monving balls in 2018 boxes
Source: 1st Mathematics Regional Olympiad of Mexico Northwest 2018 P1
September 6, 2022
combinatorics
Problem Statement
There are boxes , , ,..,. The -th box contains balls.
A move consists of the following steps:
a) Choose an integer greater than and choose a multiple of .
b) Take a ball from each of the consecutive boxes , , and move the balls to the box .
With these movements, what is the largest number of balls we can get in the box ?