Six matchsticks

Question:

You’ve got six matchsticks. Arrange them so they form four equilateral triangles.

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Answer: The intended solution (a) is to arrange the matchsticks to form a three-sided pyramid (tetrahedron). Nearly everyone resists the idea of a three-dimensional solution.

Image.png

There are two-dimensional solutions; they just seem mundane next to the pyramid. One is to make a Star of David (b) by overlapping two triangles of three matches each. The points of the star make six small equilateral triangles(plus the two big equilateral triangles, for a total of eight).Perfectionists can shift one of the matches to get exactly four(small) equilateral triangles.

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