Hints for today's case (#106)

The thief was Ana.

1. Deduction 1 · Bruno

   With everything else crossed out, Bruno is left with ONE cell: H2 (Garden). That's where they go. Check it: their card says they are in the last column, and this cell satisfies it.

   • Let's take Bruno. Their card says they are in the last column. On the whole board, that can only happen in these 5 cells (marked).
   • Look at Diego: their card says they are in a corner of their room and are in the Ballroom — that limits them to these 5 cells (purple). Diego is left in these 5 cells (purple).
   • A card says Bruno is south of Diego. None of Diego's 5 possible cells (marked) satisfies the relation with these cells of Bruno: they are crossed out (1 fewer).
   • Look at Hugo: their card says they are beside a plant and are on grass — that limits them to these 6 cells (purple). Hugo is left in these 6 cells (purple).
   • A card says Bruno is north of Hugo. None of Hugo's 6 possible cells (marked) satisfies the relation with these cells of Bruno: they are crossed out (3 fewer).
   • With everything else crossed out, Bruno is left with ONE cell: H2 (Garden). That's where they go. Check it: their card says they are in the last column, and this cell satisfies it.

2. Deduction 2 · Diego

   With everything else crossed out, Diego is left with ONE cell: D1 (Ballroom). That's where they go. Check it: their card says they are in a corner of their room and are in the Ballroom, and this cell satisfies it.

   • Let's take Diego. Their card says they are in a corner of their room and are in the Ballroom. On the whole board, that can only happen in these 5 cells (marked).
   • Continuing with Bruno: they were down to 5 cells (as we saw) — there's more to cross out.
   • As we already saw, Hugo can only be in these 6 cells (purple).
   • A card says Bruno is north of Hugo. The furthest down Hugo can be is row 3 → Bruno has to be further up: 3 cells fewer (red). Bruno is left in H1 and H2 (purple).
   • A card says Diego is north of Bruno. Try each option: with Bruno at H1 and H2, these cells of Diego satisfy the relation with none of them: they are crossed out (2 fewer).
   • Elena can only be in column A (their clues leave no other), so that column is theirs and Diego can't use it: 2 cells fewer.
   • With everything else crossed out, Diego is left with ONE cell: D1 (Ballroom). That's where they go. Check it: their card says they are in a corner of their room and are in the Ballroom, and this cell satisfies it.

3. Deduction 3 · Franco

   With everything else crossed out, Franco is left with ONE cell: C8 (Library). That's where they go. Check it: their card says they are beside a sofa and are beside a bookshelf, and this cell satisfies it.

   • Let's take Franco. Their card says they are beside a sofa and are beside a bookshelf. 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: Diego (D1). For Franco, all those cells are crossed out: 1 fewer.
   • With everything else crossed out, Franco is left with ONE cell: C8 (Library). That's where they go. Check it: their card says they are beside a sofa and are beside a bookshelf, and this cell satisfies it.

4. Deduction 4 · Gabriela

   With everything else crossed out, Gabriela is left with ONE cell: B5 (Ballroom). That's where they go. Check it: their card says they are in a corner of their room and are in the Ballroom, and this cell satisfies it.

   • Let's take Gabriela. Their card says they are in a corner of their room and are in the Ballroom. 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 Gabriela can't use it: 2 cells fewer.
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (H2) and Diego (D1). For Gabriela, all those cells are crossed out: 2 fewer.
   • With everything else crossed out, Gabriela is left with ONE cell: B5 (Ballroom). That's where they go. Check it: their card says they are in a corner of their room and are in the Ballroom, and this cell satisfies it.

5. Deduction 5 · Carla

   With everything else crossed out, Carla is left with ONE cell: F7 (Library). That's where they go. Check it: their card says they are beside a bookshelf, and this cell satisfies it.

   • Let's take Carla. Their card says they are beside a bookshelf. On the whole board, that can only happen in these 7 cells (marked).
   • Elena can only be in column A (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: Diego (D1), Franco (C8) and Gabriela (B5). For Carla, all those cells are crossed out: 5 fewer.
   • With everything else crossed out, Carla is left with ONE cell: F7 (Library). That's where they go. Check it: their card says they are beside a bookshelf, and this cell satisfies it.

6. Deduction 6 · Elena

   With everything else crossed out, Elena is left with ONE cell: A6 (Library). That's where they go. Check it: their card says they are in the first column and are not in the Ballroom, and this cell satisfies it.

   • Let's take Elena. Their card says they are in the first column and are not in the Ballroom. On the whole board, that can only happen in these 4 cells (marked).
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Franco (C8), Gabriela (B5) and Carla (F7). For Elena, all those cells are crossed out: 3 fewer.
   • With everything else crossed out, Elena is left with ONE cell: A6 (Library). That's where they go. Check it: their card says they are in the first column and are not in the Ballroom, and this cell satisfies it.

7. Deduction 7 · Ana

   With everything else crossed out, Ana is left with ONE cell: E4 (Conservatory). That's where they go. Check it: their card says they are beside a bench, and this cell satisfies it.

   • Let's take Ana. Their card says they are beside a bench. On the whole board, that can only happen in these 7 cells (marked).
   • Each row and each column holds ONE person only, and the ones already placed own theirs: Bruno (H2), Diego (D1), Franco (C8) and Elena (A6). For Ana, all those cells are crossed out: 6 fewer.
   • With everything else crossed out, Ana is left with ONE cell: E4 (Conservatory). That's where they go. Check it: their card says they are beside a bench, and this cell satisfies it.

8. Deduction 8 · Hugo

   Row 3 and column G cross at a single cell: G3 (Garden). That's where Hugo goes.

   • Hugo is the last one left. Each row and each column holds ONE person, and the only ones still free are row 3 and column G.
   • Hugo has to be in row 3 and, at the same time, in column G. Only one cell meets both: the rest is crossed out (11 fewer).
   • Row 3 and column G cross at a single cell: G3 (Garden). That's where Hugo goes.