Chinese Remainder Theorem — Modular Rings (2D)

Three concentric rotating rings — each divided into a different prime number of sectors — sit under a single fixed pointer and spin together in the plane as a shared counter N ticks upward, like the wheels of a combination lock. Every ring shows N mod m for its own modulus, exactly the way a car odometer's wheels each track a different place value. Because the moduli are pairwise coprime, the Chinese Remainder Theorem guarantees there is exactly one value of N (modulo the product M) at which all three rings simultaneously show a chosen target sector. Below the rings, a number-line trace plots the same counter N growing linearly to the right, with colored ticks marking every multiple of each modulus and a gold marker at the CRT solution x (and every M-periodic repeat of it) — so you can see the same alignment moment two different ways: angularly on the rings, and linearly on the trace. Pick sector counts for the three rings, generate a random target puzzle, then play or step the counter and watch both views converge — live readouts track the counter, each ring's residue, and the CRT solution computed directly from the extended Euclidean algorithm, so you can verify the animation lands exactly where the formula predicts.