Puzzle Pack #1 Puzzle 44 Answer

Helen is at C2, so her neighbors are B1, C1, D1, B2, D2, B3, C3, and D3. In column B, the possible criminals are Ben at B1, Gabe at B2, Keith at B3, and Olive at B4, because Vince at B5 is innocent. Among those four, the ones who are Helen’s neighbors are B1, B2, and B3, while B4 is not. Since the clue says there are exactly 3 criminals in column B and exactly 2 of those 3 are Helen’s neighbors, the third criminal in column B must be the only one there who is not Helen’s neighbor: Olive at B4. Therefore, we can determine that B4 is CRIMINAL.

Vince is at B5, so his neighbors are A4, A5, B4, C4, and C5. Olive says that the two criminals in row 4 are both among Vince’s neighbors. In row 4, Olive herself at B4 is already a criminal, so the other criminal in that row must also be one of Vince’s row-4 neighbors, which can only be A4 or C4. Steve at D4 is not Vince’s neighbor, so he cannot be that second criminal in row 4. Therefore, we can determine that D4 is INNOCENT.

Ben and Vince are in the same column, with Gabe at B2, Keith at B3, and Olive at B4 between them. Steve says there is an odd number of innocents among those people in between. Since Olive at B4 is already known to be a criminal, the only way for the number of innocents between Ben and Vince to be odd is for exactly one of Gabe and Keith to be innocent, so exactly one of them is criminal. Vince also says column B has exactly 3 criminals, and exactly 2 of those 3 are neighbors of Helen at C2. In column B, the people are Ben, Gabe, Keith, Olive, and Vince, and Helen's neighbors there are Ben at B1, Gabe at B2, and Keith at B3, while Olive at B4 and Vince at B5 are not Helen's neighbors. Since Olive is already a criminal, the third criminal in column B besides Olive and the one criminal among Gabe and Keith must be Ben, and that gives exactly 2 criminal neighbors of Helen in column B. Therefore, we can determine that B1 is CRIMINAL.

Joyce is at A3, so her three neighbors are Flora at A2, Gabe at B2, and Nicole at A4. Tom is at A5, and among those three, only Nicole at A4 is also Tom’s neighbor; Flora and Gabe are too far away to neighbor Tom. Ben says exactly 2 of Joyce’s 3 criminal neighbors also neighbor Tom, so the criminals among Joyce’s neighbors must be exactly the ones who also neighbor Tom. That forces Nicole to be criminal. Therefore, we can determine that A4 is CRIMINAL.