Problem 8 · Assume and find a contradiction · 5 points
Made by AI and not reviewed by a real person.
Four islanders are each either a knight (always tells the truth) or a liar (always lies): Ada says, “Exactly one of Ben, Cora, and Drew is a knight”; Ben says, “Ada and Cora are the same kind”; Cora says, “Ben and Drew are different kinds”; and Drew says, “Ada is a liar.” How many of the four are knights?
- 4 knights
- 3 knights
- 1 knight
- 2 knights
- It cannot be determined
Show a hint
- Before counting knights, track who would have to be the same kind or different kinds.
- Suppose Ada tells the truth. What would Drew be, and could Ben and Cora then be different kinds?
Show the answer and solution
Answer: D — 2 knights
If Ada were a knight, Drew would be a liar. Cora’s claim would then be true exactly when Ben is a knight, so Ben and Cora would be the same kind. But Ada’s claim requires exactly one of them to be a knight—a contradiction. Thus Ada is a liar and Drew is a knight. Ben’s claim now means Ben is a knight exactly when Cora is a liar, so one of them is a knight: 2 knights in all. “It cannot be determined” is tempting because either Ben or Cora could be the knight, but the total is fixed.