Puzzle Pack #2 Puzzle 42 Answer

Xia's clue says that Hal has exactly 7 innocent neighbors, and exactly 2 of those innocents are also neighbors of Mark. The only people in Hal's neighbor list who also neighbor Mark are Isaac and Larry. Since that shared group still needs 2 innocent people, Isaac and Larry have to be those 2 innocents. So Larry and Isaac must be innocent.

Larry’s clue says that the two criminals in column D must be connected. In column D, Isaac is already innocent, and the relevant unknowns here are Emily, Mark, Tom, and Zoe. If Tom were innocent while Emily were criminal, then Mark and Zoe would be the only other people left to supply the second criminal in column D. But with Isaac innocent, that does not allow the two criminals in column D to be connected, so that combination cannot happen. So Tom must be criminal and Emily must be innocent.

Tom’s clue says exactly 2 innocents are both above Tom and neighboring Larry. In that shared group, the only person already identified is Isaac, who is innocent, and there are no unknown people left in that shared group. Since the clue requires 2 innocents there, the only remaining person in that above-and-neighboring set is Mark. So Mark must be innocent.

Larry’s clue says the two criminals in column D must be connected. In column D, Emily, Isaac, and Mark are already innocent, and Tom is already a criminal, so the only remaining unknown person there is Zoe. For there to be both criminals in column D, connected as the clue says, Zoe has to be the second criminal with Tom. So Zoe must be a criminal.

Mark’s clue says Gabe has exactly 7 innocent neighbors, and Larry is already one of those innocent neighbors. That means among Gabe’s seven still-unknown neighbors, there is exactly 1 criminal. In that group, the only people who can still be that one criminal are Anna, Bobby, Debra, Floyd, Julie, and Katie, so Hal is excluded from being the criminal there. So Hal must be innocent.

Hal’s neighbors must contain exactly 7 innocents, and among Hal’s four still-unknown neighbors there is therefore exactly 1 criminal: Bobby, Debra, Gabe, and Katie. But in that group, the only people who can still be that criminal are Bobby, Gabe, and Katie. So Debra cannot be the criminal there. That makes Debra innocent.

Mark’s clue says Gabe has exactly 7 innocent neighbors, so among Gabe’s five still-unknown neighbors there is exactly 1 criminal. In that group, the only people who can still be that one criminal are Anna, Bobby, Julie, and Katie. Since Floyd is not one of those possible criminals, Floyd must be innocent.

Hal’s neighbors already include 5 known innocents, and Xia’s clue says Hal has exactly 7 innocent neighbors, so among the three unknown neighbors of Hal, exactly 1 is criminal. Those three unknown neighbors are Bobby, Gabe, and Katie. From the current board and these clues, the only ones in that group who can still be that one criminal are Bobby and Gabe, so Katie cannot be the criminal there. So Katie must be innocent.

Mark says Gabe has exactly 7 innocent neighbors. Gabe already has 5 known innocent neighbors, so among his three still-unknown neighbors, A1 Anna, B1 Bobby, and A3 Julie, exactly 1 must be criminal. In that group, the only people who can still be that one criminal are B1 Bobby and A3 Julie, so Anna cannot be the criminal there. So Anna must be innocent.

Larry’s clue says his neighbors contain an odd number of criminals. He already has 1 known criminal neighbor, so among the unknown neighbors Gabe, Paula, and Ronald, there must be an even number of criminals. Now test Paula as criminal. Gabe’s clue says Gabe has exactly 7 innocent neighbors; since 6 of Gabe’s neighbors are already known innocent, Bobby and Julie would have to supply the remaining 1 innocent between them. At the same time, Floyd and Mark must have equal numbers of criminal neighbors, but Floyd’s neighbor set is at 0 known criminals while Mark’s is already at 1, so the remaining open people Bobby, Gabe, Julie, and Ronald would have to make those counts match as well. Those same people cannot satisfy all of that with Paula counted as a criminal. So Paula cannot be criminal. That makes Paula innocent.

Olive’s clue says Olive has more criminal neighbors than Mark. Right now Mark already has 1 known criminal neighbor, while Olive has 0 known criminal neighbors. If Vicky and Will were both innocent, then among Olive’s neighbors only Julie would still be available to add any criminal neighbor for Olive, while Ronald is the only open person in Mark’s neighbors. That cannot satisfy the requirement that Olive’s total be higher than Mark’s. So Vicky and Will cannot both be innocent. That makes Vicky and Will criminal.

Paula’s clue says Vicky’s neighbors and Anna’s neighbors must contain the same number of criminals. Vicky’s neighbors already have 1 known criminal, and the only unresolved person there is Olive. From Xia’s clue, Hal’s neighbors contain exactly 1 criminal, so among Bobby and Gabe there cannot be any additional criminals; that means Anna’s neighbors do not gain any criminal from Bobby or Gabe. So Anna’s neighbors stay at 0 criminals, and Olive cannot be criminal if Vicky’s side is to match that. This leaves Olive as innocent.

Mark’s clue says Gabe’s neighbors and Will’s neighbors must contain the same number of criminals. Gabe’s neighbors already total exactly 1 criminal, while Will’s neighbors already have 1 known criminal, and the only unresolved person left among Will’s neighbors is Ronald. Since Will’s neighbor count must stay equal to Gabe’s and cannot go above 1, Ronald cannot be a criminal. So Ronald must be innocent.

Emily’s clue says Larry’s neighbors contain an odd number of criminals. In Larry’s neighboring group, there is already 1 known criminal, and the only unknown person left there is Gabe. Since 1 is already odd, Gabe cannot also be a criminal. So Gabe must be innocent.

Xia's clue says Hal has exactly 7 innocent neighbors, and exactly 2 of those innocents also neighbor Mark. Those 2 are already identified as Isaac and Larry. That leaves the rest of Hal's neighbors who do not neighbor Mark as Bobby, Debra, Emily, Gabe, Katie, and Mark, and among that group there are already 5 known innocents: Debra, Emily, Gabe, Katie, and Mark. So Bobby cannot be innocent, and Bobby must be criminal.

Isaac’s clue says Floyd and Mark must have the same number of criminal neighbors. Mark’s neighbors already contain exactly 1 criminal, and Floyd’s neighbors also already contain exactly 1 known criminal. The only unknown person left among the people this clue can still affect is Julie, in Floyd’s neighbor group, so Julie cannot add another criminal there without breaking the equality. So Julie must be innocent.