perplexus.info :: Liars and Knights : Pages and Squires

Pages and Squires (Posted on 2007-02-13)

The famous Singapore Detective, Nguyen Bao, was on vacation in the remote country of Proth. Proth is a country where the population follows the rules of Knights, Knaves, Liars, Squires and Pages. Knights always tell the truth. Knaves strictly alternate between truths and lies. Liars always lie. Squires, trying to impress people, copy the last person who made a statement, by following that person’s lie with a lie, or that person’s truth with a truth. Pages, trying to irritate people, do the opposite of the last person who made a statement, by following that person’s truth with a lie, or their lie with a truth.

As it turned out, while enjoying his vacation, Detective Nguyen was asked to give his insights into a local crime. Sometime the previous evening, the Magistrate’s Custard Pudding had disappeared. There were five people who had access to the Pudding. One or more of them could have perpetrated the crime, but the local police were baffled and were unable to crack the case.

Prior to questioning the suspects, Detective Nguyen asked the constable to have the five suspects assembled into an interrogation room. Realizing that he could not trust the constable to provide any truthful insight into the case, Detective Nguyen entered the room alone, and took a seat.

Hoping to find a suspect who would help, Detective Nguyen asked, "Who here is a Squire?"

A: "B is not a Squire."
B: "C is not a Squire."
C: "E is not a Squire."
D: "A is not a Squire."
E: "D is not a Squire."

Seeing a possible flaw with his tactic, Detective Nguyen then asked, "Who here is a Knight?"

B: "I am a Knight."
E: "I am a Knight."
C: "I am a Knight."
A: "I am a Knight."
D: "I am a Knight."

With a sense of frustration, Detective Nguyen quickly asked, "Who stole the Custard?"

C: "I didn’t do it."
B: "I didn’t do it."
D: "I didn’t do it."
A: "I didn’t do it."
E: "I didn’t do it."

Detective Nguyen took a breath. After a brief pause he asked, "How many of you were involved?"

D: "Only one of us did it."
A: "Only two of us did it."
C: "Only three of us did it."
E: "Only four of us did it."
B: "All of us did it."

Thinking to himself that perhaps there was a chance to solve this, Detective Nguyen asked, "Who did it?"

E: "B did it."
B: "D did it."
D: "A did it."
C: "E did it."
A: "C did it."

Standing up, Detective Nguyen left the room and made his report to the Magistrate.

What trait did each suspect exhibit, and who ate the pudding?

Submitted by Leming

Rating: 4.4000 (10 votes)

Solution: (Hide)

#1) At most one of the answers to Q4 is true. Therefore there can be at most one Knight (if any) and at most one of the answers to Q2 can be true.
#2) B3 and B4 contradict, making at least one of them false. Therefore B is not a Knight, and B2 is a lie.
#3) Assume that B is a Squire. Then A1 is false. If B is a Squire then B1 would copy A1 and would also be false. Then C is a Squire making C1 false and thus E is a Squire. We know B2 is a lie (#2). Then with B acting as a Squire, E1 must be a lie. Then D is a Squire, and from D1 A is a Squire. This identifies all of the suspects as Squires. Then all statements to all questions must follow the previous answer, making them all lies. If all Q3 answers are lies, then everyone ate the pudding which makes B4 true. This contradicts the statement that all answers are lies. Therefore the assumption is wrong. B is not a Squire and A1 is true.
#4) Assume that B4 is true. Then B5 is true and B is not a Liar. Also B is not a Knave since B tells two truths in a row. Also E5 would be true, but at this point B can only be a Page which would make B5 false. This would imply that D is not guilty and contradict B4. Therefore the assumption is wrong and B4 is a lie.
#5) Assume B is a Liar. Then B3 is a lie. This makes E5 the truth. From B1, C is a Squire, and from C1, E is a Squire. With E a Squire and E5 true, then B4 must be true but this contradicts the assumption. The assumption is wrong and B is not a Liar.
#6) Assume B is a Page, then A1 is true and B1 must follow as a lie. Then C and E are Squires. From B4 being false, E4 would be true and C4 would be true. But only one of Q4 can be true. This forms a contradiction. The assumption is wrong. B is not a Page and from #2, #3, and #5 B must be a Knave. Therefore B1, B3, and B5 are true.
#7) Since B5 is true, D3 becomes a lie making D2 a lie. Therefore D is not a Knight or a Knave. D3(lie) follows B3(true) so D is not a Squire.
#8) This makes E1 true, therefore E is not a Liar. B3 is true making E5 a lie, therefore E is not a Knight. Both E5 and B4 are lies, therefore E is not a Page. E2 is a lie as is E1 thus E is not a Knave. E can only be a Squire.
#9) This makes C1 a lie, therefore C is not a Knight. This makes C2 a lie. Since both C1 and C2 are lies, C is not a Knave. E2 and C2 are lies, therefore C is not a Page. From B1 (true) C is not a Squire. C can only be a Liar.
#10) C3 is a lie so A5 is true. C5 is a lie. A5 (true) following C5 (lie) prevents A from being a Squire. This makes D1 true. D is not Liar, and from #7 D must be a Page.
#11) D2 is a lie. So under the rule of Pages A2 must be true and A must be a Knight.
#12) From A4, two people are guilty. A5 and B5 show that the guilty parties are C and D.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	Math Man	2012-08-21 19:34:52
Puzzle Solution	K Sengupta	2007-05-09 13:10:09
re: Great Puzzle!	Dej Mar	2007-02-17 23:28:52
re: Great Puzzle!	Federico Kereki	2007-02-14 09:36:19
Great Puzzle!	Avin	2007-02-13 20:41:15
computer solution	Charlie	2007-02-13 17:12:20
a Solution	hoodat	2007-02-13 16:36:02

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