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.

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## Comments

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

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

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

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Yep, great job!

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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 :)

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

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

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I support this solution. :D

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Comment deleted Dec 16, 2013

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The second one is a kind of very ambiguous solution, though I like it. The first one is beautiful! To get the construction I'm talking about try to add one more requirement: All triangles must have their side equal to the whole match.

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Good luck

Edit: I mean 12 pentagonssilly me...

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So here's 3125 of them.

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I really like your answers though. It's really nice to see fresh and (technically correct) novel solutions.

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There are lots of things that can be done with matchstick puzzles :)

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I think this is also a solution if crossing is allowed

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