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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TopNewestHere'a the answer: 4 equilateral triangles with 6 identical matches – Pouya Hamadanian · 3 years, 5 months ago

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– Yash Talekar · 3 years, 5 months ago

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

– Pouya Hamadanian · 3 years, 5 months ago

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

– Nicolae Sapoval · 3 years, 5 months ago

Yep, great job!Log in to reply

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 :) – Ben Frankel · 3 years, 5 months ago

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a non-crossing solution of exactly 4 triangles – Logan Dymond · 3 years, 5 months ago

You've inspired me to createLog in to reply

– Nicolae Sapoval · 3 years, 5 months ago

Well, I could probably consider the second solution by Ben, but this is complete nonsense :DLog in to reply

– Yash Talekar · 3 years, 5 months ago

I support this solution. :DLog in to reply

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– Nicolae Sapoval · 3 years, 5 months ago

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.Log in to reply

– Chung Kevin · 3 years, 5 months ago

Ah, this was going to be my next matchstick puzzle. It is a nice one. Let me find another.Log in to reply

Good luck

Edit: I mean 12 pentagonssilly me... – Logan Dymond · 3 years, 5 months ago

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So here's 3125 of them. – Ben Frankel · 3 years, 5 months ago

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I really like your answers though. It's really nice to see fresh and (technically correct) novel solutions. – Logan Dymond · 3 years, 5 months ago

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– Pouya Hamadanian · 3 years, 5 months ago

It's the same as the official solution. I think its a dodecahedron.Log in to reply

– Nicolae Sapoval · 3 years, 5 months ago

Sorry, didn't mean to interfere with your plans.Log in to reply

There are lots of things that can be done with matchstick puzzles :) – Chung Kevin · 3 years, 5 months ago

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I think this is also a solution if crossing is allowed – Ayush Chowdhury · 3 years, 5 months ago

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