The teleporter misses its mark for the umpteenth time, and Kinesys materializes on Polygon in a square paved with perfect triangles. The locals, who have hexagonal heads, have a favorite evening pastime: challenging strangers with matches.
An elderly Polygonian lays six of them on the table. “Four equilateral triangles,” he says. “Not one more, not one less. No bending and no breaking.”
Liz sits down with a sigh and starts shuffling matches around. Dord refuses to touch them: their lengths are very similar but not identical, and that irritates him deeply. M00N circles the table, studying the matches from every angle. Including from above.
The Riddle
Using six matches, try to make four equilateral triangles without bending or breaking any of them.
Hint
You won’t manage it on the table, however hard you try. Who said the matches all have to stay flat?
Solution
The solution is to arrange the six matches into a regular tetrahedron, that is, a pyramid with a triangular base: a three-dimensional shape whose four faces are all equilateral triangles.
Most people can’t solve this puzzle because they assume the matches have to lie on a flat surface. On Polygon, where solids are everywhere, even children know better.