Brain games: puzzles, riddles, and logical games.
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The mouse hunt Games puzzles  Weight: 4 Liked the puzzle: 100% 11.01.2010
A smart cat named Leopold is hunting a mouse. A mouse is hiding in one of five holes arranged in a row. Leopold can reach into one of the holes and try to catch the mouse. If he is not successful, the scared mouse runs into a right/left neighboring hole. Is it guaranteed that Leopold will catch the mouse? If so, what should he do?
Comments:  10 | check your solution  
Tic-tac-toe, the Megamind style Games puzzles  Weight: 4 Liked the puzzle: 100% 26.02.2011
Two Megaminds decided to play tic-tac-toe using new rules. They use a regular 3x3 playing pad, but each player can choose to place either an X or an O into one of the cells. The winner is still the one who arranges three X's or three O's in a line. Is there a winning strategy in this game? Which player has it?
Comments:  1 | check your solution  
A game with coins Games puzzles  Weight: 4 Liked the puzzle: 100% 12.03.2011
Two Megaminds play a game: they have a regular round table and an unlimited supply of identical round coins. Turn by turn, they place coins on the table until someone can no longer make a move. The coins cannot overlay each other, but they can touch. Who has a winning strategy (and what is it) in this game?
Comments:  6 | check your solution  
A game of symmetry Games puzzles  Weight: 4 Liked the puzzle: 100% 17.03.2011
Two megaminds play a game on a board sized 1x81 cells. The board is initially empty. At each turn first megamind can place a stone (either black or white) in any cell. Second megamind can either swap any two stones or skip a turn. After megaminds made 81 turns each, the symmetry of the board is assessed. If the stones are located symmetrically, second megamind wins, if not - first one wins. Who will win and why?
Comments:  1 | check your solution  
A poisoned chocolate bar Games puzzles  Weight: 5 Liked the puzzle: 100% 26.12.2009
A chocolate bar consists of NxM (at least two) square pieces arranged in a rectangle. The square in the upper left corner is poisoned. Two players break off the squares from the bar and eat them. If a player chooses a certain square, he must also take all of the remaining squares that have row/column numbers not less than the chosen one. A player forced to take the poisoned square loses. Prove that the first player to make a move has a winning strategy.
Comments:  3 | check your solution  
Caesar and Brutus Games puzzles  Weight: 5 Liked the puzzle: 100% 26.12.2009
Two commanders (Caesar and Brutus) conquer a country which forms a connected graph with nodes representing cities and edges representing roads. First, Caesar chooses a city and claims it. Then, Brutus claims any of the remaining cities. Turn by turn, the commanders claim the available cities that are adjacent to the cities they have already claimed. If a commander cannot make a claim, he skips a move. The game continues until all cities have been claimed. Both commanders wish to claim a maximal number of cities. Can Brutus win in this game?
Comments:  5 | check your solution  
A game with wooden sticks Games puzzles  Weight: 5 Liked the puzzle: 100% 02.01.2010
Two MegaMinds play a game with 100 wooden sticks. The lengths of the sticks are 1,2,3,...,100 inches. Turn by turn, the players choose three of the remaining sticks which form a triangle, and burn them. The player that cannot make a move loses. Which player has a winning strategy (justify your answer)?
Comments:  3 | check your solution  
A game with sums Games puzzles  Weight: 5 Liked the puzzle: 100% 03.01.2010
Two players play the following game. An even number of cards are arranged in a row. Each card is marked with a real number. Upon his turn, a player takes a card from either end of the row. Whoever collects the greater sum is a winner. Otherwise, a draw is declared. Which player is guaranteed not to lose? What is his strategy?
Comments:  5 | check your solution  
The game of 15 Games puzzles  Weight: 5 Liked the puzzle: 50% 20.01.2010
Numbers 1,2,3,...,9 are written on a piece of paper. Two players cover these numbers turn by turn using their colored pegs. A number cannot be covered by more than one peg. The winner should cover three numbers which add up to 15. If a player covered more than three numbers, he wins provided that among the covered numbers there is a triple adding up to 15. Is there a winning strategy in this game? Which player has it?
Comments:  1 | check your solution  
A game with cells and squares Games puzzles  Weight: 5 Liked the puzzle: 20.01.2010
Two Megaminds play a game on an infinite rectangular grid. In each round, the first player traces out a 2x2 or a 3x3 square, and the second player shades one of the 1x1 cells inside of this square. Players cannot repeat their moves, i.e. no square can be traced twice and no cell can be shaded twice. The second player wins if he can make at least 15 moves, otherwise the first player wins. Who is guaranteed to win in this games?
Comments:  1 | check your solution  
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