+1678 How many unique sums can be formed by adding any three different numbers from the set $\{4,6,8,10,12,14,16\}\,?$
+129895
Consider a smaller set of numbers { 4 , 6, 8 , 10)
And we wish to choose any 2 of these
The sums are
4 6 =10
4 8 = 12
4 10 = 14
6 8 = 14
6 10 = 16
8 10 = 18
So.....we can get every even integer from 10 to 18 inclusive = (18 - 10) / 2 + 1 = 5 unique sums
So
The smallest sum in our list is
4 6 8 = 18
And the largest is
12 14 16 = 42
We can get every even integer from 18 to 42 inclusive
The number of unique sums = (42 - 18) / 2 + 1 = 24 / 2 + 1 = 12 + 1 = 13
