# An old geometric puzzle

I don't know precisely the origin of the question. I've encountered it in a Russian Problem Solving book, when I studied in 7th grade. However, the beauty of the problem still manages to amaze me. So lets end this nostalgic talk and get back to solving.

Problem. You have exactly 6 identical matches. How you can construct 4 equilateral triangles using them? You can't use additional matches or break or bend the matches you have.

Note by Nicolae Sapoval
6 years, 11 months ago

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Here'a the answer: 4 equilateral triangles with 6 identical matches

- 6 years, 11 months ago

Wow, I was thinking it was a 2D shape and was staring at the figure for 15 minutes lol.

- 6 years, 11 months ago

Sometimes just to solve a problem you've got to change your perspective.

- 6 years, 11 months ago

Yep, great job!

- 6 years, 11 months ago

If the crossing of matches is allowed, here is a possible solution (though then the riddle is too easy):

Solution with crossing

If the crossing of matches is not allowed however, I have another solution:

Solution without crossing

This solution gives 8 triangles though, not 4, so I assume it is not the "correct" solution :)

- 6 years, 11 months ago

You've inspired me to create a non-crossing solution of exactly 4 triangles

- 6 years, 11 months ago

Well, I could probably consider the second solution by Ben, but this is complete nonsense :D

- 6 years, 11 months ago

I support this solution. :D

- 6 years, 11 months ago

I think this is also a solution if crossing is allowed

- 6 years, 11 months ago