X and Y are playing a game. There are eleven 50 paise coins on the table and each player must pick up at least one coin but not more than five. The person picking up the last coin loses. X starts. How many should he pick up at the start to ensure a win no matter what strategy Y employs?

Dear student
Four coins....
There are 11 coins.
Now,X can pick up max 5 and min 1.chances of Y are also max 5 and min 1. (atleast1,not more than 5)
case1: consider X picks up 5 coins..consider the case in which Y picks 5(max) from the remaining coins and the last coin must be picked by X obviously..and X doesn't win.
case2: consider X picks up 4 coins and Y=5 coins.then the remaining coins have to be picked up and it is X's turn and the last coined is picked by Y. Hence X wins.

Similarly the strategy goes on for
X=4,Y=2 and
Hence X have to pick up 4 coins in order to start to ensure a win.

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