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How many unique sums can be formed by adding any three different numbers from the set $\{4,6,8,10,12,14,16\}\,?$

 Aug 27, 2023
 #1
avatar+128406 
+1

 

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  

 

 

cool cool cool

 Aug 27, 2023

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