Coding classes in the Orkney Islands

The model is invented. Nine crofters must each take one of nine stretches of an island wall to repair. Each crofter ranks the stretches, preferring ones near home and ones that are easier. An imaginary court ranks the crofters for each stretch, preferring experienced wallers. A pairing is unstable if some crofter and some stretch both prefer each other to what they were given, because then that crofter has every reason to swap. Computer scientists call such a pair a blocking pair. The goal is a stable matching with none.

First come, first served feels fair: crofters pick in turn, each taking their favourite free stretch. The early pickers do well, the last one gets their ninth choice, and ten pairs of crofter and stretch would both rather be together, so the arrangement would not last. The Gale-Shapley algorithm, invented in 1962, does better. Unmatched crofters propose to their favourite stretch not yet tried; each stretch holds on to its most preferred offer so far and drops the rest. It always ends, here after 32 proposals, and always gives a stable matching. The learner confirms it by brute force: of all 362,880 possible ways to pair nine crofters with nine stretches, exactly one is stable, and the algorithm found it. Stability even helped the crofters overall, with a lower rank total than first come, first served.

Who proposes can matter enormously. The learner builds a tiny three-by-three example with circular preferences. When crofters propose, all three get their first choice. When the stretches propose, all three crofters get their third choice. Both results are stable. The algorithm always favours the side that proposes, a fact with real consequences when it is used to place doctors in hospitals or pupils in schools.

An Orkney teenager should still learn to code in 2026 for exactly this reason: to check whether a clever-looking answer is also a fair one. The longer argument is in why teenagers should still learn to code in 2026.