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2011 = Sum of Squares (Posted on 2011-06-26) Difficulty: 3 of 5
(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?

No Solution Yet Submitted by K Sengupta    
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Part (I) Comment 2 of 2 |
The following table shows the total number of ways where
s12 + s22 + s32 + ... + sN2 sums to 2011, such that
s1 < s2 < s3 < ... < sN.  (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 2011-06-27 11:18:20

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