Puzzle Pack #1 Puzzle 37 Answer

Sofia’s clue says that Wally is one of Ronald’s 6 criminal neighbors. That directly identifies Wally as a criminal. So Wally must be criminal.

Sofia’s clue says Ronald has exactly 6 criminal neighbors. Among Ronald’s neighbors, Wally is already a known criminal and Sofia is already a known innocent, so the 6 still-unknown neighbors contain exactly 1 innocent person. In that unknown-neighbor group, the only people who can still be that one innocent are Kevin, Larry, Mary, Vicky, and Xia. That means Paul cannot be the innocent person there, so Paul must be criminal.

Sofia’s clue says Ronald has exactly 6 criminal neighbors. Among Ronald’s five still-unknown neighbors, that means exactly 1 of them is innocent: Kevin, Larry, Mary, Vicky, and Xia. But the only people in that group who can still be that one innocent are Kevin, Mary, Vicky, and Xia, so Larry cannot be the innocent one there. So Larry must be criminal.

Ronald’s neighbors must contain exactly 6 criminals, and among the four still-unknown neighbors of Ronald that means there is exactly 1 innocent: Kevin, Mary, Vicky, and Xia. From these clues, the only people in that group who can still be that one innocent are Vicky and Xia. So Kevin and Mary cannot be the innocent one in Ronald’s unknown-neighbor group. Therefore Kevin and Mary must be criminals.

Mary’s clue says Bonnie’s neighbors contain exactly one innocent. In Bonnie’s neighbor group, the only people who can still be that one innocent are Amy, Cheryl, Hank, and Isaac. Gus is not among those possible innocents, so Gus cannot be innocent. So Gus must be criminal.

Bonnie’s clue says her neighbors contain exactly one innocent, and among her still-unknown neighbors those four people are Amy, Cheryl, Hank, and Isaac. From the current board and these clues, the only ones in that group who can still be that one innocent are Amy, Cheryl, or Isaac. So Hank cannot be the innocent one there. That makes Hank criminal.

Mary’s clue says Bonnie’s neighbors contain exactly one innocent. Among Bonnie’s still-unknown neighbors, that means exactly one of Amy, Cheryl, and Isaac is innocent. But in that group, the only people who can still be that innocent are Amy and Cheryl. So Isaac cannot be the innocent one in Bonnie’s neighbor group. That makes Isaac criminal.

Kevin’s clue says Amy has more criminal neighbors than Xia. Right now Amy’s neighbors already have 2 known criminals, while Xia’s neighbors have 1 known criminal, and Zoe is one of Xia’s unknown neighbors. Isaac’s clue says rows 4 and 5 have the same number of criminals. Right now each of those rows already has 1 known criminal, and Zoe is also one of the unknown people in row 5. If Zoe were a criminal, then Bonnie, Ronald, Tyler, Vicky, and Xia would have to make both of those clues true at the same time, and that cannot be done. So Zoe cannot be a criminal. That makes Zoe innocent.

Amy’s clue says Amy has more criminal neighbors than Xia. Right now Amy already has 2 known criminal neighbors, while Xia has 1, and Bonnie is the only unknown neighbor around Amy. If Bonnie were innocent, Amy would stay at 2 criminal neighbors, so Ronald and Tyler in Xia’s neighborhood, together with Vicky and Xia in rows 4 and 5, would have to satisfy Amy’s comparison, Ronald’s 6 criminal neighbors, and the rule that rows 4 and 5 have equal numbers of criminals all at once. That cannot be done. So Bonnie cannot be innocent. That makes Bonnie criminal.

Bonnie’s neighbors must contain exactly one innocent, and right now the only unknown people there are Amy and Cheryl. Sofia’s neighbors must have more criminals than Bonnie’s neighbors, even though each side already has 3 known criminals. Also, among the edge neighbors of Sofia, exactly 3 are innocent, and in that group Zoe is already innocent while Wally is already criminal, so Nick, Tyler, and Xia are the people that still have to fit that count. If Ronald were innocent, then Amy, Cheryl, Nick, Tyler, and Xia would have to satisfy all of those requirements at the same time, and they cannot. So Ronald cannot be innocent. That makes Ronald criminal.

Amy’s neighbors already contain 3 criminals, while Xia’s neighbors currently contain 2. Kevin’s clue says Amy has more criminal neighbors than Xia, and the only unknown person left among the people this comparison can still affect is Tyler in Xia’s neighbors. So Tyler cannot be a criminal, because that would raise Xia’s total to 3 and no longer leave Amy with more. That makes Tyler innocent.

Sofia’s edge neighbors are D3 Nick, D4 Tyler, B5 Wally, C5 Xia, and D5 Zoe, and exactly 3 of that group are innocent. Tyler and Zoe are already innocent there, so among Nick and Xia only one of them can be innocent. The cooks must contain more criminals than the guards. Right now the cooks have 1 known criminal, and the guards have 0, with Joyce the only unknown cook and Nick and Xia the unknown guards. If Joyce were innocent, the cooks would stay at 1 criminal, while the guard clue and the neighbor clue would have to be satisfied by Nick and Xia alone, and that cannot be done. So Joyce cannot be innocent. That makes Joyce criminal.

Bonnie’s clue fixes exactly 1 innocent among her still-unknown neighbors, and those are Amy and Cheryl. Joyce’s clue says row 1 has exactly 2 innocents total, and the unknown people in that row are Amy, Cheryl, and Flora. Since Amy and Cheryl account for exactly 1 innocent, the only remaining unknown in row 1, Flora, has to provide the second one. So Flora must be innocent.

Column C has exactly 3 innocents in total. In that column, Isaac and Mary are already criminals and Sofia is already innocent, so the only people left who can fill the remaining two innocent spots are Cheryl and Xia. That also fits Flora's clue that exactly 1 of the 3 innocents in column C is Sofia's neighbor, because among Cheryl and Xia, only Xia is in Sofia's neighbor group. So Cheryl and Xia must be innocent.

Sofia’s clue says Wally is one of the exactly 6 criminals among Ronald’s neighbors. Ronald’s neighbors are Kevin, Larry, Mary, Paul, Sofia, Vicky, Wally, and Xia, and among them the only person still unknown is Vicky. Since this clue fixes the last still-unknown person involved here, Vicky must be criminal.

Mary’s clue says Bonnie’s neighbors contain exactly one innocent person. Among Bonnie’s neighbors, there is already one known innocent there, and the only unknown neighbor left is Amy. Since that one innocent is already accounted for, Amy cannot be innocent. So Amy must be criminal.

Bonnie says Sofia has more criminal neighbors than she does. Right now both neighbor groups already have 4 known criminals, and the only unknown person involved in this comparison is Nick among Sofia's neighbors. For Sofia's total to be more than Bonnie's, Nick has to be a criminal. So Nick must be criminal.