Coding classes in Luton

The learner models a flat plait as a Python list, one entry per strand, numbered by where it starts. We use a simple rule: first the outer strand on the left crosses over to the middle, then the outer strand on the right does the same, and the two moves repeat. After each crossing the program checks whether the list is back in its starting order, and counts the crossings until it is. Real plaiters use many patterns; this is one clean example chosen for the lesson.

The pattern is striking: with an odd number of strands, the plait returns after exactly twice as many crossings as there are strands. The reason is a result from permutation theory. One left-and-right pair of crossings sends each strand along a single loop through all the positions, a cycle of length n. A permutation returns to the start after a number of steps equal to the least common multiple of its cycle lengths, here just n pairs, so 2n crossings. Because the loop is a single cycle, every straw spends the same time at the edges and in the middle, which helps a plait look even.

Two slips catch learners out. Mixing up "which strand is in position 3" with "where did strand 3 go" gives the inverse arrangement, which looks plausible but is wrong. And applying the right-hand move before the left-hand one changes the in-between arrangements, because rearrangements do not generally commute, even though the return time here stays the same. The learner writes a test that composing the pair n times gives back the starting list, and prints the cycle structure to prove the single loop.

Checking output against a rule that must always hold is a skill a Luton teenager gains by coding in 2026. The longer argument is in why teenagers should still learn to code in 2026.