Hints for today's case (#55)

The thief was Franco.

1. Deduction 1 · Ana

   With everything else crossed out, Ana is left with ONE cell: F3 (Ballroom). That's where they go. Check it: their card says they are beside a statue and are in a corner of their room, and this cell satisfies it.

   • Let's take Ana. Their card says they are beside a statue and are in a corner of their room. On the whole board, that can only happen in these 2 cells (marked).
   • Carla can only be in row 1 (their clues leave no other), so that row is theirs and Ana can't use it: 1 cell fewer.
   • With everything else crossed out, Ana is left with ONE cell: F3 (Ballroom). That's where they go. Check it: their card says they are beside a statue and are in a corner of their room, and this cell satisfies it.

2. Deduction 2 · Diego

   With everything else crossed out, Diego is left with ONE cell: E2 (Ballroom). That's where they go. Check it: their card says they are beside a statue, and this cell satisfies it.

   • Let's take Diego. Their card says they are beside a statue. On the whole board, that can only happen in these 5 cells (marked).
   • Carla can only be in row 1 (their clues leave no other), so that row is theirs and Diego can't use it: 2 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3). For Diego, all those cells are crossed out: 2 fewer.
   • With everything else crossed out, Diego is left with ONE cell: E2 (Ballroom). That's where they go. Check it: their card says they are beside a statue, and this cell satisfies it.

3. Deduction 3 · Hugo

   With everything else crossed out, Hugo is left with ONE cell: D8 (Study). That's where they go. Check it: their card says they are beside a bookshelf and are not in the Ballroom, and this cell satisfies it.

   • Let's take Hugo. Their card says they are beside a bookshelf and are not in the Ballroom. On the whole board, that can only happen in these 8 cells (marked).
   • Look at Bruno: their card says they are in the Library — that limits them to these 16 cells (purple).
   • The cards pin Carla in row 1 — those lines are theirs (one person per row and column). 4 cells are crossed out for Bruno.
   • Ana is already at F3, so column F is theirs — and each column holds ONE person only. Bruno can no longer go there: 2 cells fewer. Bruno is left in these 10 cells (purple).
   • A card says Hugo is on the same diagonal as Bruno. None of Bruno's 10 possible cells (marked) satisfies the relation with these cells of Hugo: they are crossed out (2 fewer).
   • Franco can only be in column B (their clues leave no other), so that column is theirs and Hugo can't use it: 1 cell fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3). For Hugo, all those cells are crossed out: 2 fewer.
   • Each row holds ONE person, so someone has to end up in row 8. Of those still to place, Hugo is the ONLY one who can still enter there (the clues rule out the rest): that's why Hugo must go in that row.
   • And if Hugo is sure to be in row 8, all their cells OUTSIDE that row are crossed out: 2 cells fewer.
   • With everything else crossed out, Hugo is left with ONE cell: D8 (Study). That's where they go. Check it: their card says they are beside a bookshelf and are not in the Ballroom, and this cell satisfies it.

4. Deduction 4 · Elena

   With everything else crossed out, Elena is left with ONE cell: C6 (Study). That's where they go.

   • 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.
   • Look at Carla: their card says they are in the first row — that limits them to these 8 cells (purple).
   • The cards pin Irene in column I — those lines are theirs (one person per row and column). 1 cells are crossed out for Carla.
   • Ana is already at F3, so column F is theirs — and each column holds ONE person only. Carla can no longer go there: 1 cell fewer.
   • Diego is already at E2, so column E is theirs — and each column holds ONE person only. Carla can no longer go there: 1 cell fewer.
   • Hugo is already at D8, so column D is theirs — and each column holds ONE person only. Carla can no longer go there: 1 cell fewer. Carla is left in A1, C1, G1 and H1 (purple).
   • A card says Elena is on the same diagonal as Carla. Try each option: with Carla at A1, C1, G1 and H1, these cells of Elena satisfy the relation with none of them: they are crossed out (21 fewer).
   • Look at Gabriela: their card says they are beside a chair — that limits them to these 6 cells (purple). Gabriela is left in these 6 cells (purple).
   • A card says Elena is in the same room as Gabriela. None of Gabriela's 6 possible cells (marked) satisfies the relation with these cells of Elena: they are crossed out (15 fewer).
   • Carla can only be in row 1 (their clues leave no other), so that row is theirs and Elena can't use it: 8 cells fewer.
   • Irene can only be in column I (their clues leave no other), so that column is theirs and Elena can't use it: 7 cells fewer.
   • Franco can only be in column B (their clues leave no other), so that column is theirs and Elena can't use it: 3 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3), Diego (E2) and Hugo (D8). For Elena, all those cells are crossed out: 8 fewer.
   • Each row holds ONE person, so someone has to end up in row 6. Of those still to place, Elena is the ONLY one who can still enter there (the clues rule out the rest): that's why Elena must go in that row.
   • And if Elena is sure to be in row 6, all their cells OUTSIDE that row are crossed out: 3 cells fewer.
   • With everything else crossed out, Elena is left with ONE cell: C6 (Study). That's where they go.

5. Deduction 5 · Carla

   With everything else crossed out, Carla is left with ONE cell: H1 (Library). That's where they go. Check it: their card says they are in the first row, and this cell satisfies it.

   • Let's take Carla. Their card says they are in the first row. On the whole board, that can only happen in these 8 cells (marked).
   • A card says Carla is on the same diagonal as Elena, and Elena is already at C6 (Study). The marked cells do not satisfy that relation with that position: they are crossed out (2 cells fewer).
   • Irene can only be in column I (their clues leave no other), so that column is theirs and Carla can't use it: 1 cell fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3), Diego (E2), Hugo (D8) and Elena (C6). For Carla, all those cells are crossed out: 4 fewer.
   • With everything else crossed out, Carla is left with ONE cell: H1 (Library). That's where they go. Check it: their card says they are in the first row, and this cell satisfies it.

6. Deduction 6 · Bruno

   With everything else crossed out, Bruno is left with ONE cell: G5 (Library). That's where they go. Check it: their card says they are in the Library, and this cell satisfies it.

   • Let's take Bruno. Their card says they are in the Library. On the whole board, that can only happen in these 16 cells (marked).
   • Continuing with Hugo: they were down to 8 cells (as we saw) — there's more to cross out.
   • Ana is already at F3, so row 3 is theirs — and each row holds ONE person only. Hugo can no longer go there: 1 cell fewer.
   • Ana is already at F3, so column F is theirs — and each column holds ONE person only. Hugo can no longer go there: 1 cell fewer.
   • Look at Franco: their card says they are beside a plant — that limits them to these 3 cells (purple).
   • Ana is already at F3, so row 3 is theirs — and each row holds ONE person only. Franco can no longer go there: 1 cell fewer. Franco is left in B4 and B9 (purple).
   • Franco can only be in column B (their clues leave no other), so that column is theirs and Hugo can't use it: 1 cell fewer. Hugo is left in these 5 cells (purple).
   • A card says Bruno is on the same diagonal as Hugo. None of Hugo's 5 possible cells (marked) satisfies the relation with these cells of Bruno: they are crossed out (4 fewer).
   • Carla can only be in row 1 (their clues leave no other), so that row is theirs and Bruno can't use it: 4 cells fewer.
   • Irene can only be in column I (their clues leave no other), so that column is theirs and Bruno can't use it: 3 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3) and Carla (H1). For Bruno, all those cells are crossed out: 4 fewer.
   • With everything else crossed out, Bruno is left with ONE cell: G5 (Library). That's where they go. Check it: their card says they are in the Library, and this cell satisfies it.

7. Deduction 7 · Gabriela

   With everything else crossed out, Gabriela is left with ONE cell: A7 (Study). That's where they go. Check it: their card says they are beside a chair, and this cell satisfies it.

   • Let's take Gabriela. Their card says they are beside a chair. On the whole board, that can only happen in these 6 cells (marked).
   • A card says Gabriela is in the same room as Elena, and Elena is already at C6 (Study). So Gabriela can only be in the Study: everything else is crossed out (2 cells fewer).
   • Irene can only be in column I (their clues leave no other), so that column is theirs and Gabriela can't use it: 1 cell fewer.
   • Franco can only be in column B (their clues leave no other), so that column is theirs and Gabriela can't use it: 1 cell fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Hugo (D8). For Gabriela, all those cells are crossed out: 1 fewer.
   • With everything else crossed out, Gabriela is left with ONE cell: A7 (Study). That's where they go. Check it: their card says they are beside a chair, and this cell satisfies it.

8. Deduction 8 · Irene

   With everything else crossed out, Irene is left with ONE cell: I4 (Library). That's where they go. Check it: their card says they are in the last column, and this cell satisfies it.

   • Let's take Irene. Their card says they are in the last column. On the whole board, that can only happen in these 8 cells (marked).
   • Irene's card requires sharing a room with someone who has a hat — in that room none of those with a hat could fit: 5 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Ana (F3) and Bruno (G5). For Irene, all those cells are crossed out: 2 fewer.
   • With everything else crossed out, Irene is left with ONE cell: I4 (Library). That's where they go. Check it: their card says they are in the last column, and this cell satisfies it.

9. Deduction 9 · Franco

   Row 9 and column B cross at a single cell: B9 (Garden). That's where Franco goes.

   • Franco is the last one left. Each row and each column holds ONE person, and the only ones still free are row 9 and column B.
   • Franco has to be in row 9 and, at the same time, in column B. Only one cell meets both: the rest is crossed out (12 fewer).
   • Row 9 and column B cross at a single cell: B9 (Garden). That's where Franco goes.