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?

Any given knight must have another knight on one side and a liar on the other. It doesn't matter between left and right, as a mirror image will not affect the numbers: KKL.

The other knight, of course will have a liar on his own other side, while the liar will have a knight on both sides: LKKLK.

This in fact continues with a repeating pattern of ...KKLKKLKKL....

The number must therefore be a multiple of 3, and we're told it's even, so it's a multiple of 6 that's greater than 20 but less than 30.  It's 24. And 1/3 of them are liars and 2/3 knights, which is 8 and 16 respectively.

Edited on June 10, 2011, 1:17 pm

Posted by Charlie on 2011-06-10 13:15:51