How many different integers can be expressed as the sum of three different numbers in the set (1,2,3,4,5,6,7)?

Can anyone explain this one to me???
Thank you!

1 answer

The smallest integer that can be represented is 1+2+3=6
The largest integer that can be represented is 5+6+7=18
Every integer in between can be represented from the two above by replacement of one or more numbers.
The total number of different integers that can be represented is therefore:???
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