May 19–May 25, 2009

Problem

Each of ten girls around a circle chooses a number and tells it to the neighbor on each side. (Thus each person gives out one number and receives two numbers.) Each girl then announces the average of the two numbers she received. Remarkably, the announced numbers, in order around the circle, were 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

What was the number chosen by the girl who announced the number 6?

Solution

here

List of solvers

Tuan Le (high school); Louis Dang (undergraduate); Jacob Lewis, Koopa Koo, Ariana Dundon (graduate); Gary Raymond (staff); Marina Meila (faculty); Peiyush Jain, Lloyd Sakazaki, Adam Welly, Samuel Jessup, Mukund Tirumalai, Mike Goodman, Justin Shih, Steve Wilmarth (outside).

Tuan Le wins the prize!