Puzzle Pack #1 Puzzle 50 Answer

Erwin’s clue says Isaac is one of two or more criminals below Erwin. The people below Erwin are Isaac, Nancy, and Terry, so this clue is talking about criminals in that group and explicitly includes Isaac among them. Since Isaac is named as one of those criminals, Isaac must be criminal.

Erwin says Isaac is one of two or more criminals below him, so among the people strictly between Erwin and Terry there cannot be only the one known criminal, Isaac. In that between-group, Isaac is already criminal and the only other person there is Nancy. So Nancy must be criminal.

Between Vince and Zach, there are exactly 2 criminals in total. Of those, exactly 1 is a neighbor of Xavi, so exactly 1 must be between Vince and Zach without being a neighbor of Xavi. In that between-group, the only person who is not a neighbor of Xavi is Xavi, and there are no known criminals there already. So Xavi has to fill that required criminal spot. So Xavi must be criminal.

Xavi says he is one of exactly 2 criminals in row 5, so row 5 contains Xavi and just one other criminal. Nancy’s clue says there are 2 criminals to the right of Terry. The people strictly between Terry and Zach are Vince and Xavi, and among them Xavi is already a known criminal, so for there to be 2 criminals to Terry’s right, Vince must be the other one. That uses up the one other criminal in row 5 besides Xavi, so Terry must be innocent.

Terry’s clue says Xavi has exactly 3 criminal neighbors, and only 1 of those 3 is Zach’s neighbor. Among Zach’s neighbors, Xavi is already the 1 known criminal, so the other two people there, Paula and Sofia, cannot be criminals from that counted group. That leaves the other part of Xavi’s neighborhood, which is Olive and Vince and Zach, to supply the remaining 2 criminal neighbors. Since Nancy’s clue says there are 2 criminals to the right of Terry, and the only person strictly between Vince and Zach is Xavi, that counted pair is already fixed by Xavi together with one of Vince or Zach. So within Xavi’s neighbors, the remaining criminal needed besides that one must be Olive. So Olive must be criminal.

Nancy’s clue says there are 2 criminals to the right of Terry, and exactly 1 of those is Xavi’s neighbor. The only person strictly between Vince and Zach is Xavi, and that group is already known to contain exactly 1 criminal, namely Xavi, so the other criminal to the right of Terry must be Zach. Among the people to the right of Terry who are Xavi’s neighbors, Vince and Zach are the only candidates, and since exactly 1 of the 2 criminals to the right of Terry is Xavi’s neighbor, Zach fills that one criminal spot and Vince cannot be criminal. So Vince must be innocent, and Zach must be criminal.

Olive’s clue says Sofia and Terry have the same number of innocent neighbors. Terry’s neighbors already contain exactly 1 innocent, and there are no unknowns there, so Sofia’s neighbors must also contain exactly 1 innocent. Among Sofia’s neighbors, Xavi and Zach are already known criminals, so the single innocent neighbor has to come from Lisa, Maria, or Paula. Terry’s clue also fixes Xavi’s neighborhood at exactly 3 criminals, with exactly 1 of those criminals being Zach’s neighbor; since Olive and Zach are already two criminal neighbors of Xavi, that leaves exactly one of Paula or Sofia as the third criminal, so Paula cannot be the only possible innocent around Sofia. That makes Lisa a criminal.

Olive says Sofia and Terry have the same number of innocent neighbors. Terry’s neighbors already contain exactly one innocent, Vince, and there are no unknowns there, so Sofia’s neighbors must also contain exactly one innocent. In Sofia’s neighbors, the only possible unknowns are Maria and Paula, since Lisa, Xavi, and Zach are already criminals. Vince says Lisa and Paula share an odd number of innocent neighbors. Their shared neighbors are Jason, Maria, Olive, and Sofia, and Olive is already a criminal, so the number of innocents among Jason, Maria, and Sofia must be odd. Since Sofia’s neighbors need exactly one innocent and that one must be Maria or Paula, Sofia cannot be the innocent one here, which leaves Jason and Maria contributing the odd count together. That makes Jason innocent.

Lisa says Gary and Lisa share an odd number of innocent neighbors. Their common neighbors are B2 Freya, D2 Henry, B3 Jason, and D3 Maria, and Jason is already known innocent, so they already share 1 innocent neighbor there. Lisa also says she has exactly 4 innocent neighbors. Among Lisa's neighbors, Olive is criminal, and Terry's clue fixes Xavi's neighboring criminals so Paula and Sofia cannot both be innocent; that keeps Lisa's total from reaching 4 unless the non-Xavi-neighboring unknowns supply the needed innocents. With Jason already the 1 shared innocent in Lisa and Gary's overlap, making Gary innocent would upset Lisa's odd shared-innocent count with Gary. So Gary must be criminal.

Lisa has exactly 4 innocent neighbors, and among her neighbors there is already 1 known innocent. That means the 5 still-unknown neighbors of Lisa must contain exactly 2 criminals. In that group, the only people who can still be those 2 criminals are Henry, Maria, Paula, and Sofia, so Freya cannot be one of them. So Freya must be innocent.

Olive’s clue says Sofia’s neighbors and Terry’s neighbors have the same number of innocents, but Terry’s neighbors already contain 1 innocent while Sofia’s neighbors currently contain 0. Gary’s clue says Vince’s neighbors and Gary’s neighbors have the same number of criminals, but Vince’s neighbors already contain 3 criminals while Gary’s neighbors currently contain only 1. Freya’s clue says Carl’s neighbors contain an odd number of innocents, and Carl’s neighbors currently have 1 known innocent, with Barb, Donna, and Henry still unknown. If Carl were criminal, then Barb, Donna, Henry, Maria, and Paula would have to make all three of those requirements true at the same time, but they cannot. So Carl cannot be criminal. That makes Carl innocent.

Carl’s clue says Carl’s neighbors contain an odd number of innocents. Right now that neighbor group already has 1 known innocent, and the only unknown people left in that group are Barb, Donna, and Henry. Carl also says Vince and Carl have the same number of innocent neighbors. Vince’s neighbor group already has 1 known innocent, Carl’s neighbor group already has 1 known innocent, and the only unknown person left in Vince’s group is Paula. So these two clues together settle all four unknown people they still touch: none of Barb, Donna, Henry, or Paula can be innocent. That makes Barb, Donna, Henry, and Paula criminals.

In column D, Donna, Henry, and Zach are already known criminals, so the only unknown people there are Maria and Sofia. Zach’s clue says the two innocents in column D are connected. That means the only two places those innocents can be are D3 Maria and D4 Sofia, and those two are connected to each other. So Maria and Sofia must be innocent.

Donna’s clue says Nancy and Barb must have the same number of innocent neighbors. Nancy’s neighbors already have 3 innocents, and Barb’s neighbors also already have 3 innocents. The only unknown person still involved here is Alice among Barb’s neighbors, so she cannot be innocent without giving Barb more innocent neighbors than Nancy. So Alice must be criminal.