Using exactly 12 matchsticks, build a shape that encloses the most possible area
You have exactly 12 matchsticks, all the same length, and may arrange them edge to edge into any closed shape you like, straight sides only, no overlapping or breaking a match. A plain 3-by-3 square grid pattern is the obvious first guess. Can you arrange the same 12 matches to enclose more area than that square does?
Reveal the answer
Yes. A square built from 12 matchsticks (three per side) encloses 9 square units, but rearranging the same 12 matches into a different rectangle, like a 2-by-4, only gives 8 square units, less. The actual winner among simple polygons is a regular dodecagon-like arrangement bending the matches into a near-circular shape, since for a fixed perimeter a shape closer to a circle always encloses more area than a square does, a direct consequence of the classical isoperimetric inequality.