OT Last week's CarTalk puzzler

[Mark Wieder]

Jim-

Friday, November 25, 2005, 6:45:22 AM, you wrote:

I think it's simpler than that. (warning - it's Friday morning and the
caffeine hasn't really taken effect yet)

Consider any number in terms of its factors. By definition, factors
come in pairs:

the factors of 15 are 1 x 15, 3 x 5
the factors of 17 are 1 x 17
the factors of 18 are 1 x 18, 2 x 9, 3 x 6

The *only* exceptions to this are perfect squares, unless you want to
count the same factor twice:

the factors of 16 are 1 x 16, 2 x 8, and 4

Therefore, every switch will be toggled an even number of times and
turned off except for the perfect squares.

-- 
-Mark Wieder
 mwieder at ahsoftware.net