Brain games: puzzles, riddles, and logical games.
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Puzzles, riddles, logical games, mathematics on Facebook

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Walking the Earth Geometry puzzles  Weight: 3 Liked the puzzle: 90% 27.12.2009
A Megamind walked one mile South, one mile East, and one mile North, after which he arrived at the starting point of his trip. Where on planet Earth could such a trip take place?
Comments:  1 check your solution  
A Megamind in a boat Geometry puzzles  Weight: 4 Liked the puzzle: 100% 27.12.2009
A Megamind is sitting in a boat at the center of a circular lake of radius R. On the lake shore, an evil Goblin awaits. Luckily for the Megamind, the Goblin can only move along the shore. Unfortunately, the Goblin is 4 times as fast as the Megamind in his boat. The Megamind can save himself if he gets to the shore and evades meeting with the Goblin. Can the Megamind save himself? If yes - how?
Comments:  1 check your solution  
Cutting the cube Geometry puzzles  Weight: 4 Liked the puzzle: 80% 27.12.2009
What is the minimal number of straight cuts required to split a 3x3x3 cube into 27 1x1x1 cubes? Pieces can be rearranged arbitrarily between the cuts. The answer should justify the minimality.
Comments:  1 check your solution  
Six matches and triangles 2 Geometry puzzles  Weight: 4 Liked the puzzle: 100% 07.02.2010
How to make one equilateral and three isosceles (and not equilateral!) triangles using 6 sticks of the same length? Sticks cannot be broken and/or laid over each other and no free ends of the matches may be left.
Comments:  1 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  
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  
The telephone cable 2 Geometry puzzles  Weight: 5 Liked the puzzle: 100% 01.01.2010
The Megamind has a square parcel of land of size 1x1 km. Accidentally, he has found out that the devious Occupants had buried a telephone cable through his land and use it for their devious communications. The cable is buried along a straight line crossing the square land plot. After discovering this, the Megamind got his shovel and... paused to think. What is the shortest trench that the Megamind has to dig to find the cable? The trench may be disconnected. The proof of optimality is not required.
Comments:  3 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  
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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