SOLUTION: 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

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
RELATED QUESTIONS
Find all sets S , if any, such that S ⊆ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } and S (answered by Edwin McCravy)

A student was asked to form two-digit numbers using the following digits:... (answered by ikleyn)

How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that... (answered by Edwin McCravy)

A wheel is marked off into 8 sections numbered 1 to 8. The numbers 1, 4, and 7 are... (answered by Edwin McCravy)

Bonus: The number 15 is the smallest positive number which is a sum of two consecutive... (answered by greenestamps)

The following sets represent the numbers that can be used on little league jerseys.... (answered by Fombitz)

David wants to arrange the twelve numbers from 1 to 12 in a circle so that any two... (answered by Edwin McCravy)

tudent was asked to form two-digit numbers using the following digits: 0,1,2,3,4,5,6,7,... (answered by ewatrrr,ikleyn)

student was asked to form two-digit numbers using the following digits: 0,1,2,3,4,5,6,7, (answered by ewatrrr,ikleyn)