You’ve realized that there is treasure buried someplace on a small island, however not precisely the place. The island is an ideal circle with a radius of 25 meters. There are 15 islanders there, one in all whom is a joker and the remainder of whom are knights. (As common in these sorts of puzzles, knights all the time inform the reality, and jokers can reply nevertheless they need.) All of the islanders know who the joker is and the place the treasure is buried. If you may solely ask every islander one sure/no query, and you may solely dig up one sq. meter of the island, how are you going to assure that you simply retrieve the treasure?

Bonus 1: Is there a means that works even when the islanders do not know who the joker is?

Bonus 2: Is there a means that works if you need to ask all 15 questions earlier than listening to any of the solutions?

To preemptively shut some loopholes:

• The treasure is a single level with negligible space.
• If you make any of the islanders’ heads explode by asking them a query that they cannot reply with a sure or a no, you may be kicked off of the island with out having the ability to dig anyplace.