Brilli the Fortune Teller

Probability 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 NN."

What is the sum of all possible values of NN in which the statement is always true?

Details and assumptions

You may use the fact that 30×292=435 \frac{30 \times 29} {2} = 435 .


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