# Rush Hour 4×4, 5×5 & 6×6 — Balanced (solvable-only, fixed thresholds)
Enumerates boards (4×4/5×5) and/or samples for selected sizes (e.g., 6×6), BFS-solves to optimal sequences, and stratifies by difficulty.

## Policies
- sizes: 4, 5, 6
- solvable_only: True
- exclude_already_solved: True
- difficulty_scheme: fixed
- fixed_thresholds: 3,5  # easy < t1, medium < t2, hard ≥ t2
- balance_per_size: True

## Schema
- board (str) | size (int) | moves (int) | solution (list[str]) | difficulty (easy/medium/hard) | messages (chat)