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?

I got the same solution as hoodat. From the responses to question 4, it is clear that at most one person can be a knight, since exactly one person told the truth in response to that question. So then I tried each person being the knight, and only with A was I able to get a valid solution.

This was definitely one of my favorite Liar and Knight puzzles.

Posted by Avin on 2007-02-13 20:41:15