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Terrazzo hints for Monday, August 24, 2026
Mosaic № 17. Three hints, from a gentle nudge to the full answer. Open only as many as you need.
Hint 1: what kind of picture is it?
Today's subject comes from science.
The caption reads: “Bees solved an optimization problem mathematicians proved only in 1999.”
Hint 2: the Laws, in plain words
You place 7 stones into a frame of 33 cells. Every cell is filled exactly once.
- Kinship. Same-coloured stones that touch make a region. Today: gold forms one region of 15; lapis blue forms 6 separate regions of 4, 2, 1, 1, 1, 1; moss green forms 3 separate regions of 5, 1, 1; terracotta forms one region of 1.
Start with the largest region the Laws name: it has the fewest ways to fit.
The answer: what the mosaic shows
Honeycomb
Why hexagons? Because a honeycomb is a warehouse built from wax the bees must manufacture themselves, at a cost of roughly eight units of honey per unit of wax — and the hexagonal grid is the way to divide a plane into equal cells using the least possible wall. Bees arrived at this through evolution; mathematicians took longer. The 'honeycomb conjecture' was only formally proved in 1999, by Thomas Hales. The bees' comb holds honey, brood, and pollen in a structure so efficient that engineers borrow it for aircraft floors and satellite panels.