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Math Puzzles of the Month: November 2007
Toothpick Triangles

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Toothpick puzzles (more commonly called “matchstick puzzles”—but it’s safer to use toothpicks than matchsticks) are an old form of geometric puzzle. Toothpick Puzzles involved toothpicks arranged in squares. This month we’ll try some puzzles involving triangles and other shapes

 

 

 

1. Rearrange four toothpicks from the arrangement to make six triangles.

toothpicks

2. Remove one toothpick from this arrangement and rearrange the others to form six identical triangles.

toothpicks

3. Arrange the six toothpicks here to form eight equilateral triangles, that is a triangle with all three sides of equal length, and all three angles of equal degrees.

toothpicks

4. Rearrange the twelve toothpicks to form seven diamonds.

toothpicks

5.Using exactly six toothpicks, make four triangles the same size as the ones here.

toothpicks

 

Math Background

Puzzles like these have been around for more than a hundred years. They help develop geometric visualization skills. If you enjoy puzzles like this, Google “matchstick puzzles” and you’ll find dozens more. Once you get the hang of it, it’s easy to make up your own puzzles.

 

 

After you’ve tried this for yourself check our solutions.

 

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