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 Knights and Liars of the Round Table (Posted on 2011-06-10)
The Knights and Liars of the Round Table is a group of knights and liars. Each person is either a knight or a liar, and at least one of them is a knight. The number of knights and liars in all is an even number greater than 20, but less than 30. One day, they were sitting around a round table. Each one of them said, "I am sitting between two people of different types." How many people are there in all, and how many are there of each type?

 See The Solution Submitted by Math Man Rating: 3.0000 (1 votes)

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 solution | Comment 2 of 4 |

A Knight would be amid a Knight and a Liar: KKL.

A Liar would be amid either two Liars or two Knights: KLK or LLL.

As there are is at least one knight, the Liar must be between two Knights, thus the patter must be: KKLKKLKKL...

As the number is would have both factors of 2 (given the number is even) and 3 (given the pattern), the number would be divisible by 6. Since it is exclusively between 20 and 30, the number must be 24. With the ratio of 2 Knights to 1 Liar, the number of Knights would be 16 and the number of Liars would be 8.

 Posted by Dej Mar on 2011-06-10 21:51:15

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