Imagine you and 99 other people are randomly assigned a number between 1 and 100. Imagine too that there is a room containing 100 boxes, that each box has also been randomly assigned a number between 1 and 100, and that these numbers are hidden inside each box. Everyone is allowed to check up to 50 boxes to see if one can find one’s assigned number. If all 100 persons correctly find their respective boxes, each person gets $101. If at least one person is unable to find his or her assigned box, then everyone gets nothing. How much should you pay to play this game? The solution is here:
Hat tip to the amazing Ada Swanson for the pointer.