= Solution
Give each solving session a shared visited <set> keyed by immutable snapshots of <permutation> contents, for example `game.toList`, and insert the initial snapshot immediately. Have all successor objects refer to that same session's set. The refined `flip` first constructs the candidate state; if its key is present, return `None`. Otherwise add the key immediately and return `Some(candidate)`. The search enqueues only `Some` results. Keys must compare contents rather than <array> identities, and a fresh solving session must start with a fresh visited set.
Marking at generation time prevents the same state from being queued repeatedly, including the immediate cycle made by applying the same reversal twice. \b[First discovery in <breadth-first search> already has minimum depth], so discarding later discoveries cannot remove a shorter solution. The graph now has at most $n!$ admitted states. If only cycles along one path were to be rejected, a path-local set would suffice, but it would still repeat states reached by different paths; the shared session-wide set avoids both kinds of repetition. Public game fields must not be externally mutated while their states are being searched.
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