You've learned that there's treasure buried somewhere on a small island, but not exactly where. The island is a perfect circle with a radius of 25 meters. There are 15 islanders there, one of whom is a joker and the rest of whom are knights. (As usual in these kinds of puzzles, knights always tell the truth, and jokers can answer however they want.) All of the islanders know who the joker is and where the treasure is buried. If you can only ask each islander one yes/no question, and you can only dig up one square meter of the island, how can you guarantee that you retrieve the treasure?
Bonus 1: Is there a way that works even if the islanders don't know who the joker is?
Bonus 2: Is there a way that works if you have to ask all 15 questions before hearing any of the answers?
To preemptively close some loopholes:
- The treasure is a single point with negligible area.
- If you make any of the islanders' heads explode by asking them a question that they can't answer with a yes or a no, you'll be kicked off of the island without being able to dig anywhere.