Puzzle Pack #1 Puzzle 39 Answer

Vicky is at B5, so the people above her are Bobby at B1, Gabe at B2, Kay at B3, and Peter at B4. Bobby’s clue says the criminals among those four people form one connected group in that column, so there cannot be a criminal above an innocent above another criminal. Since Bobby at B1 is already known to be innocent, any criminals above Vicky must start below him and stay consecutive. That forces Kay at B3 to be criminal here. Therefore, we can determine that B3 is CRIMINAL.

Vicky is in B5, so the people above her in column B are Bobby at B1, Gabe at B2, Kay at B3, and Peter at B4. Bobby says that both criminals above Vicky are connected, so among those four people there are exactly two criminals, and they must form one orthogonally connected group. Kay adds that column B contains an odd number of criminals in total. Since Kay herself at B3 is already a criminal, the four people above Vicky already include one criminal there, and they cannot contain exactly two connected criminals without making the whole column have an even total unless Vicky is also a criminal. Therefore, we can determine that B5 is CRIMINAL.

Lucy at C3 has exactly two innocent neighbors, and among those two, only one is also a neighbor of Kay at B3. The neighbors of Lucy are B2, C2, D2, B3, D3, B4, C4, and D4, while Kay’s neighbors among them are B2, C2, B4, and C4. So Lucy’s two innocent neighbors must be split with one from {B2, C2, B4, C4} and one from {D2, D3, D4}. Bobby says both criminals above Vicky are connected, so the criminals in column B above B5 must form one continuous block. Since B3 is already criminal and B1 is innocent, B2 and B4 cannot both be criminals, which means at least one of B2 or B4 is innocent. That gives Lucy an innocent neighbor from Kay’s side among {B2, B4}, so her other innocent neighbor must come from {D2, D3, D4}. Therefore C2 and C4 cannot be innocent, because if either of them were innocent they would add extra innocent neighbors of Lucy that are also Kay’s neighbors, breaking Vicky’s clue. Therefore, we can determine that C2 is CRIMINAL and C4 is CRIMINAL.

Jane is at A3, so her neighbors are A2, B2, B3, A4, and B4. Hal says Nancy at A4 is one of Jane's 3 criminal neighbors, which means Nancy is among those neighbors and is criminal. Therefore, we can determine that A4 is CRIMINAL.