induction step: a flock of n sheep. take a sheep, a, out of the flock. the remaining n − 1 are all the same color by induction. now put sheep a back in the flock, and take out a different sheep, b. by induction, the n − 1 sheep (now with a in their group) are all the same color. therefore, a is the same color as all the other sheep; hence, all the sheep in the flock are the same color. what is wrong with this "proof"