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 :)
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.
Yep. Almost exactly the same argument I came up with.
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