Clues That Tie People Together

Most clues tell you something about one person and the board — a room, an object, a wall. Relational clues tell you about two people at once: “north of Dana”, “exactly one column west of Bella”, “in the same room as Hugh”, “not in a room next to Floyd’s”. On their own they say nothing about where anyone is. That is what makes them hard, and why hard cases lean on them.

The way to read them is in both directions. A clue that says Anna was north of Dana restricts Anna — she cannot be on the bottom row, and she cannot be anywhere Dana could not be beneath — but it restricts Dana just as much: Dana cannot be on the top row, and cannot be anywhere that has none of Anna’s possible tiles above it. Every time either list shrinks, the other one may shrink with it.

Directions and Distances

Compass clues compare rows and columns. “North of” means a higher row, in any column — not directly above. “Northeast of” combines two such conditions, higher and further right. Because two people never share a row or a column, every compass clue between people is strict: north always means at least one row up.

Offset clues are far tighter: “exactly one column west of Bella” fixes the column relationship completely, so each tile Bella might stand on allows only a single column for the other person. When one of the two is confined to a short strip, an offset clue usually confines the other to a strip just as short.

Some compass clues point at a kind of person rather than a named one — “north of a woman with glasses”. Those are read the same way, against everyone who matches the description.

Rooms Between People

Room clues between people work the same way, one level up. “In the same room as Hugh” means each of them can only be in rooms the other can reach. “In a room adjoining Floyd’s” removes every room that touches none of Floyd’s possible rooms. A negative — “not in the same room as Dana” — becomes powerful the moment Dana’s room is certain, because it then empties that room for the other person entirely. And “one of them was indoors, the other outside” splits the pair across the line between the house and the open air.

Keep Coming Back

A relational clue is never finished with on the first read. The solver applies the same clue again and again as the board changes, each time removing a few more tiles, because every cut to one person’s list can cut the other’s. Make a habit of re-reading relational clues after every placement or confinement of either person they name.

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 5 of the solve, the reasoning reads:

Dittbert is south of Caroline – impossible cells removed.

Cases That Need It

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

Other Techniques

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