Only One Fits the Line

The last tile looks at one person and asks where they can go. The hidden single turns the question round and looks at one line: which people can still reach this row? Because every Murdoku board has exactly as many rows as people, every row holds exactly one person, and so does every column. If only one person can still reach a given row, that row belongs to them.

That does not usually place them. They might reach the row on three different tiles. What it does is confine them: every tile they had outside that row is gone. A suspect who could have been anywhere in the house is suddenly restricted to one strip of it, and their list of possibilities shrinks to a handful.

How to Spot It

Hidden singles hide because you are reading the board by person, one suspect at a time, and the pattern only exists across people. The trick is to sweep the lines from time to time instead: for each row, ask who could still be in it. Rows near the edge of the plan, rows that pass mostly through blocked furniture, and rows that cross a room nobody is allowed in are the usual candidates. A row that runs through a kitchen full of tables, say, may have only two open tiles — and if one of those is already ruled out for everyone but one suspect, you have found it.

The victim counts. The victim has a row and a column like everyone else, and a line that only the victim can still reach is a line nobody else may use. The solver states those steps as plainly as any other, and they are among the most useful early in a case.

Why It Matters More Than It Looks

A hidden single is a confinement, and confinements cascade. Once a suspect is held to one row, every other row is free of them — so for every other line on the board, there is one fewer candidate. Lines that had two possible people now have one. That is how a single hidden single on a crowded board can set off three or four more in quick succession.

It is also the bridge to the next technique. A hidden single is the case of one person filling one line. When two people can only reach the same two lines, or three people the same three, the same logic still holds — that is what locked lines are.

A Worked Example

From the case Just a Little Murder — 4×4, Medium, House & Home.

C1C2C3C4
R1BBTT
R2SCCh+C
R3C
R4BB
The floor plan of “Just a Little Murder”. Letters mark objects: B Bed, 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 4 of the solve, the reasoning reads:

In row 1 everything is crossed out except R1/C1, R1/C2 – only the victim (Vidal) can be there, no suspect.

Cases That Need It

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

Other Techniques

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