Brilli the Fortune Teller

Discrete Mathematics Level 5

Brilli the ant states that "Given any set of 30 distinct integers from 1 to 50 (inclusive), there must exist 2 integers whose absolute difference is exactly \(N\)."

What is the sum of all possible values of \(N\) in which the statement is always true?

Details and assumptions

You may use the fact that \( \frac{30 \times 29} {2} = 435 \).


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