Question 2
Let $n$ be a positive integer. There are $n$ balls numbered from 1 to $n$ and three boxes of different colours.
Find the smallest $n$ such that for every placement of the $n$ balls into the three boxes there are always, in one same box, two balls such that the difference of the numbers written on them (the larger minus the smaller) is equal to the square of an integer.
Find the smallest $n$ such that for every placement of the $n$ balls into the three boxes there are always, in one same box, two balls such that the difference of the numbers written on them (the larger minus the smaller) is equal to the square of an integer.