Propagation at the Festival

Running propagation on the festival deletes twelve conceivable values down to eight and demolishes the doomed subtree before any search begins.

Track the four domains. The fireworks rule collapses Cinder to 3 alone. The van rule strikes Brook's 1, leaving 2 and 3. The opener rule works both directions: Anvil = 1 dies because no Dune slot is earlier than 1, and Dune = 3 dies because no Anvil slot is later — Anvil keeps 2 and 3, Dune keeps 1 and 2. Count the survivors: two, two, one, two — the 81 conceivable schedules have quietly become 2 × 2 × 1 × 2, eight. And notice what vanished: the entire Anvil = 1 drawer, which backtracking disproved by exhaustive failure, was deleted here by one line of reasoning, before a single assignment was tried.