Game of Stones
Two players called and are playing a game with a starting number of stones. Player always plays first, and the two players move in alternating turns. The game's rules are as follows: In a single move, a player can remove either , , or stones from the game board. If a player is unable to make a move, that player loses the game. Given the starting number of stones, find and print the name of the winner. is named First and is named Second. Each player plays optimally, meaning they will n
View Solution →Tower Breakers
Two players are playing a game of Tower Breakers! Player always moves first, and both players always play optimally.The rules of the game are as follows: Initially there are towers. Each tower is of height . The players move in alternating turns. In each turn, a player can choose a tower of height and reduce its height to , where and evenly divides . If the current player is unable to make a move, they lose the game. Given the values of and , determine which player will win. If the
View Solution →A Chessboard Game
Two players are playing a game on a chessboard. The rules of the game are as follows: The game starts with a single coin located at some coordinates. The coordinates of the upper left cell are , and of the lower right cell are . In each move, a player must move the coin from cell to one of the following locations: Note: The coin must remain inside the confines of the board. Beginning with player 1, the players alternate turns. The first player who is unable to make a move loses th
View Solution →Introduction to Nim Game
Nim is the most famous two-player algorithm game. The basic rules for this game are as follows: The game starts with a number of piles of stones. The number of stones in each pile may not be equal. The players alternately pick up or more stones from pile The player to remove the last stone wins. For example, there are piles of stones having stones in them. Play may proceed as follows: Player Takes Leaving pile=[3,2,4] 1 2 from pile[1] pile
View Solution →Misère Nim
Two people are playing game of Misère Nim. The basic rules for this game are as follows: The game starts with piles of stones indexed from to . Each pile (where ) has stones. The players move in alternating turns. During each move, the current player must remove one or more stones from a single pile. The player who removes the last stone loses the game. Given the value of and the number of stones in each pile, determine whether the person who wins the game is the first or second perso
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