MathDB
10 bowls with marbles in a circles

Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 1, p1

April 10, 2020
combinatorics

Problem Statement

Ten bowls are in a circle. They will go clockwise - starting somewhere filled with 1,2,3,...,91, 2, 3, ..., 9 or 1010 marbles. You can have two choices in every move . Add a marble to neighboring shells or from two neighboring shells - if both of them are not empty - remove one marble each. Can you achieve that after finally many moves in each bowl exactly 20112011 marbles lying?