Source: Stanford Math Circle Sunday May 30, 2010
Problem: A circle is divided into 6 sectors. The numbers 1, 0, 1, 0, 0, 0 are written into the sectors in the counter clock-wise direction. You may increase any two neighboring numbers by 1. Is it possible to make all of the numbers equal?
Disclaimer: Think simple. Very simple problem. Solved it in less than 30 seconds. :)
Solution: Posted by Aman in comments!! He claims he took less than 10 seconds \m/ \m/. This is one thing where it feels good to win, but feels awesome to be defeated \m/ \m/