Roboku
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Case 10: who took the Illuminated Book?
The guard on duty at the library admits, a little embarrassed, that he dozed off for ten minutes. When he woke up, the Illuminated Book, resting in the Vault, was gone. He swears he doesn't snore that loudly. Help the police unmask the thief.
The board
- 1Storage Room
- 2Children's Room
- 3Reception Area
- 4Archive
- 5Office
- 6Restrooms
- 7Reading Room
- 8Vault
- Shelf: no character can stand on its cell, but the stolen item can be there.
- Table: nothing can be on its cell.
- Window: the blue line on a wall.
Suspects and clues
- GGustavo
He's 2 rows away from the Reception Area. - SSandra
She's in the Office. - OOmar
He's in column D. - WWendy
She's in row 1. - AAmara
She's 4 columns away from the Reception Area. - IIlluminated Book (stolen item)
It's next to a wall, and it's not in the Storage Room.
Remember the rules: no two suspects (nor the item) ever share a row or a column, each character is in a different room, and the thief is the only one sharing a room with the stolen item. Unsure? Read how to play and the clue types.
Solution
Try it yourself first: pen and paper are enough. When you want to check, open the reasoned solution.
Show the step-by-step solution
- Gustavo's clue: He's 2 rows away from the Reception Area. It leaves a single cell: B6.
- Sandra's clue: She's in the Office. 3 cells remain possible: C2, C3 and C4.
- Omar's clue: He's in column D. 4 cells remain possible: D3, D4, D5 and D6.
- Wendy's clue: She's in row 1. 2 cells remain possible: A1 and B1.
- Amara's clue: She's 4 columns away from the Reception Area. It leaves a single cell: F2.
- The stolen item's clue: It's next to a wall, and it's not in the Storage Room. 23 cells remain possible.
- Gustavo can only be on B6. No one else can be in row 6 or column B, and no other character can be in the Storage Room.
- B1 has already been ruled out, so Wendy can only be on A1. No one else can be in row 1 or column A, and no other character can be in the Restrooms.
- Amara can only be on F2. No one else can be in row 2 or column F, and no other character can be in the Reading Room.
- There are as many suspects (counting the item) as columns, so each column holds exactly one. Only the Illuminated Book can still reach column E, so that is where it must be.
- Proof by contradiction. Suppose Omar were on D3. Following the rules above, the Illuminated Book would be left with no possible cell. So Omar is not on D3.
- The item must share its room with one character: the thief. No character can be in the Vault any more, so the Illuminated Book isn't there either.
- Every other cell the clue allowed has already been ruled out, so the Illuminated Book can only be on E5. No one else can be in row 5 or column E.
- D3, D5 and D6 have already been ruled out, so Omar can only be on D4. No one else can be in row 4 or column D, and no other character can be in the Archive.
- C2 and C4 have already been ruled out, so Sandra can only be on C3.
Conclusion: Omar is the only person sharing the Archive with the Illuminated Book, which is on E5. He is the thief.