Originally Posted by **dirtyphotons**

ask and ye shall be linked:

http://sheldonbrown.com/fixed.html#skid
edit: if the theorem above is correct, and it looks like it is, the sentence should read:

If you are an ambidextrous skidder, and the simplified ratio has an even numerator, your number of skid patches will be the same.

If you are an ambidextrous skidder, and the numerator and denominator is odd, the number of possible skid patches will be doubled.

to be fair, i was the one who called sheldon out on this originally, and being the reasonable person he is, he changed his site to reflect it. turns out we were both wrong

Look here, according to Fraction the denominator doesn't have to be odd. Only the numerator matters. I just want to get clear on this because everyone's website says a different thing and Fraction's result is backed up by his proof (which looks OK to me, but ought to be checked by someone better at math) as well as Rabbit's brute force algorithm.

Originally Posted by **fraction**

Let a / b be the reduced gear ratio (that is, a and b are integers with no common divisors other than 1). Then,

...

(2) Ambidexterous skidding doubles the number of skid patches if and only if a is odd.