Saturday, March 30, 2013

Fun with toothpicks

There are many fun problems that involve constructions with toothpicks.  One nice thing about them is that they can be enjoyed by adults and kids alike, starting at a fairly young age.  Here is by far my favorite problem of this type.

It is easy to make 4 equilateral triangles using 9 toothpicks (see below), but can you make 4 equilateral (and equal) triangles using just 6 toothpicks?

Here are a few easier problems with toothpicks that I got from this book by Martin Gardner.
Warning: the solution to the problem above is completely different from the ones below.

1) Move four toothpicks to make three identical squares (with no toothpicks left over).


I apologize for the image.  I had some trouble aligning the toothpicks!

 2) Move one toothpick and make the house face east instead of west.

3) Move two toothpicks to make four identical squares (with no toothpicks left over).
4) Move three toothpick so that the triangular pattern points down instead of up.


Please share your favorite toothpick problems!
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3 comments:

  1. UnknownMarch 30, 2013 at 9:33 PM

    I can make 6 equal equilateral triangles with 6 toothpicks: make a star of David. But I assume that's not what you had in mind? Also the toothpicks might have trouble lying flat.

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  2. UnknownMarch 30, 2013 at 11:51 PM

    The problem says nothing about the toothpicks having to lye flat, however, in your solution they are not quite triangles in the sense that the three sides do not lie in the same plane. Interesting construction though, so thanks for posting and sharing your ideas!

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  3. Mr. OApril 1, 2013 at 8:43 PM

    Sasha, I believe that the problem I sent to you today makes a great extension to your problem on making four equilateral triangles from six toothpicks. Make seven equilateral triangles using only nine toothpicks.

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