is entirely irrelevant.