SOLUTION: Mr. X has five objects, all having different weights from 1 through 5 kg. If he weights them three at a time, what is the largest possible number of different weights he can have?

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Question 1043178: Mr. X has five objects, all having different weights from 1 through 5 kg. If he weights them three at a time, what is the largest possible number of different weights he can have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Since 5C3 is only 10, we will just list them all, 
add them and count the number of different sums 
of weights:

1.  1+2+3 = 6
2.  1+2+4 = 7
3.  1+2+5 = 8
4.  1+3+4 = 8
5.  1+3+5 = 8
6.  1+4+5 = 10
7.  2+3+4 = 9
9.  2+3+5 = 10
9.  2+4+5 = 11
10. 3+4+5 = 12

So there are 7 different sums of weights, 

{6,7,8,9,10,11,12}

Edwin