(I) Determine the total number of ways in which 2011 (base ten) is expressible as the sum of squares of N distinct positive integers, whenever N = 3, 4, 5,...., 8, 9,10
(II) Keeping all the other conditions in (I) unaltered, what are the respective total number of ways if the N positive integers need not be distinct?
The following table shows the total number of ways where
s
_{1}^{2} + s
_{2}^{2} + s
_{3}^{2} + ... + s
_{N}^{2} sums to 2011, such that
s
_{1} < s
_{2} < s
_{3} < ... < s
_{N}. (I.e., it is assumed that the problem is asking for the number of combinations of squares that sum to 2011 and not the number of permutations.)
N (I)
3 : 3
4 : 34
5 : 343
6 : 1165
7 : 2296
8 : 3425
9 : 4402
10 : 4739
Edited on June 27, 2011, 11:22 am

Posted by Dej Mar
on 20110627 11:18:20 