MathDB
2022 Combo Div 2 P5

Source:

February 28, 2022
combinatorics

Problem Statement

Daniel, Ethan, and Zack are playing a multi-round game of Tetris. Whoever wins 1111 rounds first is crowned the champion. However Zack is trying to pull off a "reverse-sweep", where (at-least) one of the other two players first hits 1010 wins while Zack is still at 00, but Zack still ends up being the first to reach 1111. How many possible sequences of round wins can lead to Zack pulling off a reverse sweep?
Proposed by Dilhan Salgado