MathDB

Initially, there are

n

red boxes numbered with the numbers

1,2,\dots ,n

and

n

white boxes numbered with the numbers

1,2,\dots ,n

on the table. At every move, we choose

2

different colored boxes and put a ball on each of them. After some moves, every pair of the same numbered boxes has the property of either the number of balls from the red one is

6

more than the number of balls from the white one or the number of balls from the white one is

16

more than the number of balls from the red one. With that given information find all possible values of

n

Problem Statement