Puzzle Pack #2 Puzzle 31 Answer

Jason’s clue says Rose is one of exactly three innocents to the right of Olivia. The people to the right of Olivia are only Paula, Rose, and Terry. If Terry, Paula, and Rose were all criminals, then those same three people could not also be the exactly three innocents to the right of Olivia. So Terry, Paula, and Rose must be innocent.

Barnie and Flora are the two neighbors of Alex that also make up the exact-count group from Isaac's clue, and that group contains exactly 1 innocent. So among Alex's neighbors, Barnie and Flora already contribute an odd number of innocents. Alex's neighbors are Barnie, Ellie, and Flora, and that total must also be odd, with Ellie the only one not in that exact-count pair. If Ellie were innocent too, the number of innocents among Alex's neighbors would become even instead of odd. So Ellie must be criminal.

Ellie’s clue directly says that there are more criminals among mechs than in any other profession. In this step, that identifies Kay as a criminal.

Kay’s clue says the two innocents below Chad must be connected. Rose is already known to be one of those innocents below Chad, so the second innocent has to be orthogonally next to Rose in that column. That means the other innocent can only be Mary or Xavi. Isaac is below Chad but not next to Rose in that line, so he cannot be the other innocent in the connected pair. So Isaac must be criminal.

Terry’s clue says Isaac has exactly 6 innocent neighbors, and exactly 1 of those innocent neighbors is a mech. Among Isaac’s neighbors, Jason is already known innocent, and the only neighboring mechs are Barnie and Flora. Ellie’s clue is also in play about mechs having more criminals than any other profession. Putting those restrictions together fixes Chad as innocent. So Chad must be innocent.

Among Isaac’s neighboring unknowns who are not mechs, there is exactly 1 criminal in the group Donald, Logan, Mary, and Nicole. But in that group, the only people who can still be that criminal are Logan, Mary, or Nicole. So Donald cannot be the criminal member of that group. That makes Donald innocent.

Paula’s clue says every column has at least 2 innocents, and Isaac’s clue says the four corners contain exactly 2 innocents. Right now the corners already include 1 known innocent, Donald, and the other corner spaces are Alex, Vera, and Zara. If Zara were innocent while Olivia were criminal, then the remaining open people in columns A through D would have to satisfy both of those clues together, but they cannot. That combination makes the column minimums and the exact corner total clash. So Zara must be criminal, and Olivia must be innocent.

Isaac’s neighborhood has exactly 6 innocents, and exactly 1 of those innocent neighbors is a mech. The only mech neighbors there are Barnie and Flora, so among Barnie and Flora, exactly one must be innocent. At the same time, mechs must have more criminals than every other profession. The mechs currently have only 1 known criminal, Kay, and their only undecided members are Barnie and Flora. If Vera were criminal, the remaining open people named here would have to make both of those requirements true together, but they cannot. So Vera cannot be criminal. That makes Vera innocent.

Isaac's clue says the corner cells contain exactly 2 innocents. The corners already include 2 known innocents, and the only corner person still unknown is Alex. Since all 2 innocent spots in the corners are already used up, Alex cannot be innocent. So Alex must be criminal.

Among the still-unknown neighbors of Isaac who are not mechs, the group is Logan, Mary, and Nicole, and that group contains exactly 1 criminal. But in that group, the only people who can still be that criminal are Logan and Mary. So Nicole cannot be the criminal there, and Nicole must be innocent.

Ellie’s clue says the mechs have more criminals than any other profession. The mechs are Barnie, Flora, and Kay, and Kay is already a known criminal while there are no known innocent mechs. With Terry’s clue still leaving Isaac’s neighboring mechs unresolved, this step fixes the off-neighbor farmer slot instead. That makes Will innocent.

Isaac’s clue fixes his neighborhood at exactly 6 innocents, with exactly 1 of those innocent neighbors being a mech, so the open people B1 Barnie, B2 Flora, B3 Logan, and C3 Mary are already tightly constrained by that count. Nicole’s clue says Paula has more criminal neighbors than Chad, but right now each of them has 1 known criminal neighbor. If Xavi were innocent, then Barnie, Flora, Logan, and Mary would have to make both clues true at the same time, and that cannot be done. So Xavi must be criminal.

Kay’s clue says there are exactly two innocents below Chad, and those two must be connected. Below Chad are Isaac, Mary, Rose, and Xavi, and among them Isaac and Xavi are already criminal while Rose is already innocent. That leaves Mary as the only person who can be the second innocent below Chad alongside Rose. So Mary must be innocent.

Isaac’s neighbors contain exactly 6 innocents in total, and exactly 1 of those innocents is a mech. The non-mech neighbors in that group are Chad, Donald, Jason, Logan, Mary, and Nicole, and among them Chad, Donald, Jason, Mary, and Nicole are already known to be innocent. Since that already accounts for the 5 innocents among the non-mech neighbors, Logan cannot be innocent. So Logan must be criminal.

Mary's clue says there is exactly one innocent person in the group that is both on the edge and a neighbor of Flora. That shared group is Alex, Barnie, Chad, Ellie, and Kay, and it already contains one known innocent: Chad. So Barnie cannot also be innocent. That makes Barnie criminal.

Terry’s clue says Isaac has exactly 6 innocent neighbors, and exactly 1 of those innocent neighbors is a mech. Among Isaac’s neighboring mechs, Barnie is criminal and Flora is the only unknown person there. So the one innocent neighboring mech has to be Flora. That makes Flora innocent.