One Free Tile

Look at a row instead of a person. If every tile in it but one is either blocked by furniture or already ruled out for everyone, then someone must stand on that last open tile, because every row holds exactly one person. You may not know who. It does not matter: somebody is there.

And because somebody is there, the column through that tile is taken as well. Nobody else can stand anywhere else in that column. Every other tile in it is crossed out for everyone. This is the forced cell, and it is the mirror image of the hidden single: the hidden single finds the only person for a line, the forced cell finds the only tile.

Where It Appears

Forced cells live where furniture is dense. A row that runs along a wall lined with shelves, a row through a garage full of cars, the edge of a plan where several rooms are off limits to everyone — these are the lines that run out of tiles. Early in a case it is worth scanning each row and column for open tiles: on furniture-heavy boards one or two lines are often down to a single tile before you have read a single clue.

They also appear later, once placements have cleared rows and columns. A line that started with six open tiles can be down to one after two placements cut across it. That is the moment to look, and it is easy to miss because no new clue told you anything.

Reading the Result

The forced cell removes tiles from a column, not from a person, so its effect is spread across everyone. Afterwards, check the suspects whose lists ran through that column. Sometimes one of them is left with a single tile elsewhere; sometimes a column that had two possible people now has none of its own and becomes a hidden single for someone else.

Note what the forced cell does not say: it does not place anyone on the free tile. The tile is occupied, but by whom is still open, and treating it as decided for one specific suspect is a common slip.

A Worked Example

From the case MicroMacro 2.0 — 5×5, Medium, House & Home.

C1C2C3C4C5
R1Ch+CCCh
R2T+CCTT
R3SCC
R4CCC
R5ChChTT
The floor plan of “MicroMacro 2.0”. Letters mark objects: C Carpet, T Table, Ch Chair, S Shelf.

The clues in play:

This step comes before anyone in the case is placed, so reading it does not give the solution away.

At step 8 of the solve, the reasoning reads:

In column 4 only R3/C4 is free – someone must be there, so row 3 is taken: the other cells of that row are crossed out.

Cases That Need It

34 of the 142 cases in the casebook use this technique at least once. A selection, smallest board first:

Other Techniques

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