Solution: The Whisper During the Heatwave at the Grand Hotel

The clues

• 
  JonasThe shy librarian.

  He was not beside a bed. He was alone in the room.

• 
  PaulaThe opera singer between engagements.

  She was in the Cloakroom.

• 
  DarioThe jazz musician.

• 
  GretaThe gardener who talks to her roses.

  She was on a chair.

• 
  Mateo · VictimThe waiter who hears everything.

  The victim. He was alone with the killer. He was in the Restaurant.

• 
  ZoeThe tattoo artist.

  She was in the second row. She was on a sofa.

• 
  VeraThe widow who sets the crosswords.

  She was on a sofa.

Step by step

The order our solver finds. Each step uses only the clues and what the steps before it proved, and its heading links to the technique.

1. Last cell left Every other cell is ruled out for Zoe, by her testimony or by a row or column already taken. Placed: Zoe: row 2, column 6 (Corridor).
2. Room counting The victim, Mateo, cannot be in the highlighted cells: his room there could not hold exactly one other person. The cells meant: row 5, column 4.
3. Room counting Jonas cannot be in the highlighted cells: he would not be alone there. The cells meant: row 1, column 1; row 1, column 2; row 1, column 4; row 1, column 5; row 3, column 1; row 3, column 2; row 3, column 4; row 4, column 4; row 5, column 4; row 5, column 5.
4. Shared rows and columns Paula, Greta, Mateo and Vera can only be in the left column, the second column from the left, the fourth column from the left and the fifth column from the left between them, so nobody else can be in those columns.
5. Room counting The victim, Mateo, cannot be in the highlighted cells: his room there could not hold exactly one other person. The cells meant: row 1, column 4; row 3, column 4; row 4, column 4. Placed: Mateo: row 5, column 5 (Restaurant).
6. The only one who fits Only Greta can still reach the fourth column from the left, so she must be there. Placed: Greta: row 1, column 4 (Restaurant).
7. Pinned suspects Paula can only be in the third row, so nobody else can be there. Placed: Vera: row 4, column 1 (Roof Terrace); Paula: row 3, column 2 (Cloakroom).
8. Pinned suspects Jonas can only be in the right column, so nobody else can be there.
9. Room counting Jonas cannot be in the highlighted cells: he would not be alone there. The cells meant: row 7, column 7. Placed: Jonas: row 6, column 7 (Spa); Dario: row 7, column 3 (Reading Room).