A number of Knights and Liars went on a camping trip. Having pitched their tents for the night at the end of a long day's hike, Thomas (the best cook by far) settled down near the camp fire to make stew whilst everyone else sat in a circle around him, watching. Looking around, Thomas noticed that each person seemed to be sat between two people they knew, whereas Thomas himself knew no-one except his good friend Richard. 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. Thomas 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 everyone else and always receiving the same reply, he turned to Richard and asked the question once more. Surprisingly, Richard answered differently to everyone else.
Thinking for a moment, Thomas asked Richard: "Are you sitting between two Knights?", to which Richard smiled and gave the same reply as he had previously.
Nodding, Thomas declared: "So, the Knights are outnumbered by the Liars here!", and turned back to making the stew once more.
If "n" people in total went on the camping trip, how many Knights and Liars are there, and what are Thomas and Richard?
(In reply to
re: Okay - I have to ask by Happy)
Thanks!
I'm totally paranoid about getting them wrong too, but the idea of this one (an unspecified number of knights/liars in a circle, no specific information on the actual answers given, plus an extra character who is himself unknown to be a liar or knight - all this combining to make a simplicity that seemed far too minimal to contain an actual solution) has been floating around my head for about a week now, since reading the other knights/liars problems here - I just *had* to come up with something for it. It's taken me ages to come up with questions and a format that worked. Plus I had my own aesthetic parameters I wanted to stick to (e.g. Thomas just making the one declarative statement at the end) which confounded me for a while... Ah well.
Funnily enough, the tricky part for me when posting this was not phrasing the problem or solution, but remembering which character was Richard and which was Thomas! :-D I'd been working on the problem for so long that everything else was well known to me, but I just made the names up on the spot and I kept getting them confused, totally messing up my attempts to detail out a solution. Ha. Typical... ;-)
Anyway - that's why I was interested in other people's questions...
Glad the puzzle was fun. Or at least, was actually solvable... ;-)
re(2): Okay - I have to ask
