SP31412 GAMEMVS - ShaatChara

Meena and Razu have been playing Shaat Chara for many years. But they think the game is too violent. So, they came up with a new game. In this game, instead of just 1 pile, they start with n piles of stones. The game is for two players. Each player takes turn alternatively. In each turn a player can select any of the piles that has at least 1 stone left, and then remove some stone (at least one) from it. The game goes on like this until there are no stones left. The player who can’t make a move loses. At first, Razu was very happy because there was no chance of injury in this game. But he quickly grew frustrated, because Meena was winning all the games. Meena is very clever. She always plays optimally. That means, if there is a chance to win, she will always win. So, Razu came to you with a particular state of the game. He wants to know how many possible moves he may take such that Meena’s win is not guaranteed.

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