Sergei just came back from MOP — Mathematical Olympiad Summer Program, where he was a grader. The first question I asked him was, “What was your favorite math problem there?” Here it is:
There are wisemen, hats and rooms. Hats are of different color and there are enough hats of each color for every wisemen. There are enough rooms, so that you can assign a different room for every color. At some moment in time the sultan puts hats on the wisemen’s heads, so as usual they see all other hats, but do not see their own hat color. At the same time, each wiseman has to choose a room to go to. If two wisemen have the same hat color, they should go to the same room. If they have different hat colors, they should go to different rooms. What strategy should the wisemen decide upon before this event takes place?
Oh, I forgot to mention the most interesting part of this problem is that you shouldn’t assume that the number of wisemen or hats or rooms is finite. You should just assume that they have the power of choice.Share: