Puzzle Pack #1 Puzzle 46 Answer

Row 2 contains A2, B2, C2, and D2, and the clue says the two criminals in that row are both neighbors of Mark at C3. Mark’s neighbors in row 2 are only B2, C2, and D2, because A2 is too far from C3 to be a neighbor, even diagonally. So the two criminals in row 2 must be among B2, C2, and D2, which leaves A2 outside that pair. Therefore, we can determine that A2 is INNOCENT.

Mark is at C3, so his neighbors in row 2 are B2 Helen, C2 Isaac, and D2 John. Xavi says both criminals in row 2 are Mark's neighbors, which means row 2 has exactly two criminals and they must be among Helen, Isaac, and John; since Gus at A2 is already innocent, the only innocent in row 2 besides Gus must be one of those three. Gus also says there is an odd number of innocents to the right of Helen, and the people to Helen’s right are Isaac at C2 and John at D2, so among those two there must be exactly one innocent. That uses up the one innocent available among Helen, Isaac, and John, so Helen cannot be innocent. Therefore, we can determine that B2 is CRIMINAL.

David is at C1, and his neighbors are Bruce at B1, Flora at D1, Helen at B2, Isaac at C2, and John at D2. Helen says Flora is one of David's 3 criminal neighbors, which directly tells us that Flora is among those three criminals around David. Therefore, we can determine that D1 is CRIMINAL.

David is at C1, so his neighbors are Bruce at B1, Helen at B2, Isaac at C2, and Flora at D1. Helen says Flora is one of David's 3 criminal neighbors, and we already know Helen and Flora are criminals, so David's criminal neighbors are exactly Helen, Flora, and one of Bruce or Isaac. Xavi says both criminals in row 2 are Mark's neighbors; since Helen at B2 is one criminal in row 2, the other criminal in row 2 must also neighbor Mark at C3, so it cannot be Gus at A2 or John at D2 and must be Isaac at C2. That makes Isaac the third criminal neighbor of David, leaving Bruce as the only non-criminal among David's neighbors. Therefore, we can determine that B1 is INNOCENT.

Mark is at C3, and the two criminals in row 2 must therefore be among his neighbors. Mark’s neighbors are B2, C2, D2, B3, D3, B4, C4, and D4, so the row 2 neighbors of Mark are only B2, C2, and D2. Since Helen at B2 is already a criminal, Xavi’s clue forces exactly one of C2 Isaac or D2 John to be the other criminal in row 2, which means A2 Gus is not a criminal and fits the row as already known innocent. Karen is at A3, so the row 4 people neighboring her are only A4 Paula and B4 Rose. Bruce says exactly one innocent in row 4 is neighboring Karen, so among Paula and Rose, exactly one is innocent. Flora at D1 has neighbors C1 David, C2 Isaac, and D2 John. Because Flora is criminal, the number of her innocent neighbors depends only on David, Isaac, and John, while Vicky at A5 has neighbors A4 Paula, B4 Rose, and B5 Will. Since Vicky has more innocent neighbors than Flora, and among Paula and Rose exactly one is innocent, Vicky’s side already has one innocent there and needs Will to be innocent to be strictly higher. That same comparison leaves David unable to be innocent on Flora’s side, so David must be criminal. Therefore, we can determine that B5 is INNOCENT and C1 is CRIMINAL.

Mark is at C3, so his neighbors in row 2 are B2, C2, and D2. Xavi says both criminals in row 2 are Mark's neighbors, and since Helen at B2 is already a criminal, the other row 2 criminal must be either Isaac at C2 or John at D2, which means Gus at A2 is not the second one. Karen is at A3, and her neighbors in row 4 are only A4 and B4. Bruce says exactly one innocent in row 4 is neighboring Karen, so among Paula at A4 and Rose at B4, exactly one is innocent. Flora at D1 already has two criminal neighbors, David at C1 and Helen at B2. David says Flora and Karen have the same number of criminal neighbors, so Karen must also have exactly two criminal neighbors. Karen's neighbors are Gus at A2, Helen at B2, Lisa at B3, Paula at A4, and Rose at B4; Gus is innocent and Helen is criminal, and exactly one of Paula and Rose is innocent, so among Paula and Rose there is exactly one criminal. That gives Karen one criminal from Helen and one criminal from Paula or Rose, so Lisa cannot also be criminal. Therefore, we can determine that B3 is INNOCENT.

Lisa is at B3, so her neighbors are A2, B2, C2, A3, C3, A4, B4, and C4. Her clue says that both criminals in row 4 are her neighbors, so every criminal in row 4 must be among A4, B4, and C4. D4 is in row 4 but is not Lisa's neighbor, so D4 cannot be one of those two criminals. Therefore, we can determine that D4 is INNOCENT.

Row 4 is Paula at A4, Rose at B4, Susan at C4, and Tom at D4. Lisa at B3 says both criminals in row 4 are her neighbors, so the two criminals in that row must be among A4, B4, and C4, since those are Lisa’s row 4 neighbors and D4 is not. Bruce’s clue says exactly one innocent in row 4 is neighboring Karen at A3; the row 4 people neighboring Karen are only A4 and B4, so exactly one of A4 and B4 is innocent, which means the other is criminal. That already gives one criminal in A4/B4, and Lisa’s clue says there are two criminals total in row 4, both next to her, so the second criminal must be C4. Therefore, we can determine that C4 is CRIMINAL.

Karen is at A3, so the people in row 4 who neighbor her are only Paula at A4 and Rose at B4. Bruce’s clue says exactly one innocent in row 4 is neighboring Karen, so among A4 and B4, exactly one is innocent. The teachers are Karen at A3, Lisa at B3, and Isaac at C2. Tom’s clue says exactly one teacher has an innocent directly below them. Lisa does, because Will at B5 is not directly below her but Rose at B4 is, and Isaac does not, because Mark at C3 is directly below him and is not known innocent; Karen has Paula at A4 directly below her. Since Lisa is already the one teacher with an innocent directly below, Karen cannot also have an innocent directly below, so Paula is not innocent. That makes Rose the one innocent in row 4 neighboring Karen. Since Rose at B4 is innocent, Isaac cannot be the teacher with an innocent directly below, so Mark at C3 is not innocent. Therefore, we can determine that C3 is CRIMINAL.

Flora is at D1, so her only neighbors are C1, C2, and D2. Since C1 is criminal, Flora cannot have more than two innocent neighbors there, and in fact she already has at least one criminal neighbor. Vicky is at A5, and her neighbors are A4, B4, and B5. B5 is innocent, so for Vicky to have more innocent neighbors than Flora, Vicky would need at least two innocent neighbors among those three spots. Mark’s clue compares the number of criminal neighbors around Will at B5 and David at C1. David’s neighbors are B1, B2, C2, D1, and D2, and we already know B2 and D1 are criminal, so David has 2 criminal neighbors plus any criminals among C2 and D2. Will’s neighbors are A4, A5, B4, C4, and C5, and we already know C4 is criminal and C5 is innocent, so to match David’s count, both A4 and B4 cannot be innocent together. That means Vicky cannot have two innocent neighbors there, so Flora’s statement can only be true if Vicky herself is criminal rather than an extra innocent neighbor. Therefore, we can determine that A5 is CRIMINAL.

In row 5, we already know that Vicky at A5 is criminal, while Will at B5 and Xavi at C5 are innocent. That means the row currently has 2 innocents and 1 criminal among the known people, with Zara at D5 still unknown. Will’s clue says there are more innocents than criminals in row 5, so Zara cannot be criminal, because then row 5 would have 2 innocents and 2 criminals. Therefore, we can determine that D5 is INNOCENT.

Karen is at A3, so the people in row 4 who neighbor her are only Paula at A4 and Rose at B4. Bruce says exactly one innocent in row 4 is neighboring Karen, so among Paula and Rose, exactly one is innocent. Tom is at D4 and already has innocent neighbors at D5 and C5, while his other neighbors are C3, C4, and D3. Zara says Karen and Tom have an equal number of innocent neighbors. Karen already has innocent neighbors at A2, B3, and Gus at A2? No, specifically Karen’s neighbors are A2, B2, B3, A4, and B4, and among those A2 and B3 are innocent while exactly one of A4 and B4 is innocent, giving Karen exactly 3 innocent neighbors. So Tom must also have exactly 3 innocent neighbors. Since D5 and C5 are already innocent and C3 and C4 are criminal, the only way for Tom to reach 3 innocent neighbors is for D3, Olive, to be innocent. Therefore, we can determine that D3 is INNOCENT.

Karen is one of Helen’s neighbors, and she is also one of Xavi’s neighbors. Helen’s neighbors are A1, B1, C1, A2, C2, A3, B3, and C3, while Xavi’s neighbors are B4, C4, D4, B5, and D5. Among those, Helen already has four known innocent neighbors: Gus, Bruce, Lisa, and Karen if A3 is innocent, while Xavi already has four known innocent neighbors: Tom, Will, and Zara, plus Rose if B4 were innocent. Olive’s clue says Helen has more innocent neighbors than Xavi, so Karen cannot be criminal here, because then Helen would not exceed Xavi’s innocent-neighbor total. Therefore, we can determine that A3 is INNOCENT.

Karen says there are 12 innocents in total. On the board, 11 people are already known to be innocent, so exactly one of the four unknown people must be innocent. David says Flora and Karen have an equal number of criminal neighbors. Flora at D1 has criminal neighbors C1 and C2, plus John at D2 if he were criminal, while Karen at A3 has only one possible criminal neighbor left, Adam at A1 being too far away and her other neighbors already fixed. Since Flora already has at least two criminal neighbors and Karen has only one, the only way their counts can match is if neither Isaac at C2 nor John at D2 adds extra criminals for Flora, and Karen’s count stays at two from Helen at B2 and Mark at C3. That means C2 and D2 are both innocent. With C2 and D2 innocent, the single remaining unknown innocent required by Karen’s total cannot be one of them anymore, so it must be Adam at A1. Therefore, we can determine that A1 is INNOCENT.

Karen is at A3, so the people in row 4 who neighbor her are only A4 and B4. Bruce says exactly one innocent in row 4 is neighboring Karen, so exactly one of Paula at A4 and Rose at B4 is innocent. Lisa is at B3, and her neighbors are A2, B2, C2, A3, C3, A4, B4, and C4. Among these, Karen at A3 is innocent, Helen at B2, Mark at C3, and Susan at C4 are criminal, so the unknown neighbors affecting Adam’s clue are Gus at A2, Isaac at C2, Paula at A4, and Rose at B4. Gus is innocent, and Bruce’s clue tells us exactly one of Paula and Rose is innocent, so Adam’s clue that Lisa has an odd number of innocent neighbors means Isaac cannot also be innocent, because that would make the total even. Therefore, we can determine that C2, Isaac, is CRIMINAL.

Mark is at C3, so his neighbors are B2, C2, D2, B3, D3, B4, C4, and D4. The clue says that both criminals in row 2 are Mark's neighbors, and row 2 contains Gus at A2, Helen at B2, Isaac at C2, and John at D2. Among those four, the only people in Mark's neighborhood are Helen, Isaac, and John, so the two criminals in row 2 must be among those three. Since Helen and Isaac are already known to be the two criminals in row 2, John cannot be one of them. Therefore, we can determine that D2 is INNOCENT.

Flora is at D1, so her neighbors are C1, C2, and D2, and only D2 is innocent. That means Flora has 1 innocent neighbor. Vicky is at A5, whose neighbors are A4, B4, and B5; since B5 is innocent, Flora’s clue says Vicky must have more than 1 innocent neighbor, so at least one of A4 or B4 must also be innocent. Isaac’s clue says coders are the profession with the unique highest number of criminals, and the coders are Mark, Rose, and Susan, with Mark and Susan already criminal, so Rose cannot also be criminal or coders would have 3 criminals, more than builders and judges can ever reach but also more than needed to keep this clue consistent with the already known profession counts; thus B4 is innocent. Then Vicky’s neighbors A4, B4, and B5 include two innocents already, so A4 must be innocent as well for Flora’s statement to hold. Therefore, we can determine that A4 is INNOCENT.

Karen is at A3, so the people in row 4 who neighbor her are only A4 and B4. Bruce’s clue says exactly one innocent in row 4 is neighboring Karen. Since A4, Paula, is already known to be innocent, that one innocent neighbor is accounted for. So B4, Rose, cannot also be innocent. Therefore, we can determine that B4 is CRIMINAL.