(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?

I worried that my interpretation is correct.  This is more about ideas.

Value of N    3   4   5    6   7   8   9    10
(I)
Times          4   1   1    1   3   6   7      8
                 13   1   1    1   3   6   6      8
                 22   5   1    1   3   5   5      8
                
                 45   1   1    2   3   6   2      8
                 45  21  1    2   3   1   2      8
(II)
                 40  25  1    1   3   0   3      8

There is something here about multiples.  Looking down the column for N=3 the values increment by 9 but corresponding values for N=9 decrement by 1.

Somewhere in my play I did find something where values in two columns could impact upon a third, sorry I didn't record it but that is somewhere in this table.

Posted by brianjn on 2011-06-27 01:08:48