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?

If a person is a Knight, then the two persons sitting beside him must be a Knight and a Liar.  But if a person is a Liar, that person must have a Knight sitting on each side. (A liar can't have Liars on both sides because everyone would then be a Liar, hence no Knights).

Beginning with a Knight in the second chair.  The first and third chairs must be filled with opposites, so place a Liar in 1 and a Knight in 3.  Chair 4 must now be a Liar and Chair 5 a Knight.  Chair 6 is now a Knight and Chair 7 a Liar.

A pattern evolves --> L K K L K K L K K L K K L K K . . .

Continuing with the pattern, we must find an odd number between 22 and 28 which contains a Liar.  This occurs at 25.  Thus chair 25 becomes the repetition of Chair 1.

Thus, there are 24 chairs - 8 Liars, 16 Knights.

Posted by hoodat on 2011-06-14 20:25:50