Four distinct integers $a$, $b$, $c$ and $d$ have the property that when added in pairs, the sums 10, 18, 19, 20, 21, and 29 are obtained. What are the four integers in increasing order? (place a comma and then a space between each integer)
+128475 Let the integers in increasing order be a, b, c, d
All we know for sure is that
a + b = 10
a + c = 18
b + d = 21
c + d = 29
Subtracting the first equation from the second we have that c - b = 8 ⇒ c = 8 + b
Either a + d = 19 or b + c = 19
Let's assume the second is true
Then 2b + 8 = 19 but b isn't an integer here
So
a +d = 19
And
b + c = 20
So
b + 8 + b = 20
2b + 8 = 20
2b =12
b = 6
a = 4
c= 14
d = 15
So
a b c d
4 6 14 15
