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arithmetic – Get the treasure from an island of knights and a joker


You’ve got discovered 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, certainly one of whom is a joker and the remainder of whom are knights. (As standard in these sorts of puzzles, knights all the time inform the reality, and jokers can reply nevertheless they need.) All the islanders know who the joker is and the place the treasure is buried. When you can solely ask every islander one sure/no query, and you may solely dig up one sq. meter of the island, how will you assure that you just retrieve the treasure?

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

Bonus 2: Is there a method that works if it’s a must 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.
  • When 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.
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