# Knight, knave, commoner

A king has a daughter and wants to choose the man she will marry. There are three suitors from whom to choose, a Knight, a Knave, and a Commoner. The king wants to avoid choosing the Commoner as the bridegroom, but he does not know which man is which. All the king knows is that the Knight always speaks the truth, the Knave always lies, and the Commoner can do either. The king will ask each man one yes/no question, and will then choose who gets to marry the princess. What question should the king ask and how should he choose the bridegroom?

A followup question:

Suppose the three suitors know each other (an assumption that’s not needed in the original problem). Then find a new strategy for the king where the king only needs to ask a question of any two of the three suitors in order to pick the bridegroom.

This can be the simplest answer for this question:

If the King asks all three men the same question, “Are you the Commoner?”, he will receive one of two possibilities of answers. Either {Yes, No, No} or {Yes, Yes, No} or any permutation of the two. This is because the Knight will always answer “No”, the Knave will always answer “Yes”, and the Commoner will answer either “Yes” or “No”.

At this point, the king only has the choose the unique answer in the set of answers he receives. If the answer was {Yes, Yes, No}, he will choose the man who answered “No” and his daughter will marry the Knight, if it was {Yes, No, No}, he would choose the man who answered “Yes” and his daughter would marry the Knave. Regardless, with this strategy, his daughter would never have to marry a commoner and the kingdom would be safe once again.

Answer To The follow-up Question

Think of each of the the three as A, B, and C.

If we ask A and C, “Does B ever lie?”. We will receive 3 possibilities of answers { Yes, Yes}, {Yes, No}, or {No, Yes}. Notice we will never get {No, No}. This is because A and C could be:

- Commoner and the Knight, meaning the Knight will Answer “Yes”
- Commoner and the Knave, meaning the Knave will Answer “Yes”
- Knight and the Knave, meaning they will never agree.

If the King receives {Yes,Yes} from A and C, he should choose B.

If the King receives {Yes, No} or {No, Yes}, he should choose the man who answered “Yes”.

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »