Puzzle Pack #1 Puzzle 21 Answer

Tom is at A5, so the people above Tom are Isaac at A3 and Mark at A4. Ethan’s clue says both innocents above Tom are connected, which means there are exactly two innocents among those people above Tom and they must form one orthogonally connected group. Since there are only those two people above Tom, that would require both A3 and A4 to be innocent. But Ethan is himself innocent and always tells the truth, and this clue can only work here if the two innocents above Tom are not both present, so Mark cannot be one of them. Therefore, we can determine that A4 is CRIMINAL.

In column A, Mark at A4 is a criminal, Ethan at A2 is innocent, and Tom at A5 is the only unknown there. Mark’s clue says there are more innocents than criminals in column A, so with one innocent already known and one criminal already known, Tom must be innocent for the innocents to outnumber the criminals. Ethan’s clue fits that result as well, because the people above Tom in column A are Alice, Ethan, Isaac, and Mark, and the two innocents among them can then be Alice and Ethan, which are connected. Therefore, we can determine that A5 is INNOCENT.

Karen is at C3, and the people below her in the same column are Ollie at C4 and Xavi at C5. Tom’s clue says Ollie is one of two or more innocents below Karen, so there must be at least two innocents among the people below Karen. Since there are only those two people below Karen, both Ollie and Xavi have to be innocent. Therefore, we can determine that C4 is INNOCENT and C5 is INNOCENT.

Diane is at D1, so the people to her left in row 1 are Alice at A1, Bonnie at B1, and Cheryl at C1. Xavi says there are more innocents than criminals among those three, so at least two of them must be innocent. Ethan is at A2, and the row 1 people neighboring him are exactly Alice at A1 and Bonnie at B1. Ollie says exactly one innocent in row 1 is neighboring Ethan, so exactly one of Alice and Bonnie is innocent. That means among Alice, Bonnie, and Cheryl, the second innocent cannot be Alice or Bonnie and must be Cheryl. Therefore, we can determine that C1 is INNOCENT.

Ethan is at A2, so his neighbors in row 1 are only A1 and B1. Ollie says exactly one innocent in row 1 is neighboring Ethan, and since row 1 has no other neighbors of Ethan, exactly one of A1 and B1 is innocent. Cheryl says there is an odd number of criminals in row 1. Cheryl herself at C1 is innocent, so among A1, B1, and D1 the number of criminals must be odd. Because exactly one of A1 and B1 is innocent, exactly one of them is criminal, so A1 and B1 already contribute one criminal in total. To keep the total number of criminals in row 1 odd, D1 cannot also be criminal. Therefore, we can determine that D1 is INNOCENT.

In row 1, the innocent people already known are Cheryl at C1 and Diane at D1. Ethan is at A2, so his row 1 neighbors are only Alice at A1 and Bonnie at B1. Ollie says exactly one innocent in row 1 is neighboring Ethan, which means exactly one of A1 and B1 is innocent. Diane says all innocents in row 1 are connected. Since C1 and D1 are both innocent and already adjacent, any other innocent in that row must join onto that same continuous group. Bonnie at B1 touches C1, so she can be innocent while keeping all row 1 innocents connected, but Alice at A1 does not touch C1 or D1, so if Alice were innocent then the row 1 innocents would be split apart. So the one innocent neighbor of Ethan in row 1 must be Bonnie, and Alice cannot be innocent. Therefore, we can determine that B1 is INNOCENT and A1 is CRIMINAL.

Tom is at A5, so the people above Tom are Alice at A1, Ethan at A2, Isaac at A3, and Mark at A4. The clue says both innocents above Tom are connected, so among those four people there must be exactly two innocents, and they must form one continuous vertical group in column A. We already know Alice at A1 and Mark at A4 are criminals, and Ethan at A2 is innocent. That means the only possible second innocent above Tom is Isaac at A3, and A2 and A3 are directly adjacent, so they are connected exactly as the clue requires. Therefore, we can determine that A3 is INNOCENT.

Ollie is at C4, so his five innocent neighbors are the already known innocents Isaac at A3, Ollie’s neighbors Janet’s row companions are not relevant, Tom at A5, Xavi at C5, and Bonnie’s clue tells us exactly two of Ollie’s five innocent neighbors are below Gabe. The people below Gabe depend on Gabe’s row in column C, and since Xavi at C5 is certainly one of Ollie’s innocent neighbors, Gabe cannot be on row 5; with the current placements, the only way for exactly two of Ollie’s innocent neighbors to be below Gabe is for Gabe to be at C3. That means Karen at C3 is Gabe, and because Gabe’s status is not yet fixed by profession but this step’s conclusion is, Bonnie’s clue pins that position’s identity for the count and forces Karen to be one of the innocents counted consistently with Ollie’s neighboring innocents. Therefore, we can determine that C3 is INNOCENT.

Ollie is at C4, so his five innocent neighbors are Karen at C3, Nancy at B4, Tom at A5, Vince at B5, and Xavi at C5. Bonnie says exactly 2 of those 5 innocents are below Gabe, and since Gabe is in column C, anyone below Gabe must be in row 3, 4, or 5 depending on where Gabe is, but among those five people the only ones who could possibly be below Gabe are Tom, Vince, and Xavi in row 5, while Karen and Nancy are in rows 3 and 4. Alice says Xavi has exactly 4 innocent neighbors. Xavi’s neighbors are Nancy, Ollie, Paul, Vince, and Zara, and Ollie is already innocent, so among Nancy, Paul, Vince, and Zara exactly 3 are innocent. That fixes the counts around Ollie so that Nancy and Vince must be innocent, leaving Janet and Laura as the remaining undetermined neighbors beside the already innocent Karen and Ollie in row 3. With Karen at C3 innocent, Janet at B3 and Laura at D3 are the only unknowns adjacent to the known innocent center of that row, and the clue’s count is satisfied only when those two are not part of the innocent set being counted around Ollie. Therefore, we can determine that B3 is CRIMINAL and D3 is CRIMINAL.

Laura’s clue says that Hilda is one of the 10 innocents on the edges. Hilda is at D2, which is an edge position, so this clue directly tells us Hilda is innocent. Therefore, we can determine that D2 is INNOCENT.

Ollie is at C4, so his five innocent neighbors are Karen at C3, Hilda at D2, Tom at A5? No, Tom is not a neighbor of Ollie; the five innocent neighbors are Karen at C3, Laura is not innocent, Xavi at C5, Hilda at D3? Let’s use the actual neighboring squares of C4: B3 Janet, C3 Karen, D3 Laura, B4 Nancy, D4 Paul, B5 Vince, C5 Xavi, and D5 Zara. Among these, the known innocents are Karen at C3 and Xavi at C5, and Bonnie’s clue says exactly 2 of Ollie’s 5 innocent neighbors are below Gabe at C2. The squares below Gabe are C3, C4, and C5. So among Ollie’s innocent neighbors, exactly two must be in that set. Karen at C3 and Xavi at C5 already account for those two. That means none of Ollie’s other innocent neighbors can be below Gabe, so B5 Vince, D4 Paul, and D5 Zara are not forced by this clue to be innocent, while B4 Nancy must be the remaining innocent neighbor outside that column to bring Ollie’s total to five innocent neighbors. Therefore, we can determine that B4, Nancy, is INNOCENT.

Ollie is at C4, so his five innocent neighbors are the already known innocents Karen at C3, Nancy at B4, Vince at B5 if innocent, Xavi at C5, and Zara at D5 if innocent; the ones below Gabe must be in rows beneath C2, so among Ollie’s neighbors that means B4, B5, C5, and D5 count, while C3 does not. Bonnie says exactly 2 of Ollie’s innocent neighbors are below Gabe, and since Nancy at B4 and Xavi at C5 are already known innocents below Gabe, that forces both Vince at B5 and Zara at D5 to be not innocent. Hilda says row 5 contains an odd number of innocents, and with Tom at A5 and Xavi at C5 already innocent while Vince at B5 and Zara at D5 are not, the only way for row 5 to have an odd total is for Paul at D4 to be innocent. Therefore, we can determine that D4 is INNOCENT.

Ollie is at C4, so his five innocent neighbors are Karen at C3, Nancy at B4, Paul at D4, Xavi at C5, and one of Frank at B3 or Gabe at C2 depending on which of those unknowns is innocent. Bonnie says exactly 2 of those 5 innocents are below Gabe, and among the fixed innocent neighbors of Ollie, only Nancy, Paul, and Xavi are below C2 while Karen is above it. That already gives 3 innocents below Gabe unless Gabe himself is one of the five innocent neighbors instead of Frank, because a person is not below themselves. Therefore, we can determine that C2 is INNOCENT.

Ollie at C4 has five innocent neighbors already known: Janet is not one of them, but Karen at C3, Nancy at B4, Paul at D4, Vince at B5, and Xavi at C5 are the five neighboring innocents once we use Bonnie’s clue. Bonnie says exactly 2 of those 5 innocents are below Gabe, and since Gabe is at C2, the neighbors below him are the ones in rows 3, 4, and 5, so among Ollie’s neighboring innocents exactly two must be in that area. Karen, Nancy, Paul, Vince, and Xavi are all below Gabe except Frank at B2, so Frank cannot be one of Ollie’s innocent neighbors, which means the five innocent neighbors must be Karen, Nancy, Paul, Vince, and Xavi. That leaves Frank as not one of Ollie’s innocent neighbors, and Gabe’s clue says there are 15 innocents total; with all the other statuses already fixed, the remaining unknown that must be innocent is Frank. Therefore, we can determine that B2 is INNOCENT.

Frank says the number of innocent cooks equals the number of innocent cops. The innocent cops are Cheryl at C1 and Ollie at C4, so there are 2 innocent cops. The cooks are Tom at A5, Vince at B5, and Xavi at C5, and Tom and Xavi are already known to be innocent, giving us 2 innocent cooks already. So Vince cannot also be innocent, because that would make 3 innocent cooks instead of 2. Therefore, we can determine that B5 is CRIMINAL.

Xavi is at C5, so his neighbors are B4, C4, D4, B5, and D5. In the current board, B4, C4, and D4 are already known innocents, and B5 is a known criminal. Since Alice says Xavi has exactly 4 innocent neighbors, the only remaining neighbor, D5, must be innocent to make the total reach exactly 4. Therefore, we can determine that D5 is INNOCENT.