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How many distinct positive integers can be represented as the difference of two numbers in the set {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}?

 Dec 21, 2021
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The greatest difference we may have is 18 (19-1), and the smallest is 2. Since all of these numbers are separated by 2, we can make all of the even numbers from 2 to 18, which accounts for 9 numbers. Notice that since all of the numbers are of the form 2a+1 (where a is an integer), their difference must be divisible by two, which means we can only have even numbers. Thus, the answer is 9.

 Dec 22, 2021

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