At a banquet attended by 45 Liars and Knights, everybody sat at a big round table.
At the end of the feast, each of the attendees was asked about their neighbors, and each stated that they were seated between one Liar and one Knight.
As it later turned out, two of the Knights were mistaken in their statements.
How many Knights, and how many Liars were in attendance at the banquet?
I solved it by repeating the LKK pattern until I had filled 43 seats. The 43rd seat is occupied by a Liar, since I've repeated the LKK pattern 14 times and am 1/3 through the 15th repetition. Then I put a Knight after the last Liar, so he would precede the first Liar. If two Liars are side by side, then each one would be telling the truth when saying that he has a Liar on one side and a Knight on the other. So they must be separated by a mistaken Knight. The other mistaken Knight can be inserted in between any two consecutive Knights. This is a fun puzzle.
:-)
answering Aeternus
