Either player 1 wins the first set and player 2 wins the second set = p * (1 – p).Or player 2 wins the first 2 sets = (1 – p)^2.Either player 1 wins the first 2 sets = p^2.Let’s say the probability of player 1 winning is p. For a 3-set tennis match, would you bet on it finishing in 2 or 3 sets? In a best of 3 tennis match, the player that first wins 2 sets wins the match. How Many Sets in a Match? (medium)Īsked in a trader interview at D.E. Therefore, the 10 perfect square doors (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) are the only ones that will be open at the end. That means every door will be toggled an even number of times, except perfect squares which will be toggled an odd number of times. ![]() For perfect squares, one of the factors is the corresponding factor to itself, so there is no corresponding flip. This means for every flip by a factor there is a corresponding flip by another factor – with the exception of perfect squares. ![]() For example, the 6th door will be toggled on the 1st pass, 2nd pass, 3rd pass, and 6th pass – all the factors of 6.īy definition, each factor of a number must be multiplied by another factor to get to the number, so the factors are paired. Notice that the n-th door will be toggled on the passes that are a factor of n.
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