Hints for today's case (#10)

The thief was Diego.

1. Deduction 1 · Bruno

   With everything else crossed out, Bruno is left with ONE cell: C2 (Ballroom). That's where they go. Check it: their card says they are on a rug, and this cell satisfies it.

   • Let's take Bruno. Their card says they are on a rug. On the whole board, that can only happen in these 2 cells (marked).
   • Bruno's card requires someone with a hat diagonally adjacent — here no suspect with a hat could touch that cell: 1 cell fewer.
   • With everything else crossed out, Bruno is left with ONE cell: C2 (Ballroom). That's where they go. Check it: their card says they are on a rug, and this cell satisfies it.

2. Deduction 2 · Carla

   With everything else crossed out, Carla is left with ONE cell: D3 (Garden). That's where they go.

   • Let's take Carla. Their card doesn't mark a fixed area, so we start with every free cell and cross them out one by one.
   • Look at Diego: their card says they are not in the Library — that limits them to these 39 cells (purple). Diego is left in these 39 cells (purple).
   • A card says Carla is north of Diego. None of Diego's 39 possible cells (marked) satisfies the relation with these cells of Carla: they are crossed out (8 fewer).
   • Look at Franco: their card says they are on a bench — that limits them to these 5 cells (purple). Franco is left in these 5 cells (purple).
   • A card says Carla is in the same room as Franco. None of Franco's 5 possible cells (marked) satisfies the relation with these cells of Carla: they are crossed out (24 fewer).
   • Bruno's card requires someone with a hat diagonally adjacent, and Carla is the ONLY one with a hat who still reaches those diagonals: they are forced there and their outside cells are crossed out (5 cells fewer).
   • Ana can only be in row 1 (their clues leave no other), so that row is theirs and Carla can't use it: 6 cells fewer.
   • Bruno can only be in row 2 (their clues leave no other), so that row is theirs and Carla can't use it: 5 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (C2). For Carla, all those cells are crossed out: 4 fewer.
   • With everything else crossed out, Carla is left with ONE cell: D3 (Garden). That's where they go.

3. Deduction 3 · Franco

   With everything else crossed out, Franco is left with ONE cell: B6 (Garden). That's where they go. Check it: their card says they are on a bench, and this cell satisfies it.

   • Let's take Franco. Their card says they are on a bench. On the whole board, that can only happen in these 5 cells (marked).
   • Elena can only be in column A (their clues leave no other), so that column is theirs and Franco can't use it: 1 cell fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (C2) and Carla (D3). For Franco, all those cells are crossed out: 3 fewer.
   • With everything else crossed out, Franco is left with ONE cell: B6 (Garden). That's where they go. Check it: their card says they are on a bench, and this cell satisfies it.

4. Deduction 4 · Hugo

   With everything else crossed out, Hugo is left with ONE cell: H8 (Library). That's where they go. Check it: their card says they are in the last row and are in the last column, and this cell satisfies it.

   • Let's take Hugo. Their card says they are in the last row and are in the last column. On the whole board, that can only happen in ONE cell (marked).
   • With everything else crossed out, Hugo is left with ONE cell: H8 (Library). That's where they go. Check it: their card says they are in the last row and are in the last column, and this cell satisfies it.

5. Deduction 5 · Ana

   With everything else crossed out, Ana is left with ONE cell: G1 (Conservatory). That's where they go. Check it: their card says they are in the first row and are in a corner of their room, and this cell satisfies it.

   • Let's take Ana. Their card says they are in the first row and are in a corner of their room. On the whole board, that can only happen in these 2 cells (marked).
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Hugo (H8). For Ana, all those cells are crossed out: 1 fewer.
   • With everything else crossed out, Ana is left with ONE cell: G1 (Conservatory). That's where they go. Check it: their card says they are in the first row and are in a corner of their room, and this cell satisfies it.

6. Deduction 6 · Elena

   With everything else crossed out, Elena is left with ONE cell: A5 (Garden). That's where they go. Check it: their card says they are in a corner of their room, and this cell satisfies it.

   • Let's take Elena. Their card doesn't mark a fixed area, so we start with every free cell and cross them out one by one.
   • As we already saw, Franco can only be in these 5 cells (purple).
   • A card says Elena is in the same room as Franco. None of Franco's 5 possible cells (marked) satisfies the relation with these cells of Elena: they are crossed out (13 fewer).
   • Ana can only be in row 1 (their clues leave no other), so that row is theirs and Elena can't use it: 2 cells fewer.
   • Bruno can only be in row 2 (their clues leave no other), so that row is theirs and Elena can't use it: 1 cell fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (C2), Carla (D3) and Hugo (H8). For Elena, all those cells are crossed out: 5 fewer.
   • With everything else crossed out, Elena is left with ONE cell: A5 (Garden). That's where they go. Check it: their card says they are in a corner of their room, and this cell satisfies it.

7. Deduction 7 · Diego

   With everything else crossed out, Diego is left with ONE cell: F4 (Conservatory). That's where they go. Check it: their card says they are not in the Library, and this cell satisfies it.

   • Let's take Diego. Their card doesn't mark a fixed area, so we start with every free cell and cross them out one by one.
   • Continuing with Carla: they were down to 53 cells (as we saw) — there's more to cross out.
   • The cards pin Ana in row 1 and Bruno in row 2 — those lines are theirs (one person per row and column). 11 cells are crossed out for Carla. Carla is left in these 42 cells (purple).
   • A card says Diego is south of Carla. None of Carla's 42 possible cells (marked) satisfies the relation with these cells of Diego: they are crossed out (7 fewer).
   • Ana can only be in row 1 (their clues leave no other), so that row is theirs and Diego can't use it: 6 cells fewer.
   • Bruno can only be in row 2 (their clues leave no other), so that row is theirs and Diego can't use it: 5 cells fewer.
   • Elena can only be in column A (their clues leave no other), so that column is theirs and Diego can't use it: 4 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (C2), Carla (D3), Franco (B6), Hugo (H8), Ana (G1) and Elena (A5). For Diego, all those cells are crossed out: 16 fewer.
   • With everything else crossed out, Diego is left with ONE cell: F4 (Conservatory). That's where they go. Check it: their card says they are not in the Library, and this cell satisfies it.

8. Deduction 8 · Gabriela

   Row 7 and column E cross at a single cell: E7 (Library). That's where Gabriela goes.

   • Gabriela is the last one left. Each row and each column holds ONE person, and the only ones still free are row 7 and column E.
   • Gabriela has to be in row 7 and, at the same time, in column E. Only one cell meets both: the rest is crossed out (10 fewer).
   • Row 7 and column E cross at a single cell: E7 (Library). That's where Gabriela goes.