# Push Z150 to the Quiet Western Front

Discrete Mathematics Level 2

If we pick 77 numbers randomly from the set $$\{1,2,3,4,...,150\}$$, we are guaranteed to have at least $$k$$ pairs where the difference between the two numbers is 19. What is the maximum possible value of $$k?$$

Please treat a pair as a combination, not a permutation.

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