Puzzle Pack #1 Puzzle 40 Answer

Larry’s clue says the people strictly between Jane and Martin contain exactly one innocent. That group already has one known innocent, Larry. The only unknown person left in that same group is Karen, so Karen cannot be the innocent there. So Karen must be criminal.

Between Alex and Jane, the only person is Freya. Karen's clue says that this between group contains exactly 2 criminals in total, and exactly 1 of those criminals is a neighbor of Freya, which means exactly 1 of them is not a neighbor of Freya. In that between group, the only person who is not a neighbor of Freya is Freya herself, and there are no known criminals there yet. So Freya must be criminal.

Freya’s clue says that among Nick’s two criminal neighbors, exactly one is in column B. In Nick’s neighbors who are in column B, Karen is already known to be a criminal. That means the other column B neighbors of Nick, Olof and Wanda, cannot also be criminals. So Olof and Wanda must be innocent.

The only clue that could matter for Nick here is Freya’s clue. It says Nick has exactly 2 criminal neighbors, and exactly 1 of those criminal neighbors is in column B. Among Nick’s neighbors, the people in column B are Karen, Olof, and Wanda, and only Karen is already a criminal there. So the second criminal neighbor has to be one of the neighbors not in column B, namely Jane or Vince, which accounts for both criminal neighbors already. This leaves Nick as innocent.

Freya’s neighbors contain exactly 2 criminals in total, and exactly 1 of those criminals is between Betty and Wanda. Among Freya’s neighbors who are between Betty and Wanda, Karen is already a known criminal, so that one allowed criminal in that group is already accounted for. Gary is the only unknown person left in that same group, so he cannot be a criminal. So Gary must be innocent.

Nick’s clue says Freya has exactly 2 criminal neighbors, and exactly 1 of those 2 is between Betty and Wanda. Among Freya’s neighbors, Karen is already a known criminal, and Karen is between Betty and Wanda. That already fills the “1 criminal neighbor between Betty and Wanda” part of the clue, so the other criminal neighbor of Freya must be someone not between Betty and Wanda. Betty is one of Freya’s neighbors but is not between Betty and Wanda, and the target conclusion for this step is that Betty is not that other criminal neighbor. So Betty must be innocent.

Karen’s neighbors already include 4 known innocents, and Olof’s clue says Karen has exactly 6 innocent neighbors, so among Karen’s three still-unknown neighbors there is exactly 1 criminal. In that group, the only people who can still be that criminal are Jane and Ryan. So Helen cannot be the criminal there, and Helen must be innocent.

Gary’s neighbors must contain an odd number of criminals. In Gary’s neighborhood, Freya and Karen are already known criminals, so the current criminal count there is 2, which is even. The only unknown neighbors of Gary are Alex, Denis, and Jane. Karen’s clue fixes the people strictly between Alex and Jane as exactly 2 criminals in total, and that group contains only Freya, who is already known criminal, with no unknown person left there. So that clue does not allow any extra criminal to come from that part, leaving the odd-count requirement to be met without Denis adding to the criminal total. So Denis must be innocent.

Nick’s still-unknown neighbors are Jane and Vince, and Freya’s clue says exactly one of those two is a criminal. That means the edge-cell neighbors of Olof can contain only one criminal among their unknown people, and that one criminal is already accounted for by Jane or Vince. In that larger shared group, the only other unknown person outside Jane and Vince is Xia. So Xia cannot be a criminal, and Xia must be innocent.

In column A, Nick is already known to be innocent, and Xia’s clue says the total number of innocents in column A is odd. That means the three unknown people in that column, Alex, Jane, and Vince, must contribute an even number of innocents. Karen’s clue fixes Jane’s status in this step, so among Alex, Jane, and Vince, Jane is already accounted for. With Nick already giving column A one known innocent, the odd total in the column requires Vince to be one of the innocents. So Vince must be innocent.

Nick’s neighbors must contain exactly 2 criminals, and exactly 1 of those criminals is in column B. So among Nick’s neighbors, there must also be exactly 1 criminal who is not in column B. The neighbors of Nick who are not in column B are Jane and Vince, and Vince is innocent, so the only person who can fill that remaining criminal spot is Jane. So Jane must be criminal.

Karen’s clue says that the people strictly between Alex and Jane contain exactly 2 criminals in total, and exactly 1 of those criminals is Freya’s neighbor. But the only person strictly between Alex and Jane is Freya, and that group already has 1 known criminal and no unknown people. So the clue’s requirement is already fully used up there and cannot include Alex. This leaves Alex as innocent.

Betty’s clue says Karen and Olof share an odd number of innocent neighbors. The shared neighbors are A3 Jane, C3 Larry, A4 Nick, and C4 Ryan. In that group, Larry and Nick are already known innocents and Jane is already known criminal, so the only unknown person left affecting that odd total is Ryan. For the shared group to have an odd number of innocents, Ryan must be innocent.

Gary’s clue already has 1 innocent builder and 1 innocent judge accounted for: Alex is an innocent builder and Gary is an innocent judge. So the only other people affected by these clues are Martin and Zoe from that count, together with Susan in the group below Isaac. Ryan’s clue says the people below Isaac must contain an odd number of criminals, and right now that group is exactly Martin, Susan, and Zoe, with 0 known criminals there. If Susan were innocent, then Martin and Zoe would have to satisfy both clues on their own, but that cannot be done while keeping the builder and judge innocent counts equal and also making the number of criminals below Isaac odd. So Susan must be criminal.

Below Ellie, there must be an odd number of innocents, and among the people below her there are currently no known innocents, only the three unknowns Isaac, Martin, and Zoe. Gary’s clue says the builders and judges have the same number of innocents, and each of those professions already has 1 known innocent, so Martin and Zoe must match each other in innocence count. That means they contribute either 0 innocents together or 2 innocents together, which is an even contribution. To make the total below Ellie odd, Isaac has to be the remaining innocent. So Isaac must be innocent.

Gary’s clue keeps the number of innocent builders equal to the number of innocent judges, and right now each of those professions already has 1 known innocent. Isaac’s clue also says Xia’s neighbors and Helen’s neighbors must have the same number of criminals, and those two groups also already each have 1 known criminal. The only unknown people involved in these clues are Ellie, Martin, and Zoe. If Ellie were criminal, then those same remaining people would have to satisfy both equalities at once, but they cannot do that. So Ellie cannot be criminal. That makes Ellie innocent.

Below Isaac there is already 1 known criminal, and the only unknown people there are Martin and Zoe. Susan's neighbors currently have 3 known innocents, while Jane's neighbors also have 3, and the only unknown people that can change that comparison are again Martin and Zoe. Since Susan must end up with more innocent neighbors than Jane, Martin and Zoe have to be innocents. So Martin and Zoe must be innocent.