Question 269228: You wish to split the numbers [1,2,3,4,5,6,7,8] into two sets of 4 numbers, such that the following 2 conditions are satisfied.
• The sums of the numbers in both sets are equal
• The sums of the squares of the numbers in both sets are equal
I have found the two sets of nymbers [1,4,6,7] and [2,3,5,8] but i cannot find a relationship between the sets that will enable me to split the original list.
Help please !!
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! You've actually solved the problem. The numbers in the two sets need to add up to a common total and their squares also need to add to a common total:
Set A = {1,4,6,7}
Set B = {2,3,5,8}
Sum of A's elements is 1+4+6+7 = 18
Sum of B's elements is 2+3+5+8 = 18
Squares of A = {1,16,36,49}
Squares of B = {4,9,25,64}
Sum of A squares is 1+16+36+49 = 102
Sum of B squares is 4+9+25+64 = 102
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