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Included mostly puzzles and brain teasers, very fast round. Practice probability as much as you can.
1. John is given a balance and n weights of weight 2, 2^2, . . . , 2^n. He has to place each of the n weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step he can choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed.
Determine the number of ways in which he can be do this task.
