Ten in a circle, each says both neighbours are knaves

Question

Ten islanders, each a knight (always truthful) or a knave (always lying), sit evenly around a round table. Each of the ten says: "Both of my neighbours are knaves." How many knights can there be at the table? Find every possible number.

Accepted Answer

Either 4 or 5 knights. No other number is possible. The rules. A knight's statement is true, so both neighbours of a knight are knaves. A knave's statement is false, so at least one neighbour of a knave is a knight. Upper bound. Knights cannot sit next to each other (a knight's neighbours are knaves). Around a table of ten, that allows at most 5 knights, alternating knight, knave, knight, knave, ... Check the knaves in this pattern: each knave sits between two knights, so "both my neighbours are knaves" is false, as required. 5 works. Lower bound. Every knave needs at least one knight beside …

Ten in a circle, each says both neighbours are knaves

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