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The maximum difference is 18, so the answer will naturally be between 1 and 18.  

It is impossible to represent an odd number difference, thus the differences must always be even.  Numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, for a total of 9 possibilities.  

Proof that you cannot get an odd difference with only odd numbers.  

If a is an odd number then it can be written as 2x+1, where x is an integer.  

If b is an odd number, then it can be written as 2y+1, where y is an integer.  

a-b (odd minus odd) = 2x-1-(2y+1) = 2x-2y.  Factoring, we have 2(x-y).  Because both x and y are integers, 2(x-y) will always be even, never odd.  

     ways to make a difference of

9                                                       2

8                                                       4

7                                                       6

6                                                       8

5                                                     10

4                                                     12

3                                                     14

2                                                     16

1                                                     18

9  distinct    positive differences

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