Solution: The Empty Vase at the Grand Hotel

The clues

• 
  Walter · VictimThe estate’s groundskeeper.

  The victim. He was alone with the killer.

• 
  QuentinThe butler of forty years.

• 
  OscarThe antiques dealer.

  He was beside a bed. He was in the fourth column from the left.

• 
  KarimThe family lawyer.

  He was in the Spa with another man. He was on an armchair.

• 
  TheoThe paperboy.

  He was beside a bed.

• 
  RafaelThe bicycle courier.

  He was not in the Lobby.

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 Oscar, by his testimony or by a row or column already taken. Placed: Oscar: row 1, column 4 (Bar); Karim: row 6, column 3 (Spa).
2. Room counting The victim, Walter, cannot be in the highlighted cells: his room there could not hold exactly one other person. The cells meant: row 3, column 1; row 4, column 2; row 5, column 6.
3. Follow it to a contradiction If Theo were in the highlighted cell, Quentin would have no cell left. So he is not there. The cells meant: row 5, column 2.
4. Follow it to a contradiction If Theo were in the highlighted cell, Karim would have no cell left. So he is not there. The cells meant: row 5, column 5. Placed: Theo: row 3, column 2 (Roof Terrace).
5. Room counting The victim, Walter, cannot be in the highlighted cells: his room there could not hold exactly one other person. The cells meant: row 2, column 5; row 2, column 6.
6. Follow it to a contradiction If Walter were in the highlighted cell, Karim would have no cell left. So he is not there. The cells meant: row 2, column 1.
7. Follow it to a contradiction If Walter were in the highlighted cell, Karim would have no cell left. So he is not there. The cells meant: row 5, column 5.
8. Follow it to a contradiction If Rafael were in the highlighted cell, a room count would come out wrong. So he is not there. The cells meant: row 2, column 1.
9. The only one who fits Only Quentin can still reach the second row, so he must be there.
10. Follow it to a contradiction If Walter were in the highlighted cell, a room count would come out wrong. So he is not there. The cells meant: row 4, column 6. Placed: Walter: row 5, column 1 (Spa); Rafael: row 4, column 6 (Ballroom); Quentin: row 2, column 5 (Lobby).