Counting the Whole Scene

Some clues are not about any individual. “No room was empty.” “Exactly two rooms were empty.” “Exactly one person stood on a mud puddle.” They describe the scene as a whole, and they are listed separately from the suspects’ own clues for that reason. They are counting clues, and every counting clue gives you two deductions, one from each end.

From the Top: The Count Is Already Reached

If the clue says exactly one person stood on a mud puddle, and somebody is already certain to be on one, then nobody else may stand on any puddle. Every puddle tile is struck out for everyone else. The same holds for rooms: if exactly two rooms were empty and all the others are already certainly occupied, those two must stay empty, and nobody may be placed in them.

“The only person on a chair” works the same way for a single suspect’s clue: once anyone is confirmed on a chair, the chairs are closed to everyone else.

From the Bottom: Exactly Enough Candidates Remain

Run the count the other way. If a single puddle-stander is required and just one suspect can still reach any puddle, that suspect is confined to the puddles. If no room may be empty and some room can be reached by only one person, that person must be in that room — otherwise it would stand empty.

This second direction is the more powerful and the easier to miss. “No room was empty” looks like a gentle clue, but on a plan with as many rooms as suspects it means every room gets exactly one suspect, and a remote box room that only one person can reach claims that person outright.

The Victim and Empty Rooms

One detail decides many of these: the victim never opens a room on their own. The victim always shares a room with the murderer, so a room is occupied as soon as one suspect is certain to be in it, and “no empty room” is really a claim about suspects. A room with no possible suspect in it is empty, whatever the victim does.

A Worked Example

From the case Still Waters — 7×7, Hard, Pool & Spa.

C1C2C3C4C5C6C7
R1
R2
R3
R4
R5
R6
R7
The floor plan of “Still Waters”. Letters mark objects: —.

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 18 of the solve, the reasoning reads:

The allowed empty rooms are already fixed (0) – so Paddling Pool must be occupied, and only Cyrus can be there.

Cases That Need It

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

Other Techniques

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