More "knights" and "liars" These problems are generally known as the "knights and knaves" problems, but the two words are similar enogh looking to confused, so I call the knaves liars :) Sink your teeth into this one: http://www.flooble.com/perplexus/show.php?pid=32 levik Monday, April 29, 2002 Each liar said they were between a knight & a liar. This means that no liar was next to a knight and a liar, which implies that nowhere was a liar sitting next to another liar. (They could all have been liars, but we have at least two knights). Each liar was then surrounded by 2 knights (KLK). Each knight said to be between a liar and a knight, which would give us 15 sets of KLK. However, 2 of the knights got it wrong, meaning they were either sitting next to 2 liars, or 2 knights. Assume one was sitting next to 2 knights, giving a KLKKKLK combination. This extra knight means that we have to remove another person somewhere else, to leave use with 45 people. Removing a liar gives use 2 more knights who got it wrong. Removing a knight from the middle of a KLKKLK combination gives us a knight sitting next to 2 liars, who got it wrong. Similarly considering the situation when we remove a knight leaving a knight between two liars, we have to add a knight sitting next to two other knights. To conclude, if you're still with me, we have 15 liars and 30 knights, seated almost in a KLK KLK KLK ... combination, but with one knight out of place. Paul Viney Paul Viney Monday, April 29, 2002 Yep.  Almost exactly the same argument I came up with. Paul Brinkley Tuesday, April 30, 2002   Fog Creek Home