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
View Solution →Nimble Game
Two people are playing Nimble! The rules of the game are: The game is played on a line of squares, indexed from to . Each square (where ) contains coins. For example: The players move in alternating turns. During each move, the current player must remove exactly coin from square and move it to square if and only if . The game ends when all coins are in square and nobody can make a move. The first player to have no available move loses the game. Given the value of and the number
View Solution →