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Omni-MATH / There are 21 competitors with distinct skill levels numbered 1,2,…,21. They participate in a pingpong tournament as follows. First, a random competitor is chosen to be "active", wh…

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problem

There are 21 competitors with distinct skill levels numbered 1,2,…,211,2, \ldots, 21. They participate in a pingpong tournament as follows. First, a random competitor is chosen to be "active", while the rest are "inactive." Every round, a random inactive competitor is chosen to play against the current active one. The player with the higher skill will win and become (or remain) active, while the loser will be eliminated from the tournament. The tournament lasts for 20 rounds, after which there will only be one player remaining. Alice is the competitor with skill 11. What is the expected number of games that she will get to play?
Plain-text mathematical notation (without MathML)
There are 21 competitors with distinct skill levels numbered 1,2,…,21. They participate in a pingpong tournament as follows. First, a random competitor is chosen to be "active", while the rest are "inactive." Every round, a random inactive competitor is chosen to play against the current active one. The player with the higher skill will win and become (or remain) active, while the loser will be eliminated from the tournament. The tournament lasts for 20 rounds, after which there will only be one player remaining. Alice is the competitor with skill 11. What is the expected number of games that she will get to play?
Original LaTeX notation
There are 21 competitors with distinct skill levels numbered $1,2, \ldots, 21$. They participate in a pingpong tournament as follows. First, a random competitor is chosen to be "active", while the rest are "inactive." Every round, a random inactive competitor is chosen to play against the current active one. The player with the higher skill will win and become (or remain) active, while the loser will be eliminated from the tournament. The tournament lasts for 20 rounds, after which there will only be one player remaining. Alice is the competitor with skill 11. What is the expected number of games that she will get to play?

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task_id
24f178e1-703d-5201-b431-0a2106e3b1b6
task_key
test--24f178e1-703d-5201-b431-0a2106e3b1b6
task_revision_id
1
config / split
/ test

Official source

initial import