Geometrical Puzzles

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Three Spirals
Three Spirals
by The Grabarchuk Family
Which spiral (A, B, or C) is the biggest one?
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Columbus Easter Egg
Columbus Easter Egg
by Serhiy Grabarchuk
The Egg consists of differently colored parts. Which is bigger - the total area of the light parts (yellow tones) or the total area of the dark parts (blue tones)?
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Heart in Heart
Heart in Heart
by Peter Grabarchuk
Which region is bigger - A (blue) or B (red)?
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Sphere Between Cubes
Sphere Between Cubes
by Peter Grabarchuk
A cube is inscribed in, and a cube is circumscribed outside the same sphere. What are their relative volumes? Any ideas how to calculate them?
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Square to Triangle
Square to Triangle
by Serhiy Grabarchuk, Jr.
Provided with a perfect square, a pencil, a piece of paper your goal is to use your creativity to draw a... perfect equilateral triangle. How hard is it to convert a square into a triangle?
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Hexagon-Circle-Hexagon
Hexagon-Circle-Hexagon
by Charles W. Trigg
The same circle is simultaneously inscribed in one regular hexagon and circumscribed outside another regular hexagon. Is this information sufficient to determine the ratio of the hexagons' areas?
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The Earth Belt
The Earth Belt
by Martin Gardner
Imagine a steel belt is stretched tightly around a big planet. What things can be possibly slipped under the belt, if a meter of steel added to the belt raises it off the sphere's surface by the same distance all the way around?
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Outside the Hole
Outside the Hole
after Martin Gardner
A disk of certain diameter is removed from a piece of paper creating a circle hole in it. The goal is to calculate the area which still remained around the hole.
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Spider Ride
Spider Ride
by Henry E. Dudeney
What is the shortest trip for a spider to get from one spot on a rectangular box to another? Does the straight and clear line that it seems to be at first sight will be the shortest?
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Hexagon Inside the Cube
Hexagon Inside the Cube
after Martin Gardner
It is quite easy to get the cross sections in form of a square or a regular triangle from a cube. Is it so easy to get the cross section of a regular hexagon from the same cube?
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Rays Through the Squares
Rays Through the Squares
after Martin Gardner
The three rays that come through the three squares create the three angles. A proof is required to be found that the sum of two angles equals the third one.
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Hole in the Sphere
Hole in the Sphere
by Samuel I. Jones
It is known that a cylindrical hole six inches long is drilled straight through the center of a solid sphere. Is this information sufficient for calculating the exact volume remaining in the sphere?
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Acute Dissection
Acute Dissection
by Mel Stover
It is required to dissect an obtuse triangle into acute triangles only. The first question is whether it is possible at all? If the answer is "Yes", then the next question would be "How?"
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Rectangle Around
Rectangle Around
after Martin Gardner
Figure out the diagonal of a rectangle when it is inscribed in the quadrant of a circle. How long, do you think, it will take you to get the right answer to this geometrical question?
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Square Intersection
Square Intersection
after Martin Gardner
This geometrical problem is about an elegant and neat way how to figure out the exact area of the overlapping of two squares. Don't you want to discover this way by yourself?
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Cube Angle
Cube Angle
after Martin Gardner
Two lines are drawn on the two sides of a cube. They are drawn form the same corner and the question is which angle do these lines form? How to figure that out?
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Six Cubes
Six Cubes
by Martin Gardner
Is there any successful way to arrange six identical cubes into some shape so that every cube in the shape will get in touch with others?
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Last Updated: August 8, 2012 top
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