Reversing coins there are n coins, each showing either heads or tails. we would like all the coins to show the same face. what is the minimum number of coins that must be reversed?

If there are n coins, then the smallest (minimum) amount of coins we need to flip is 1. The reason why is because the best case scenario would be flipping all heads except the last coin which is tails. This scenario is rare if n is large, but still possible.