spatial puzzles (2D)

2D Spatial Puzzles

Also check out my new project MUSICAL MATH VIDEOS.  Subscribe on You Tube to get more when the are released!

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For the solution, click here.

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Topologist's Map of the United States

To a topologist, two shapes are "the same" if one can be stretched, twisted, and distorted into the other shape without breaking or tearing it.  Shape, angle, size, distance, and position can be completely different, and yet the two shapes are topologically equivalent.

This is a topologist's map of the 48 contiguous United States.  While the states are not recognizable, you can work out which is which by how the states are connected to each other.  For example, which is the only state that borders exactly one state?  Can you find it on the topologist's map?  Can you identify all the states?  (One note:  Lake Michigan is included as one of the polygons, and the state of Michigan is represented as a single polygon, which was necessary to avoid some strange results.  So all together there are 49 polygons here.)

For a printable version click here.

For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.

For more museum guard problems (and solutions), click here. 

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For the solution, click here.

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This problem has surprisingly many solutions.  For the solution, click here.

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For printable game boards, click here.

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For the solution, click here.

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It is possible to make an area as small as 2 square units (and perhaps smaller?) with 12 toothpicks!  For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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Solution:  We can make any number of triangles from 1 up to 10.  There are multiple solutions for each number.  For examples, click here.

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For the solutions, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.

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For the solution, click here.