Terrazzo hints for Sunday, September 13, 2026

Today's subject comes from nature.

The caption reads: “They emerge after thirteen years, or seventeen. Never twelve.”

You place 12 stones into a frame of 61 cells. Every cell is filled exactly once.

• Kinship. Same-coloured stones that touch make a region. Today: gold forms 3 separate regions of 5, 5, 1; lapis blue forms 4 separate regions of 6, 6, 1, 1; moss green forms 3 separate regions of 8, 5, 1; terracotta forms 3 separate regions of 12, 5, 5.
• Solitude. No two sun cells may touch, not even corner to corner.
• The Vein. The vein cells must form one unbroken path between the frame's two notches, with no branches and no loops.

Start with the largest region the Laws name: it has the fewest ways to fit.

The Prime Cicadas

Periodical cicadas spend nearly their whole lives underground drinking root sap, then surface in the billions to sing, mate and die within weeks. The intervals are always thirteen or seventeen years — both prime. The favoured explanation is arithmetic: a predator with a two-, three- or five-year population cycle will rarely coincide with a prime-numbered brood, because primes share no factors with the smaller cycles. A twelve-year cicada would meet its two-, three-, four- and six-year enemies constantly. Evolution did not know it was doing number theory. It simply killed off every brood whose timing could be divided.