View Full Version : knights and liars... (logics puzzle)

9th January 2003, 08:47
Ok, after having posted some math puzzles, perhaps now is the time for a logics puzzle... :)
(to be honest, I'm strugling a bit with this one...)

A number of knights and liars went on a camping trip. Liars only lie and knigts only speak the truth.

Having pitched their tents for the night at the end of a long day's hike, Jan settled down near the camp fire to make stew whilst everyone sat in a circle around him.

Looking around, Jan noticed that each person seemed to be sat between two people they knew, whereas Jan himself knew no-one except his good friend Bart.
So, getting everyone's attention, he asked a person at random in the circle the following question:
"You and the two people that are sitting next to you: is there an odd number of liars in that little group ?"
The person replied.
Jan then asked another person at random, and that person gave the same reply as the first. Again and again he asked, and every time the reply was the same. Finally, having asked every one else and always receiving the same reply, he turned to Bart and asked the question once more.
Surprisingly, Bart answered differently to everyone else.

Thinking for a moment, Jan asked Bart: "Are you sitting between two knights ?", to which Bart smiled and gave the same reply as he had previously.

Nodding, Jan declared: "So, the knights are outnumbered by the liars here !"

If "n" people in total went on the camping trip, how many knights and liars are there, and what are Jan and Bart ?

Any hints on taking this on ? We don't know any of the replies, nor if Jan is a liar or not (in which case the final statement could be affected)
Thanks !


9th January 2003, 14:15
still playing with it, but I'm suspecting that THIS:

Nodding, Jan declared: "So, the knights are outnumbered by the liars here !"

is a lie, therefor Jan is a liar. Just a guess...gotta play w/ it first.

Edit: Oh, you said that already.

11th January 2003, 08:00
Well, I tried writing it down for a number of situations. If there are 4 persons in total (thus including Jan), than there appear to be 2 solutions... 5 persons yields no solutions, 6 persons gives one solution; but I can't seem to find one for 7 or 8...
(trying to deduct a pattern from the solutions I found thus far)...