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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.

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Note by Nicolae Sapoval
3 years, 10 months ago

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

Pouya Hamadanian - 3 years, 10 months ago

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

Yash Talekar - 3 years, 10 months ago

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

Pouya Hamadanian - 3 years, 10 months ago

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Yep, great job!

Nicolae Sapoval - 3 years, 10 months ago

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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 :)

Ben Frankel - 3 years, 10 months ago

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

Logan Dymond - 3 years, 10 months ago

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

Nicolae Sapoval - 3 years, 10 months ago

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I support this solution. :D

Yash Talekar - 3 years, 10 months ago

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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.

Nicolae Sapoval - 3 years, 10 months ago

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@Nicolae Sapoval Ah, this was going to be my next matchstick puzzle. It is a nice one. Let me find another.

Chung Kevin - 3 years, 10 months ago

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@Chung Kevin 20 pentagons with 30 matchsticks

Good luck

Edit: I mean 12 pentagons

silly me...

Logan Dymond - 3 years, 10 months ago

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@Logan Dymond I tried really hard but failed to make 20 pentagons with 30 matchsticks...

So here's 3125 of them.

Ben Frankel - 3 years, 10 months ago

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@Ben Frankel Ahahaha well, if you can figure out the "official" solution to the 4 triangle 6 matchstick puzzle it should clue you in to the solution to the 20 pentagon 30 matchstick puzzle.

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

Logan Dymond - 3 years, 10 months ago

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@Logan Dymond It's the same as the official solution. I think its a dodecahedron.

Pouya Hamadanian - 3 years, 10 months ago

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@Chung Kevin Sorry, didn't mean to interfere with your plans.

Nicolae Sapoval - 3 years, 10 months ago

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@Nicolae Sapoval Oh, no worries. I'm glad that you shared this problem. It shows me that I'm not the only one who loves this (especially since I wasn't getting replies from others).

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

Chung Kevin - 3 years, 10 months ago

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I think this is also a solution if crossing is allowed

Ayush Chowdhury - 3 years, 10 months ago

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