page eighteen

The Inquest

Every other room here hands you a world and a set of dials. This one hands you a set of facts and expects you to think. Today's number shuts a few people in a building, one to a room, and something goes missing; the thief leaves one thing behind on the floor. Every statement below is true and exactly one arrangement of the sheet satisfies all of them at once — which is not a promise, it is a thing the page proved with a solver before it drew any of this.

Statements

    Click a statement to cross it off once you have squeezed it dry.

    The sheet

    A statement turns green when what you have written satisfies it and red when it does not. Nothing else is checked for you.

    Name the thief

    Length
    Case — Statements —
    —

    N deals a new case, T goes back to today's, H fills in one square.

    How the case is put together

    1. 01

      Deal the building

      A setting is drawn from six — a shut-up country house, a hotel out of season, a night sleeper, a museum after closing, a theatre after the curtain, a polar station in the dark — and it supplies the rooms, the people, their trades, what is lying on each floor and what has been taken. Each of those is shuffled independently across the rooms, and that arrangement is the answer. Nobody sees it.

    2. 02

      Write down everything true

      Several hundred true statements about that arrangement are then generated: who shares a room with what, who is next door to whom, who is west of whom by exactly two doors, who is at the end of the corridor, who is definitely not in the Still Room. All of them are true. Almost none of them are needed.

    3. 03

      Cut it down to one answer

      Statements are added one at a time until a solver can find only one arrangement that fits them, and then removed one at a time for as long as one arrangement is still all that fits. What is left is a minimal set: take away any single statement and the case goes ambiguous. Six to eleven statements at the short end, fifteen to twenty-four at the long one.

    The solver

    Every room in the line is a position, and every name, trade, object and clock face is a variable whose value is one of those positions. Each variable keeps a bitmask of the positions it could still occupy. A statement narrows a variable by asking, for each position left in its mask, whether any combination of the other variables' remaining positions would make that statement true; positions with no such support are struck out. On top of that, a value pinned to one room takes that room away from every other value in its column, and a room only one value can still occupy is handed to it. That runs to a fixed point; where it stalls, the search picks the variable with the fewest positions left and tries each of them, and it counts solutions rather than stopping at the first.

    Counting rather than stopping is the whole point. A puzzle with two answers is not a puzzle, and the only way to know a case has exactly one is to go looking for a second and come back empty-handed. The count above the sheet says one solution, proved because that search has already been run — on your machine, in the moment the page loaded, on the case in front of you rather than on a sample of others. Dealing one costs about a millisecond at the short end and about ten at the long one, which is why you did not notice it happening.

    The same date integer that draws the flow field on the front page deals this case, and it is doing seventeen other jobs besides — it grows the Garden, writes the Chimes, deals the Lattice, files the Almanac, scatters the Observatory, raises the Atlas, breeds the Menagerie, lights the Orrery, invents the Codex, runs the Chronicle, builds the Folly, cuts the gears of the Engine, threads the Loom, opens the Exchange, invents the rules of the Gambit and locks the doors of the Warren. Nothing here is saved between visits. Tomorrow the building is somewhere else and none of these people exist.