Puzzle Pack #2 Puzzle 37 Answer

Daniel’s clue says that Paula is one of Karen’s four innocent neighbors. That directly tells us Paula is innocent. So Paula must be innocent.

Claire and Vera have exactly 1 innocent between them who is also a neighbor of Floyd, and that shared group is just Helen and Logan. Karen’s neighbors must contain exactly 4 innocents, and those neighbors are Floyd, Helen, Logan, Olof, and Paula, with Paula already known to be innocent. So among Karen’s neighbors, Helen and Logan contribute exactly 1 innocent, Paula is the second, and the only remaining unknown neighbors outside that smaller shared group are Floyd and Olof. Those two must provide the other 2 innocents, so Floyd and Olof must be innocent.

Karen’s neighbors must contain exactly four innocents, and among those neighbors Floyd, Olof, and Paula are already innocent. That leaves Helen and Logan as the only two unknown neighbors who can complete Karen’s total of four innocent neighbors. Below Claire, there must be an odd number of criminals, and the only unknown people there are Helen, Logan, and Vera. If Vera were criminal, then Helen and Logan would still have to satisfy Karen’s neighbor clue at the same time, and that combination does not fit both clues together. So Vera cannot be criminal. That makes Vera innocent.

Karen’s clue means her still-unknown neighbors, Helen and Logan, contain exactly 1 innocent. Paula’s clue means the three people above Paula, Claire, Helen, and Logan, contain exactly 2 innocents. Since Helen and Logan already account for exactly 1 of those 2 innocents, the only remaining person in that group, Claire, has to provide the other one. So Claire must be innocent.

Above Ziad, the people are Ethan, Joyce, Nicole, and Thor, and Floyd's clue says that group contains an odd number of criminals. Claire's clue also says Isaac's neighbors contain exactly 6 innocents, with exactly 2 of those innocents being above Ziad, and the above-Ziad neighbors of Isaac are Ethan, Joyce, and Nicole. So the clues fix the innocence count among Ethan, Joyce, and Nicole, while Thor is the only person above Ziad who is not part of that restricted trio. To keep the total above Ziad at an odd number of criminals, Thor must be innocent.

Karen’s clue means her neighbors contain exactly 4 innocents, and three of them are already known: Floyd, Olof, and Paula. So among Karen’s still-unknown neighbors, Helen and Logan, exactly 1 is innocent. Claire’s clue means Isaac’s neighbors who are not above Ziad contain exactly 4 innocents. In that group, Claire and Daniel are already innocent, and Helen and Logan contribute exactly 1 more innocent, so the only still-unknown person left there has to provide the last innocent needed. That person is Mark, so Mark must be innocent.

Mark says exactly 2 of the 10 innocents on the edge are his neighbors, so among edge people who are not Mark's neighbors, exactly 3 must be criminals. In the still-unknown part of that non-neighbor edge group, those 3 criminals have to come from Berat, Karen, Uma, Wanda, and Ziad. Ethan is not one of the people who can fill those criminal spots, so Ethan cannot be criminal. So Ethan must be innocent.

Mark says exactly 2 of the 10 innocent people on the edges are his neighbors. The edge cells already have 7 known innocents, so 3 of the 7 unknown edge people must also be innocent. Among Mark's neighbors on the edge, Thor is already known innocent, and the only other edge neighbors of Mark are Joyce and Nicole. Since exactly 2 innocent edge people are Mark's neighbors, exactly one of Joyce or Nicole must also be innocent. That gives 2 innocent edge neighbors of Mark and 8 innocent edge people who are not Mark's neighbors. The other 2 needed innocent edge people therefore have to come from edge cells outside Mark's neighborhood, so there is no room for Isaac or Sue to be criminals in Mark's neighborhood. So Isaac and Sue must be innocent.

Mark says exactly 2 of the 10 innocents on the edges are his neighbors, so 8 edge innocents are not his neighbors. Among the edge cells, there are already 7 known innocents, and 5 of those known innocents are not Mark's neighbors: Claire, Daniel, Ethan, Floyd, and Vera. That means the remaining 3 edge innocents who are not Mark's neighbors must come from the unknown edge cells that are not Mark's neighbors, namely Berat, Karen, Uma, Wanda, and Ziad. This leaves Karen as innocent.

Karen’s clue says there are exactly 4 innocents among Karen’s neighbors, and those neighbors are Floyd, Helen, Logan, Olof, and Paula. Floyd, Olof, and Paula are already known innocents, so Helen and Logan must provide the last one innocent among those two. Ethan’s clue says Daniel has more innocent neighbors than Olof, and right now each of them already has 3 known innocents among their neighbors. With Helen and Logan being the only relevant unknowns tied into those counts here, the one that can raise Daniel’s innocent-neighbor total is Helen, while Logan cannot also be innocent because Karen’s neighbor clue allows only one of Helen and Logan to be innocent. So Helen must be innocent and Logan must be criminal.

Daniel’s neighbors already have 4 known innocents, while Olof’s neighbors already have 3 known innocents. The only unknown in Daniel’s neighbor group is Joyce, and the only unknown in Olof’s neighbor group is Uma. Since Daniel must have more innocent neighbors than Olof, Uma cannot be innocent. So Uma must be criminal.

In column C, Daniel, Isaac, Mark, and Sue are all already innocent, so Wanda is the only unknown person left in that column. That leaves Wanda as criminal.

Joyce’s neighbors already include four known innocents, while Floyd’s neighbors include three known innocents. The clue says Joyce has more innocent neighbors than Floyd. The only unknown in Joyce’s neighbor group is Nicole, and the only unknown in Floyd’s neighbor group is Berat, so for Joyce’s total to stay higher, Nicole has to be innocent. So Nicole must be innocent.

Floyd’s clue says the people above Ziad contain an odd number of criminals. In that group, there are currently 0 known criminals, and the only unknown person there is Joyce. Since Joyce is the only person left who can change that count from 0 to an odd number, Joyce must be criminal.

Logan’s clue says that only one person in column C has no criminal neighbors. In column C, every person is already identified: Daniel, Isaac, Mark, and Sue are innocent, and Wanda is criminal. The only way for that clue to be true with those fixed identities is for Ziad not to be a criminal neighbor creating an extra zero-neighbor case in column C. So Ziad must be innocent.

Mark’s clue says the edge cells contain exactly 10 innocents in total, and exactly 2 of those innocents are his neighbors. In the edge cells that are Mark’s neighbors, the two innocents are already D3 Nicole and D4 Thor, so the other edge cells must contain the remaining 8 innocents. That remaining edge group already has 8 known innocents: B1 Claire, C1 Daniel, D1 Ethan, A2 Floyd, A3 Karen, A4 Olof, B5 Vera, and D5 Ziad. Since A1 Berat is the only unknown left in that group, Berat cannot be innocent. So Berat must be criminal.