SOLUTION: The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values o

Question 548396: The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values of d
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values of d?

The three smallest sums are 
a+b, which is 1.
a+c, which is 2.
b+c, which is 3.

The next larger sum is a+d=4
 
We solve this system of 3 equations in 3 unknowns:

a + b     = 1
a     + c = 2
    b + c = 3

and get a=0, b=1, and c=2

Since we know that 

a + d = 4

we substitute 0 for a, and get:

0 + d = 4
    d = 4

So the only values possible are a=0, b=1, c=2, and d = 4

Answer: d can only be 4.

Edwin

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