Puzzle Pack #1 Puzzle 44 Answer

Vince’s clue says column B has exactly 3 criminals, and exactly 2 of those criminals are Helen’s neighbors. So in column B, exactly 1 criminal is not a neighbor of Helen. The people in column B who are not neighbors of Helen are Olive and Vince, and Vince is already innocent. That leaves Olive as the one criminal there, so Olive must be criminal.

Olive’s clue says both criminals in row 4 are Vince’s neighbors. The people strictly between Nicole and Steve are Olive and Ruby, and both of them are Vince’s neighbors. Since one of those two is already known to be Olive the criminal, the other row 4 criminal accounted for by the clue must be Ruby, not Steve. So Steve must be innocent.

Column B must contain exactly 3 criminals, and since Olive is already a criminal and Vince is already innocent, the three unknown people in that column contain exactly 1 innocent person. From these clues, the only people in that group who can still be that innocent are Gabe and Keith. So Ben cannot be the innocent person there. That makes Ben criminal.

Joyce’s neighbors contain exactly 3 criminals in total, and exactly 2 of those criminals are also neighbors of Tom. In the overlap between Joyce’s neighbors and Tom’s neighbors, Olive is already a known criminal, and the only other unknown person there is Nicole. So that overlap still needs one more criminal, and Nicole must be that person. That makes Nicole criminal.

Olive’s clue says that both criminals in row 4 are Vince’s neighbors. Among the people strictly between Nicole and Steve, Olive is already a known criminal and Ruby is the only unknown there, and that same pair is exactly the overlap with Vince’s neighbors. Since the two row 4 criminals are already Nicole and Olive, Ruby cannot be one of them. So Ruby must be innocent.

Nicole’s clue says that the two innocents in row 3 are both neighbors of Gabe. Among the people in row 3, the ones who are Gabe’s neighbors are only Joyce, Keith, and Logan. Mark is in row 3 but he is not in that group, so he cannot be one of the two innocents in row 3. So Mark must be criminal.

Joyce’s neighbors must contain exactly 3 criminals. Nicole and Olive are already criminals there, and among the unknown people in column B, exactly 1 of Gabe and Keith is criminal, so that already accounts for the one remaining criminal in Joyce’s neighbor group. The only other unknown person in Joyce’s neighbors outside that smaller group is Flora, so she cannot be criminal. So Flora must be innocent.

Ruby’s clue says Keith has an odd number of innocent neighbors. Keith already has 2 known innocent neighbors, Flora and Ruby, so among Keith’s unknown neighbors there must be an odd number of innocents. Helen is one of those unknown neighbors of Keith, and this step determines that she cannot be one of the innocents needed there. So Helen must be criminal.

Tom’s neighbors already contain exactly 1 innocent, and Flora’s clue says Tom and Isaac have the same number of innocent neighbors. Isaac’s neighbors therefore also need exactly 1 innocent. Among Isaac’s neighbors, Helen and Mark are already criminals, so the only possible innocents there are Cheryl, Donna, and Logan. Helen’s clue says column C has more innocents than any other column, and column C already has 1 known innocent, so column C must gain an additional innocent to be ahead of the other columns. Within Isaac’s neighbors, the column C people are Cheryl and Logan, so the needed innocent for Isaac’s neighbor count has to come from Cheryl or Logan, not from Donna. That makes Donna criminal.

Donna’s clue says Isaac is one of the exactly 9 criminals on the edges. That directly identifies Isaac as a criminal.

Helen says column C has more innocents than any other column, so column C must end up with the unique highest innocent count. In column C, Helen is already a criminal and Ruby is already innocent, so the only unknowns there are Cheryl, Logan, and Xena. That clue requires enough innocents in column C for it to stand above the other columns, and this fixes Xena as innocent. So Xena must be innocent.

Flora’s clue says Tom and Isaac have the same number of innocent neighbors. Tom’s neighbors are already fully known, and among them only Vince is innocent, so Tom has exactly 1 innocent neighbor. Isaac’s neighbors currently have no known innocents, and the only unknowns there are Cheryl and Logan, so to match Tom’s total, exactly one of Cheryl and Logan must be innocent. That means one of Cheryl and Logan is innocent and the other is criminal. So Cheryl must be criminal, and Logan must be innocent.

Olive’s neighbors must contain an odd number of criminals. Among Olive’s neighbors, the only known criminal is Nicole, so the current criminal count there is 1, and the unknown neighbors are Joyce, Keith, and Tom. This step determines Tom from that odd-criminal requirement on Olive’s neighborhood. So Tom must be criminal.

Tom’s clue says Gabe has exactly 5 criminal neighbors, and exactly 2 of those criminal neighbors are above Xena. Among Gabe’s neighbors, the people above Xena are Cheryl, Helen, and Logan, and only Cheryl and Helen are criminals there, so those 2 criminal-above-Xena spots are already fully used. That means the other 3 criminal neighbors of Gabe must all come from Gabe’s neighbors who are not above Xena. In that group, Ben is already a criminal and Flora is already innocent, so the remaining two criminal spots have to be filled by the unknown people there. Anna is one of those unknown people, so Anna must be criminal.

Anna’s clue says Ben has more criminal neighbors than Ruby. Right now Ben’s neighbors have 3 known criminals and Ruby’s neighbors have 2, and among the people relevant to these clues the remaining unknowns are Gabe, Keith, and Zach. Now test the opposite assignment: Keith criminal and Gabe innocent. With Gabe innocent, Ben’s neighbor count stays at 3. With Keith criminal, Ruby’s neighbor count rises to 3, and Zach is the only other unknown left among those clue-related people, so this assignment cannot keep Ben’s total higher than Ruby’s. That opposite assignment clashes with Anna’s clue, so Keith cannot be criminal and Gabe cannot be innocent. So Keith must be innocent and Gabe must be criminal.

Nicole’s clue says both innocents in row 3 are Gabe’s neighbors. The people strictly between Joyce and Mark are Keith and Logan, and both of them are already known to be innocent. Keith and Logan are also both in Gabe’s neighbor set, so they account for the two innocents in row 3 named by the clue. That makes Joyce criminal.

Donna’s clue says Isaac is one of exactly 9 criminals on the edge. In the edge cells, there are already 9 known criminals, and the only edge person still unknown is Zach. Since those 9 edge criminal spots are already fully accounted for, Zach cannot also be a criminal. So Zach must be innocent.