Question

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet five inhabitants: Peggy, Betty, Abe, Marge and Ted. Peggy says, “Abe and Ted are both knights.” Betty says, “Abe and I are different.” Abe says that Betty is a knave. Marge tells you that it's not the case that Peggy is a knave. Ted claims that Abe and Peggy are both knights or both knaves. Can you determine who is a knight and who is a knave?

Answer 1

Betty and Ted both are knights, Peggy, Abe and Marge are knaves.

Explanation:

In the first statement Peggy says Abe and Ted are both knights, but in the second statement Betty says "Abe and I are different". If what Peggy said was truth, Betty has to be a Knave but if she is a knave she won't tell the truth. But she has told the truth and thus its makes her a Knight, and since Betty is a Knight that makes Abe a Knave. Since Abe is a Knave and Peggy said that Abe is a Knight is a Lie, and hence Peggy is also a Knave.

Next Marge says that Peggy is not a Knave and since that is a False that makes Marge also a Knave. Lastly Ted says that either Abe or Peggy is Knights or Knaves and it turns out to be both Abe and Peggy are Knaves and thats a truth and thus it makes Ted a Knight.