Question 489206
Yes, if and only if n is a divisor of 2010: n=1,2,3,5,67.
Because there are an even number in the entire set, any divisor n of 2010 will allow you to creat n subsets of equal size and with equal totals.
Use the "Gauss in grade school" trick to ensure that all subsets total a multiple of 2011:
A1 gets 1 and 2010, A2 gets 2 and 2009, etc., repeating A1 after An in this cycle.
n=1 is a trivial case, but meets the requirements.
Any n not a divisor will fail to have the same size sets.