TOT 1998 Spring AJ6 10 people, circle table, 100 nuts totally, 10 nuts at end
Source:
May 11, 2020
gamegame strategycombinatorics
Problem Statement
people are sitting at a round table. There are some nuts in front of each of them, nuts altogether. After a certain signal each person passes some of his nuts to the person sitting to his right . If he has an even number of nuts, he passes half of them; otherwise he passes one nut plus half of the remaining nuts. This procedure is repeated over and over again. Prove that eventually everyone will have exactly nuts. (A Shapovalov)