27 boxes, each has >=12 marbles May Olympiad (Olimpiada de Mayo) 2012 L1 P4
Source:
September 29, 2021
combinatorics
Problem Statement
There are boxes located in a row; each contains at least marbles. The allowed operation is transfer a ball from a box to its neighbor on the right, as long as said neighbor contains more pellets than the box from which the transfer will be made. We will say that a distribution initial of the balls is happy if it is possible to achieve, by means of a succession of permitted operations, that all the balls are in the same box. Determine what is the smallest total number of marbles with the that you can have a happy initial layout.