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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#CosinesGroup #ThinkingOutOfTheBox

Easy Math Editor

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Comments

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

Pouya Hamadanian - 7 years, 6 months ago

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

A Former Brilliant Member - 7 years, 6 months ago

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

Pouya Hamadanian - 7 years, 5 months ago

Yep, great job!

Nicolae Sapoval - 7 years, 6 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 :)

Ben Frankel - 7 years, 6 months ago

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

Logan Dymond - 7 years, 6 months ago

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

Nicolae Sapoval - 7 years, 6 months ago

I support this solution. :D

A Former Brilliant Member - 7 years, 6 months ago

I think this is also a solution if crossing is allowed

ayush chowdhury - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$