In Bobby’s lab he is doing research on centipedes. In his research, he noticed that all the centipedes in his study have the same number of legs, except for one that have 2 more legs than all the others. He also notes that there are a combined total of 600 legs. If the number of centipedes in the lab is between 30-50, how many legs does the centipede with the 2 extra legs have?

###### 15 legs.

The easiest way to think about this is to find the factors. By removing 2 legs from the total of 600 legs, we’re left with 598 legs.

Factors of 598:

1, 2, 13, 23, 26, **46**, 299, 598

The only factor that is between 30 and 50 is 46. Thus there are a total of 46 centipedes. An normal centipede has 598/46 = 13 legs. With 2 extra legs, that particular centipede will have a total of 15 legs.

*Trivia:*

A centipede will have various amount of legs through out its life. It grows by increasing body segments, and each body segment will always have a pair of legs. Because of this, it will always have an even number of legs. And more strangely, all centipedes will always grow by 2 body segments at a time, so the *pairs* of legs always ends up being odd.

So perhaps Bobby was using mutated centipedes after all?