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 are 1, 2, 3, and 4, what are all possible values of d?
+773 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.
Hope this helps, whymenotsmart!
