# Puzzle 5: Word Puzzle

30-Jan-2014: The original puzzle is broken, so here’s a replacement.

Expected difficulty Medium • Answer and solution follow below the puzzle

On an island, there are two kinds of people: knights who answer questions truthfully and knaves who answer questions falsely. You encounter five people from this island, named Alice, Bob, Charlie, Dave, and Erin. As a bored person, you want to figure out whether they are knights or knaves. When questioned, these are the answers, each answer stated by a different person. Statements in parentheses are statements that you know to be true.

Alice: At least one of us is a knight.
Bob: Exactly two of us are knights.
Charlie: At most three of us are knights.
Dave: The number of knights among us is not four.
Erin: YEAAAAAAAAAAAAAAAAAAAAAY

Which of them are knights?

Answer and solution; highlight below:

Alice and Charlie must tell at least one truth. If Bob is a knight, then Dave too; this is impossible as together with Alice and Charlie we have at least three knights. So Bob is a knave.

Since Alice and Charlie must tell at least one truth, there is at least one knight, so Alice is a knight.

If Charlie is a knave, then there are at least four knights. But Bob and Charlie are knaves, so there are at most three knights remaining, impossible. So Charlie is a knight. Thus the number of knights cannot exceed three, and so Dave is a knight, and so Erin is a knave.

Thus, the knights are Alice, Charlie, and Dave.