TopsOJ Summer 2025 - Guts Round - Problem 17

Tiger is a bad kid. Consider a word of length 6n, where n is some positive integer, consisted of the word BADKID repeated n times. If as n grows arbitrarily large, the expected amount of D's in a randomly chosen string of length 101 approaches \frac{x}{y} for relatively prime positive integers x and y, compute x+y.