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AIME 2019a Problem 2

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Jenn randomly chooses a number JJ from 1,2,3,…,19,201, 2, 3,\ldots, 19, 20. Bela then randomly chooses a number BB from 1,2,3,…,19,201, 2, 3,\ldots, 19, 20 distinct from JJ. The value of B−JB - J is at least 22 with a probability that can be expressed in the form mn\frac{m}{n} where mm and nn are relatively prime positive integers. Find m+nm+n.

Dataset text AIME 1983 to 2026. Quoted with source.

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