Puzzle Packs/Puzzle Pack #2/Puzzle 14

Puzzle Pack #2 Puzzle 14 Answer

Medium·Puzzle 14

A1

👩‍🍳

Alice

cook

B1

👷‍♀️

Barb

builder

C1

💂‍♀️

Chloe

guard

D1

👩‍💻

Diane

coder

A2

🕵️‍♂️

Eric

sleuth

B2

🕵️‍♂️

Floyd

sleuth

C2

💂‍♂️

Hal

guard

D2

👨‍💻

Isaac

coder

A3

👨‍💼

Kyle

clerk

B3

👩‍💼

Lisa

clerk

C3

💂‍♀️

Mary

guard

D3

👩‍💻

Nicole

coder

A4

👷‍♂️

Ollie

builder

B4

👨‍✈️

Paul

pilot

C4

👨‍💼

Rob

clerk

D4

👩‍🍳

Uma

cook

A5

👨‍⚕️

Vince

doctor

B5

👩‍✈️

Wanda

pilot

C5

🕵️‍♂️

Xavi

sleuth

D5

👩‍⚕️

Zoe

doctor

Replay Reasoning

Step 1 of 18
Step Result
B4 · Paul is INNOCENT
B3 · Lisa is INNOCENT
Why this is true
Mary is at C3, so her six innocent neighbors are the six people around her, and the ones who also neighbor Ollie at A4 are exactly Lisa at B3 and Paul at B4. Kyle at A3 is already known to be innocent, and Kyle says exactly 2 of those shared neighbors are innocent. Since there are only those two shared neighbors, both of them must be the two innocents Kyle is counting. Therefore, we can determine that B4 is INNOCENT and B3 is INNOCENT.
Based on this clue:
"Exactly 2 of Mary's 6 innocent neighbors also neighbor Ollie" Kyle (A3)
Progress
Innocent 3·Criminal 0·Unknown 17

Answer Explanation

18 / 18 steps visible
Step 1

Mary is at C3, so her six innocent neighbors are the six people around her, and the ones who also neighbor Ollie at A4 are exactly Lisa at B3 and Paul at B4. Kyle at A3 is already known to be innocent, and Kyle says exactly 2 of those shared neighbors are innocent. Since there are only those two shared neighbors, both of them must be the two innocents Kyle is counting. Therefore, we can determine that B4 is INNOCENT and B3 is INNOCENT.

Step 2

Chloe is at C1, and Xavi is at C5, so the people above Xavi in column C are Chloe, Hal, Mary, and Rob. Paul’s clue says Chloe is one of the 2 criminals among those four people above Xavi, so it directly includes Chloe in that criminal pair. Therefore, we can determine that C1 is CRIMINAL.

Step 3

Xavi is at C5, so the people above Xavi are Chloe at C1, Hal at C2, Mary at C3, and Rob at C4. Chloe’s clue says that exactly two of those four are innocents, and those two innocents must be connected in that column. Since Chloe herself is already known to be a criminal, the only way to have two connected innocents above Xavi is Hal and Mary together or Mary and Rob together. But Hal cannot be one of them, because Mary would then have to be the second innocent and the clue would still force Mary to be innocent either way. Therefore, we can determine that C3, Mary, is INNOCENT.

Step 4

Mary is at C3, and Rob is at C4, so the people above Rob are the three people in column C above C4: Chloe at C1, Hal at C2, and Mary at C3. Mary’s clue says exactly 2 of those 3 people are innocent. We already know Chloe is criminal and Mary is innocent, so the only way to have exactly 2 innocents above Rob is for Hal to be innocent as well. Therefore, we can determine that C2 is INNOCENT.

Step 5

Chloe is at C1, and Xavi is at C5, so the people above Xavi are Chloe at C1, Hal at C2, Mary at C3, and Rob at C4. Paul says Chloe is one of 2 criminals above Xavi, so exactly two of those four people are criminals. We already know Hal and Mary are innocent, and Chloe is criminal, so the only way to make the total above Xavi equal 2 criminals is for Rob to be the other one. Therefore, we can determine that C4 Rob is CRIMINAL.

Step 6

Hal says column A is the only column with exactly 2 criminals, so no other column can also have exactly 2. In column C, Chloe at C1 and Rob at C4 are already criminals, while Hal at C2 and Mary at C3 are innocent. That means column C already has exactly 2 criminals unless Xavi changes that total. So Xavi cannot be innocent, because then column C would also have exactly 2 criminals. Therefore, we can determine that C5 is CRIMINAL.

Step 7

Uma at D4 is a neighbor of Xavi at C5, and Xavi is already known to be criminal. Xavi’s clue says everyone has at least one innocent neighbor, so Xavi himself must have at least one innocent neighbor. Xavi’s neighbors are Rob at C4, Wanda at B5, Uma at D4, and Paul at B4; since Rob is criminal and Paul is already known innocent, the clue is satisfied through Paul, and among the unknown neighbors this leaves Uma able to be identified here only because D4 is one of the innocent neighbors required around that area. Therefore, we can determine that D4 is INNOCENT.

Step 8

In column D, Uma says all innocents there form one connected group. We already know Uma at D4 is innocent, and if Nicole at D3 were not innocent, then the innocents in column D would be split apart because D4 would be separated from any innocent above it. So the clue forces D3 to be part of that connected innocent group. Therefore, we can determine that D3 is INNOCENT.

Step 9

Eric is at A2, so the innocents below Eric are the innocent people lower in column A. Kyle at A3 is innocent, while Ollie at A4 and Vince at A5 are the only other people below Eric in that column whose status could matter. Someone neighboring Ollie must be one of Ollie’s adjacent and diagonal neighbors, so among the innocents below Eric, Kyle at A3 does neighbor Ollie at A4, but Vince at A5 would also neighbor Ollie if Vince were innocent. Nicole’s clue says exactly one innocent below Eric is neighboring Ollie, so Kyle must be that one and Vince cannot be innocent. Therefore, we can determine that A5 is CRIMINAL.

Step 10

In column D, we already know D3 and D4 are innocent, while D1, D2, and D5 are still undecided. Uma’s clue says all innocents in column D are connected, so any innocents in that column must form one unbroken vertical group. Vince’s clue says column D has more innocents than any other column, and since column C already has three innocents, column D must have all four of D1, D2, D3, and D4 or all five spots innocent except for none; in particular it must have at least four innocents. Because D5 cannot be innocent without breaking the connected block with the known innocents above it, the needed extra innocent has to be D2. Therefore, we can determine that D2 is INNOCENT.

Step 11

Mary is at C3, and her six innocent neighbors are B2 Floyd, C2 Hal, D2 Isaac, B3 Lisa, B4 Paul, and D4 Uma. Among those six, the ones who also neighbor Ollie at A4 are only Lisa at B3 and Paul at B4. Kyle says exactly two of Mary's innocent neighbors also neighbor Ollie, so Mary's innocent neighbors must be exactly those two shared neighbors. That means Floyd cannot be one of Mary's innocent neighbors. Therefore, we can determine that B2 Floyd is CRIMINAL.

Step 12

Wanda at B5 and Diane at D1 must have the same number of innocent neighbors. Diane’s neighbors are Chloe at C1, Hal at C2, and Isaac at D2, and exactly two of those are innocent because Hal and Isaac are innocent while Chloe is criminal. Wanda’s neighbors are Ollie at A4, Paul at B4, Rob at C4, Vince at A5, Xavi at C5, and Zoe at D5, and among those only Paul is already known to be innocent; Rob, Vince, and Xavi are criminal, so Wanda can match Diane’s total of two innocent neighbors only if Ollie is also innocent. Therefore, we can determine that A4 is INNOCENT.

Step 13

Uma at D4 has exactly two criminal neighbors, because her neighbors are C3, C4, C5, D3, and D5, and only C4 and C5 are criminals among the ones already known. Ollie’s clue says Barb has more criminal neighbors than Uma, so Barb at B1 must have at least three criminal neighbors. Barb’s neighbors are A1, A2, B2, C1, and C2, and since B2 and C1 are already criminals while C2 is innocent, at least one of A1 or A2 must also be criminal. That means column A already contains Vince plus at least one of A1 or A2, giving column A exactly two criminals, so Hal’s clue makes every other column not have exactly two criminals. Column D currently has no known criminals except possibly D1 and D5, so if D5 were criminal then column D would have exactly two criminals with D1, which Hal’s clue rules out. Therefore, we can determine that D5 is INNOCENT.

Step 14

Floyd is at B2, so his edge neighbors are A1, B1, C1, and A2; among those, only C1 is already known not to be innocent. Zoe says an odd number of edge innocents neighbor Floyd, so among A1, B1, and A2 there must be either one innocent or all three innocent. Hal says column A is the only column with exactly 2 criminals, and since A3 and A4 are already innocent while A5 is criminal, column A can reach exactly 2 criminals only if exactly one of A1 and A2 is criminal. That means among A1, B1, and A2 there are exactly two innocents, so B1 cannot be criminal because then A1 and A2 would both have to be innocent, giving Floyd three edge innocents instead of an odd total. Therefore, we can determine that B1 is INNOCENT.

Step 15

Column A contains exactly two unknowns, Alice at A1 and Eric at A2, while A3 and A4 are innocent and A5 is criminal. Since Hal says column A is the only column with exactly 2 criminals, column A must indeed total exactly 2 criminals, so exactly one of Alice and Eric is criminal. Column B already has one criminal, Floyd at B2, and Wanda at B5 is the only unknown there, with the other three people in that column innocent. If Wanda were criminal, then column B would also have exactly 2 criminals, which Hal says cannot happen because only column A has that total. Therefore, we can determine that B5 is INNOCENT.

Step 16

Column D already has four known innocents: Isaac at D2, Nicole at D3, Uma at D4, and Zoe at D5. Column B also already has four known innocents, and no column can have more than five people total. Since the clue says column D has more innocents than any other column, D must have more innocents than column B, so D1 also has to be innocent to give column D a total of five innocents. Therefore, we can determine that D1 is INNOCENT.

Step 17

Alice at A1 has neighbors B1, A2, and B2, while Diane at D1 has neighbors C1, C2, and D2. Diane already has two innocent neighbors there, because C2 and D2 are innocent, while C1 is criminal. Alice already has one innocent neighbor there, because B1 is innocent and B2 is criminal, so for Alice and Diane to have equal numbers of innocent neighbors, A2 must also be innocent. Therefore, we can determine that A2 is INNOCENT.

Step 18

Hal says column A is the only column with exactly 2 criminals. In column A, Eric, Kyle, and Ollie are already innocent, and Vince is already criminal, so the only way for column A to have exactly 2 criminals is for Alice at A1 to be the second one. Therefore, we can determine that A1 is CRIMINAL.

Answer (spoilers)

Criminal
Alice, Chloe, Floyd, Rob, Vince, Xavi
Innocent
Barb, Diane, Eric, Hal, Isaac, Kyle, Lisa, Mary, Nicole, Ollie, Paul, Uma, Wanda, Zoe