APMO · 10. Games, invariants and processes
Monovariants, parity weights, invariants modulo a prime and periodic processes: how to prove what a process can and cannot reach, with explicit constructions for the possible cases.
Design a monovariant from the rule of a move and compare the start with the end.
Use normalisation and growth arguments to show that a process must stop.
Find parity invariants for toggle problems and complete the answer with constructions.
Work with residues of fractions modulo a prime to build frozen configurations.
Analyse a deterministic process through one period, using complex numbers and the Chinese remainder theorem.