MathDB

There are 2010 boxes labeled

B_1,B_2,\dots,B_{2010},

and

2010n

balls have been distributed among them, for some positive integer

n.

You may redistribute the balls by a sequence of moves, each of which consists of choosing an

i

and moving exactly

i

balls from box

B_i

into any one other box. For which values of

n

is it possible to reach the distribution with exactly

n

balls in each box, regardless of the initial distribution of balls?

B3