Brain games: puzzles, riddles, and logical games.
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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  
A 52 card trick Logic puzzles  Weight: 5 Liked the puzzle: 100% 26.12.2009
A famous magician takes a standard 52 card deck and gives it to the audience. The spectators choose any 5 cards (they may do it any way they like) and pass these cards to the magician's assistant. The assistant announces 4 of these cards out loud. The magician responds by naming the fifth card. Except for the suit and denomination of each card, the assistant passes no other information to the magician. How does the magician "know" the fifth card?
Comments:  8 check your solution  
A birthday dinner Logic puzzles  Weight: 5 Liked the puzzle: 0% 26.12.2009
A large and merry group of N guys and N girls went to celebrate a birthday in a restaurant. They were randomly seated at a big rotating table by a hurried waiter who quickly took their drink orders. Every girl ordered a wine, and every guys ordered a beer. Bringing the drinks, the waiter brought the right number of beers/wines, but forgot who ordered what and placed the drinks randomly in front of everyone. The party was enraged because more than a half got the wrong drink and demanded to see the manager. The manager appeared and said: "My apologies, but this is not such a big deal. In fact, I can rotate the table without touching the drinks so that more than half of you will get what you ordered." Is the manager's claim correct?
Comments:  1 check your solution  
Guess your color Logic puzzles  Weight: 5 Liked the puzzle: 100% 26.12.2009
Three MegaMinds enter a room, one by one. Upon entrance, each MegaMind is given a hat that can be white or black. Each MegaMind can see the other two hats, but not his own. After they have spent 5 minutes in the room, the MegaMinds are separated and asked the following question: "What is the color of your hat?" They can say "black" or "white" or simply refuse to answer. If nobody answers or if somebody gives a wrong answer, they will spend the rest of their lives in a dungeon. What should each MegaMind do? What are the chances that they will be set free? There is no preliminary agreement or exchange of any information among them.
Comments:  5 check your solution  
A game with three dice Logic puzzles  Weight: 5 Liked the puzzle: 100% 26.12.2009
A MegaMind has three dice whose faces are marked with numbers 1,..,6. Some numbers can be repeated. He offers to play the game in which his opponent can choose any die, and the MegaMind will choose one of the remaining two. Then they discard the last die, and start rolling. Whoever rolls a lower number, pays the opponent a predetermined sum, say $1. In case of equality, the MegaMind lose. How did the MegaMind mark the dice if it is known that he plays this game nearly every day, and usually wins?
Comments:  3 check your solution  
Triangular cake Geometry puzzles  Weight: 5 Liked the puzzle: 50% 26.12.2009
A birthday cake has a form of triangle. Two Megaminds divide as follows: One chooses a point in the triangle, and the other cuts the triangle by a segment passing through this point. The cutter then takes the bigger part. What is the maximal part of the cake guaranteed to be left to the first Megamind? The thickness of the cake is constant.
Comments:  2 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  
Toy cars on a surface Geometry puzzles  Weight: 5 Liked the puzzle: 27.12.2009
Four toy cars are moving with constant velocities on a flat surface. Their velocities are not parallel, and the cars had started to move a while ago. After a collision, each car continues to move with the same velocity, but it disintegrates after three collisions. Five collisions involving two cars each had already happened, and two toys had disintegrated. What is the fate of the remaining two toys?
Comments:  1 check your solution  
18 crystals Weighing puzzles  Weight: 5 Liked the puzzle: 100% 30.12.2009
Once upon a time, a Megamind worked as an optometrist for an Occupier who was color blind. The Occupier had a dream that he may regain perfect vision if the Megamind made him a set of 9 red and 9 blue crystals. The crystals should be of the same size, but the blue ones should be heavier than the red ones. Crystals of the same color should weigh the same. The Megamind completed the order and brought two sets of crystals: blue in his right hand and red in the left. The Occupier was suspicious, he did not trust the Megamind. Fortunately, the Occupier has a balance scale. How can the Megamind convince the Occupier that all crystals in one hand are blue and in the other - red. He can use no more than three weighings.
Comments:  5 check your solution  
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