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?
Both the questions I've posted here I've sat around and invented myself. It seems to take quite a lot of time as I try really hard not to include redundant conditions that make the puzzle too easy, and I try to make my solution descriptive enough to be understood - plus I like making puzzles that aren't blatantly easy. ;-) Plus, as I'm making the puzzles up myself, I'm totally paranoid that I've made a logical error somewhere and my question is unsolvable or my answer is just plain wrong. Heh. I spend ages checking and rechecking everything before submitting because of this... Hey-ho.
Does anyone else feel this about their problems, or is everyone else just posting problems that have been around for ages, or they've found elsewhere (I know I've seen several of them elsewhere...)? Are the questions verified as actually being solvable when they're posted here?
(And lastly: nice analysis TomM!)
Okay - I have to ask
