Grandma's Lighthouse

The centerpiece: rooms aren't playtested, they're proved

The rooms aren't playtested for solvability, they're proved, in a headless test that runs on every change (tests/puzzle_model.gd). It reimplements the room rules on plain data: border walls, fixed furniture, one-tile pushes with no pulling, gates that latch open when the right object rests on the right cell. Each arrangement packs into a single integer (coordinates are 0-7, three bits each, player in bits 0-5, each pushable in the next six, each gate one bit above), so a state becomes a dictionary key with no allocation, which is what makes a millions-of-nodes search fast enough to run constantly. Breadth-first search, solved states absorbing, the first solved state found is also the shortest solution, which doubles as the room's difficulty measure. Across the five shipped rooms that shortest solution runs from 7 moves (Entryway) to 49 (Her Study), with the Kitchen at 36 and the Lamp Room at 34, and the search touches between 329 and 639,681 distinct arrangements per room, median 52,369.

What that check prints for the Entryway, the smallest room:

$ godot --headless --path . --script res://tests/verify_entryway.gd

[ENTRYWAY]
  object count           : 2
  optimal solve length   : 7 moves
  re-handling required   : no — every object is handled in one pass
  reachable arrangements : 1783
  deepest arrangement    : 28 moves from start
  dead ends (fairness)   : 1062 of 1780 non-solved  (718 still solvable)
  safe explore window    : 6 move(s) — shallowest dead end that far in
  shortest path into it  : SSEEEE
  ok   a solution exists from the start state
  ok   replaying that solution lands every object home
  ok   reset restores a solvable state (reset returns to the start)
  ok   undo buffer (256) covers the deepest arrangement (28)
  ok   no placement strands the room: all 4 reachable placements stay
       solvable from the start layout — undo always recovers
  ok   the open exit is reachable from the player in every solved state
ENTRYWAY PUZZLE TEST: PASS — solvable, undo/reset always recover

Real output from the headless run; the other four rooms print the same shape with bigger numbers.

It asserts two things and deliberately not a third: a solution exists from the start; undo and reset always land somewhere solvable (the hard one, every set of committed objects the player can reach must itself leave the room solvable from the start layout with those pre-placed, the analyzer enumerates those placements and checks each); not dead ends, wedging an object that isn't yet home is fair, undo takes it back, the player loses time, not the room. They're counted and reported, never failed on. The raw dead-end count is useless as a design signal because it explodes combinatorially the moment one crate is wedged, so first_dead_end, moves from the start to the shallowest dead end, is a fairness reading instead: how far a player explores before a wrong move costs them a rewind.

Honest limits

The search caps at 2,000,000 distinct arrangements. As the rooms are tuned today the biggest is the Lamp Room at 639,681 arrangements explored, comfortably inside the cap, but a denser 5-6 object room with an 80-move solution would blow past it, and the report is built for that: solved states sit shallow so solvability, the shortest solution, and per-object metrics stay exact; max_depth and dead-end counts degrade to lower bounds, and the report says so and downgrades the undo-buffer check to a warning rather than printing a number it can't stand behind. The undo history holds 256 moves, set above the deepest arrangement measured (145, in the Lamp Room). The whole five-room proof runs headless in about 35 seconds, five engine boots and all.