Coding classes in Derbyshire

Picture two gears meshing. Number the wheel's teeth 0 to 95 and the pinion's 0 to 23. At every contact one wheel tooth touches one pinion tooth, and both gears move on by one. The learner writes a loop that records each pair that touches and stops when a pair comes round for the second time, because after that the whole pattern repeats exactly. Then they ask a practical question: how many different wheel teeth does each pinion tooth ever meet? If a pinion tooth is chipped, those are the teeth it will damage, over and over.

The pattern in the table is exact. The number of contacts before repeating is the least common multiple of the two tooth counts, and each pinion tooth meets the wheel's tooth count divided by their greatest common divisor. When the two counts share no factor, like 96 and 25, the divisor is 1, so every tooth meets every tooth and wear spreads evenly over the whole wheel. Millwrights and clockmakers have a name for a tooth added for exactly this reason: a hunting tooth.

There is a price, and it is the second lesson. A 96 and 24 pair gives a speed ratio of exactly 4; a 96 and 25 pair gives 3.840, and 96 and 23 gives 4.174. The learner writes a short search for coprime pairs close to the ratio they need, and finds, for example, that 97 teeth against 24 gives 4.042. Engineering is full of choices like this, where a perfect number on paper is traded for a machine that lasts. A program that checks every option is how you make that trade knowingly.

So a Derbyshire teenager should learn to code in 2026, in the valley where the factory system began, to be the person who knows which question was missing. The longer argument is in why teenagers should still learn to code in 2026.