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1707 (Posted on 2012-08-23) Difficulty: 3 of 5
In how many distinct ways can 1707 be represented as a sum of 3 squares?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution solution | Comment 1 of 4

The following solution assumes the 3 squares are members of the set of positive integers and solely represented by such and the only function/operator to be used is the arithmetic plus (+). 

If the three squares are a, b, and c, and order doesn't matter, i.e., a+b+c is the same as a+c+b, b+a+c, b+c+a, c+a+b, and c+b+a, then there are 6 ways that 3 squares can represent 1707:

(1) 1+25+1681 = 12+52+412 = 1707
(2) 25+841+841 = 52+292+292 = 1707
(3) 49+289+1369 = 72+172+372 = 1707
(4) 121+361+1225 = 112+192+352 = 1707
(5) 121+625+961 = 112+252+312 = 1707
(6) 169+169+1369 = 132+132+372 = 1707

If each permutation is to be considered distinct, then there are 6 permuatations for each set where all 3 squares are different from each other and 3 for each set where 2 of the 3 squares are the same, for a total of 30 distinct ways.

 

Edited on August 23, 2012, 12:41 pm
  Posted by Dej Mar on 2012-08-23 12:35:38

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