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How many different positive integers can be represented as a difference of two distinct members of the set $\{1, 2, 3, 4, 5, 6 \}$?

 Mar 9, 2023
 #1
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Well, the problem states you can only have positive answers so you can only subtract downward. Therefore, excluding one, each number has one minus itself differences. For example, 2 would have 1 difference (2-1).  You would have 1+2+3+4+5 = 15

 

Answer: 15

 Mar 9, 2023
 #2
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To find the number of different positive integers that can be represented as a difference of two distinct members of the set {1,2,3,4,5,6}, we can list all possible differences and count the distinct values.

The possible differences are:

 

1-2 = -1 1-3 = -2 1-4 = -3 1-5 = -4 1-6 = -5 2-3 = -1 2-4 = -2 2-5 = -3 2-6 = -4 3-4 = -1 3-5 = -2 3-6 = -3 4-5 = -1 4-6 = -2 5-6 = -1

 

So, there are 15 possible differences, but some of them are negative, so we need to take the absolute value to get the distinct positive integers:

 

|-1| = 1 |-2| = 2 |-3| = 3 |-4| = 4 |-5| = 5

 

Therefore, there are 5 different positive integers that can be represented as a difference of two distinct members of the set {1,2,3,4,5,6}: 1, 2, 3, 4, and 5.

 Mar 9, 2023

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