Brain games: puzzles, riddles, and logical games.
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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  
Three Megaminds and three pistols Probability theory  Weight: 5 Liked the puzzle: 50% 24.01.2010
Three MegaMinds wanted to figure out who is the smartest and decided to have a shoot-out. They stood in a triangle and prepared to discharge their pistols. They must shoot consecutively, until only one remains standing. The first MegaMind is the best shooter, he has 90% chances of hitting the target. The second has 80%, and the third - 10%. Anybody can aim at anybody. How should they choose their targets to maximize their chances to survive?
Comments:  1 | check your solution  
Four spheres and a cylinder Geometry puzzles  Weight: 5 Liked the puzzle: 100% 26.01.2010
Four spheres and an infinite cylinder are arranged on a plane so that all these solids touch each other and the plane. The cylinder has radius 1cm. Describe the spatial arrangement of these solids and find the radii of all spheres.
Comments:  7 | check your solution  
Mad Max 2 Logic puzzles  Weight: 5 Liked the puzzle: 100% 29.01.2010
A circular road in a desert is 100 miles long. Some finite number of barrels are placed randomly along the road. These barrels contain a total of 100 liters of gasoline, but otherwise each barrel contains a random amount of gas. A car takes 1 liter of gas per mile. Can Mad Max (the driver) travel the entire circle in either direction if his car has an empty gas tank? He may start from any barrel.
Comments:  1 | check your solution  
10101...01 Algebra, arithmetic  Weight: 5 Liked the puzzle: 100% 07.02.2010
For which values of n, the decimal number 10101..01 (the alternating sequence of n ones and n-1 zeros) is a prime?
Comments:  1 | check your solution  
Rabbits in the store Algebra, arithmetic  Weight: 5 Liked the puzzle: 100% 09.02.2011
In a pet store, the first Megamind bought two plus a half of the remaining rabbits. The second Megamind bought three plus a third of the remaining rabbits. The third Megamind bought four plus a fourth of the remaining rabbits. At some point, one of the Megaminds could not make his purchase. What is the maximal number of satisfied customers (Megaminds)?
Comments:  3 | check your solution  
A game with cookies Games puzzles  Weight: 5 Liked the puzzle: 0% 21.02.2011
A cookie jar contains 2000 cookies. Turn by turn, two players take 1,2, or 3 cookies from the jar and eat them (yes, that's a lot of cookies to eat!). A player cannot take the same number of cookies as his opponent did in the preceding move. The winner must eat the last cookie from the jar or render his opponent unable to make a move. Who wins in this game?
Comments:  1 | check your solution  
The players' weights Algebra, arithmetic  Weight: 5 Liked the puzzle: 04.03.2011
Once upon a time, 23 Megaminds decided to play a soccer game. In the process of choosing teams, they observed a curious property: no matter who was elected as a referee, the remaining 22 players could be split into two teams with equal total weight. Is it possible that not all Megaminds weighed equally? Each Megamind weighed an integer number of kilograms.
Comments:  1 | check your solution  
Sum of all divisors of a square Algebra, arithmetic  Weight: 5 Liked the puzzle: 50% 19.03.2011
Prove that the sum of all divisors of a nonzero square integer is odd.
Comments:  1 | check your solution  
Divide a parallelogram Geometry puzzles  Weight: 5 Liked the puzzle: 100% 02.04.2011
How to divide a parallelogram into 9 isosceles triangles?
Comments:  1 | check your solution  
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