The Magician

Problem:

Magician David Blaine and his assistant perform the following trick. There is a circle drawn on a blackboard. A member of the audience marks 2017 different points on the circle, then the assistant erases one of them. After that, David Blaine enters the room for the first time, looks at the drawing and shows a semicircle that contains the erased point. How can they agree on a strategy for this trick?

Solution

Here is one of the possible solutions. Consider 2017 arcs between the points. Let AB be the longest among them (if there is more than one, choose it arbitrarily), assume AB goes clockwise. Then the assistant will erase A. Now, when David Blaine enters the room, there is exactly one longest arc with the right endpoint B. Let C be the left endpoint. Then David Blaine can simply show the semicircle that starts at C and goes clockwise.