Puzzle Pack #1 Puzzle 31 Answer

Xena is at C5, so the people above her are Chad at C1, Hal at C2, Lucy at C3, and Paul at C4. Kevin is at B3, and his neighbors in that column are only Hal, Lucy, and Paul, because Chad at C1 is too far away to be Kevin’s neighbor. Vince’s clue says that both criminals above Xena are Kevin’s neighbors, so any criminal in C1 through C4 must be one of Hal, Lucy, or Paul. That leaves Chad as unable to be one of those criminals above Xena. Therefore, we can determine that C1 is INNOCENT.

Xena is at C5, so the people above her are C1 Chad, C2 Hal, C3 Lucy, and C4 Paul. Vince says both criminals above Xena are Kevin's neighbors, and Kevin at B3 neighbors C2, C3, and C4 among those four, but not C1. Since Chad at C1 is already innocent, the two criminals above Xena must be chosen from C2, C3, and C4. Chad also says that exactly one of Gary's four criminal neighbors is in column C. Gary is at B2, so his neighbors in column C are C1 Chad, C2 Hal, and C3 Lucy. Because Chad is innocent, the single criminal among Gary's column C neighbors must be either Hal or Lucy. That means the other criminal above Xena cannot be C2 or C3, so it has to be C4 Paul. Therefore, we can determine that C4 is CRIMINAL.

Xena is at C5, so the people above her are Chad at C1, Hal at C2, Lucy at C3, and Paul at C4. Paul says he is one of the 2 criminals below Chad, so in Chad’s column there are exactly 2 criminals below C1, and since Paul at C4 is one of them, exactly one of Hal, Lucy, and Xena is also a criminal. Vince says both criminals above Xena are Kevin’s neighbors; the only people above Xena are Chad, Hal, Lucy, and Paul, and among them Kevin’s neighbors are only Hal, Lucy, and Paul. Since Chad is already innocent, the two criminals above Xena must be Hal and Paul or Lucy and Paul, which leaves Xena as the one in Chad’s column below him who is not criminal. Therefore, we can determine that Xena is INNOCENT.

Above Xena in column C are Chad at C1, Hal at C2, Lucy at C3, and Paul at C4. Xena says all innocents above her are connected, and since Chad at C1 is innocent and Paul at C4 is criminal, the innocents above Xena must form one unbroken vertical group starting from C1, so C2 must also be innocent. That leaves the criminals above Xena as C3 and C4, namely Lucy and Paul. Vince says both criminals above Xena are Kevin's neighbors, and C3 and C4 are indeed both neighbors of Kevin at B3. Therefore, we can determine that C2 is INNOCENT and C3 is CRIMINAL.

Kevin is at B3, and Gary is at B2, so Gary is one of Kevin's neighbors. Lucy's clue says that Gary is one of Kevin's 5 innocent neighbors, which directly tells us Gary is innocent. Therefore, we can determine that B2 Gary is INNOCENT.

Gary is at B2, and his neighbors are A1, B1, C1, A2, C2, A3, B3, and C3. Chad says that among Gary's four criminal neighbors, only one is in column C. Since C1 and C2 are already innocent and C3 is already criminal, the only way Gary can have four criminal neighbors with just one of them in column C is for A1, B1, and A3 all to be criminal. That gives Anna at A1 and Ben at B1 immediately. Hal’s clue is about the innocents below Ben who neighbor Noah. Ben is at B1, so the people below him are B2, B3, B4, and B5, and among those, the ones who neighbor Noah at A4 are B3, B4, and B5. We already know B5 is innocent, so for the number of innocent people in that group to be odd, B3 and B4 must have opposite statuses. Lucy says Gary is one of Kevin’s five innocent neighbors, so Kevin at B3 is not innocent, which means B3 is criminal; therefore B4 must be innocent. Since Noah at A4 neighbors B3, B4, A3, and A5, and we already have A3 and B3 criminal while B4 is innocent, Noah cannot be criminal here, so Noah is innocent. Therefore, we can determine that A1 is CRIMINAL, A4 is INNOCENT, and B1 is CRIMINAL.

Isaac is at D2, so the people below him are Mary at D3, Ruby at D4, and Zoe at D5. Anna says exactly 2 of those 3 are innocents. Ben says there is only 1 innocent below Mary, and the only people below Mary are Ruby and Zoe, so among D4 and D5 exactly 1 is innocent. That means the total of 2 innocents below Isaac must be made up of 1 innocent among Ruby and Zoe plus Mary herself. Therefore, we can determine that D3, Mary, is INNOCENT.

Gary at B2 has eight neighbors: Anna, Ben, Chad, Ellie, Jason, Kevin, Hal, and Lucy. Chad says exactly four of those neighbors are criminals, and only one of those four is in column C; since Chad at C1 is innocent and Lucy at C3 is criminal, the other three criminal neighbors of Gary must be Anna, Ben, and exactly one of Ellie, Jason, or Kevin. That means among Ellie, Jason, and Kevin, exactly two are innocent. Mary says Gary and Vince have the same number of innocent neighbors. Gary already has Chad and Hal as known innocent neighbors, plus exactly two innocents among Ellie, Jason, and Kevin, so Gary has exactly four innocent neighbors in total. Vince at B5 neighbors Noah, Olivia, Paul, Sarah, and Xena; with Noah and Xena innocent and Paul criminal, he can have four innocent neighbors only if both Olivia and Sarah are innocent. Therefore, we can determine that A5 is INNOCENT and B4 is INNOCENT.

Below Ben in column B, the people are Gary at B2, Kevin at B3, Olivia at B4, and Vince at B5. Among those four, the ones who neighbor Noah at A4 are Kevin at B3 and Olivia at B4, because Noah’s neighbors include adjacent and diagonal spaces. Hal says an odd number of innocents in that group neighbor Noah, and Olivia is already known innocent, so Kevin must also be innocent to make the number of innocent neighbors there odd. Therefore, we can determine that B3 is INNOCENT.

Isaac is in D2, so the people below him are Mary at D3, Ruby at D4, and Zoe at D5. Anna says exactly 2 innocents are below Isaac, and Mary is already known to be innocent, so exactly one of Ruby and Zoe is innocent. Sarah compares Xena’s innocent neighbors with Donna’s. Xena’s neighbors are Olivia, Paul, Vince, and Zoe, and among those Olivia and Vince are innocent while Paul is criminal, so Xena has 2 or 3 innocent neighbors depending on Zoe. Donna’s neighbors are Chad, Hal, Isaac, Mary, and Ruby, and among those Chad, Hal, and Mary are already innocent, so Donna already has at least 3 innocent neighbors, and would have 4 if Ruby were innocent. Since Xena has more innocent neighbors than Donna, Ruby cannot be innocent, so Ruby is criminal and Zoe is the second innocent below Isaac. That means the two innocents below Isaac are exactly Mary and Zoe. Therefore, we can determine that D2 is CRIMINAL.

Gary says columns A and D contain the same number of innocents. In column A, A1 is criminal, A4 and A5 are innocent, and among A2 and A3 only one can be innocent because Anna says there are exactly 2 innocents below Isaac, and below Isaac are D3, D4, and D5, so with D3 already innocent exactly one of D4 and D5 is innocent; that forces only one of A2 and A3 to be innocent as well when columns A and D must match. Column D already has D3 as innocent and exactly one of D4 or D5 as innocent, so column D has 2 innocents total. Therefore column A must also have 2 innocents total, which means both A2 and A3 cannot be innocent, so D1 must be innocent to make column D reach the needed total. Therefore, we can determine that D1 is INNOCENT.

Gary is at B2, so his neighbors are A1, B1, C1, A2, C2, A3, B3, and C3. We already know four of those are criminals: A1, B1, and C3, plus exactly one more because Chad says only 1 of Gary's 4 criminal neighbors is in column C, which must be C3 since C1 and C2 are innocent. That means Gary has exactly 4 criminal neighbors in total. Donna says Gary has the most criminal neighbors, so nobody else can also have 4. Ruby at D4 already neighbors four known criminals: C3, C4, D5, and D2. Since she cannot tie Gary for the most, D5 cannot be criminal, so Zoe is innocent. Then Ruby's criminal neighbors are only C3, C4, and D2, which is 3, and if Ruby herself were criminal, Gary would still have the unique most. But Ruby is directly constrained by this same comparison: with Zoe innocent, the only way to avoid creating another position matching Gary's maximum through the D-column cluster is for Ruby not to add to that criminal structure. Therefore, we can determine that D4 is INNOCENT.

Isaac is at D2, so the people below him in the same column are Mary at D3, Ruby at D4, and Zoe at D5. Anna’s clue says exactly 2 of those 3 people are innocents. Mary and Ruby are already known to be innocent, so those are the 2 innocents below Isaac. That leaves Zoe as the only one below Isaac who is not innocent. Therefore, we can determine that D5 is CRIMINAL.

Anna at A1 has neighbors B1, A2, and B2, and two of those are already criminal: Ben at B1 and Anna herself is not counted, while Gary at B2 is innocent. So Anna’s number of criminal neighbors depends only on Ellie at A2: Anna has 2 criminal neighbors if Ellie is criminal, and 1 if Ellie is innocent. Donna at D1 has neighbors C1, C2, and D2, and among them only Isaac at D2 is criminal, so Donna has exactly 1 criminal neighbor. Since Zoe says Donna and Anna have an equal number of criminal neighbors, Anna must also have exactly 1 criminal neighbor, which means Ellie cannot be criminal. Therefore, we can determine that A2 is INNOCENT.

Gary is at B2, so his neighbors are Anna at A1, Ben at B1, Chad at C1, Ellie at A2, Hal at C2, Jason at A3, Kevin at B3, and Lucy at C3. Among those eight people, Chad’s clue says exactly 4 are criminals, and only 1 of those 4 is in column C. We already know three neighboring criminals: Anna at A1, Ben at B1, and Lucy at C3. Of those, only Lucy is in column C, so the clue’s “only 1 in column C” is already used up, and the fourth neighboring criminal cannot be Chad at C1 or Hal at C2. The only remaining neighbor who could be that fourth criminal is Jason at A3. Therefore, we can determine that A3 is CRIMINAL.