Locked Lines

Suppose two suspects, between them, can only stand in rows 3 and 6. You do not know which one takes which row. You do not need to. Two people, two rows, and every row holds exactly one person: those two rows are full. Nobody else can be in row 3 or row 6, and every tile in those rows is struck out for every other suspect and the victim.

This is the most common move in harder Murdoku cases, and in the casebook it appears in more than half of all cases. Sudoku players will recognise it as a naked pair, triple, and so on. The principle extends to any size: if some group of k people can only reach k lines between them, those lines are theirs.

Finding Pairs

Start with pairs; they are by far the most frequent. Look for two suspects whose possible tiles all sit in the same two rows, or the same two columns. They do not need to share tiles, or rooms, or anything else — only the lines. A suspect confined to a bedroom along the east wall and another confined to a bathroom beside it may well span only the same two columns, and that is enough.

Clues that tie two people together are a rich source. “Directly north of Bella” means the two of them occupy a column each, but if Bella is already confined, the person north of her often ends up confined to the same narrow band. Relational clues and locked lines feed each other constantly.

Rows and Columns Are Separate Questions

A pair can lock its rows without locking its columns, and the reverse. Check both. The solver reports them as different steps for a reason: a group that fills two columns frees nothing in the rows, and a group that fills three rows says nothing about where in those rows they stand.

Larger groups are harder to see but follow the same rule. If three suspects between them reach only columns 1, 2 and 4, the rest of the board loses those three columns. Groups of four or more turn up on the biggest boards, usually late in the case when most people are already confined to small areas.

A Common Mistake

The group must be closed: every possible tile of every member has to lie in the named lines. One stray tile outside — one suspect who could still, just possibly, be in row 8 — and the group locks nothing. Before you strike out a whole row, make sure each member of the group really has no option elsewhere.

A Worked Example

From the case MicroMacro 1.5 — 5×5, Easy, House & Home.

C1C2C3C4C5
R1Ch+CCCh
R2T+CCTT
R3SCC
R4CCC
R5ChChTT
The floor plan of “MicroMacro 1.5”. 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 6 of the solve, the reasoning reads:

Bella: only row 1 possible – blocked for others.

Cases That Need It

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

Other Techniques

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