Welcome to the zoo!

There are critters with zero legs, two legs, four legs, and fifty legs. Hug a caterpillar today (but not too tightly).

There is at least one critter with each number of legs. The more legs, the more of those critters, and vice versa. The total number of critter legs is 600.

What is the maximum number of critters in the zoo?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, May 28, 2014 at noon Pacific Time.** I will post the answer shortly after.