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Omni-MATH / Mattis is hosting a badminton tournament for 40 players on 20 courts numbered from 1 to 20. The players are distributed with 2 players on each court. In each round a winner is dete…

Problem

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problem

Mattis is hosting a badminton tournament for 4040 players on 2020 courts numbered from 11 to 2020. The players are distributed with 22 players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court 11, and the player who won on court 2020 stay in place. For the remaining 3838 players, the winner on court ii moves to court i+1i + 1 and the loser moves to court i−1i - 1. The tournament continues until every player has played every other player at least once. What is the minimal number of rounds the tournament can last?
Plain-text mathematical notation (without MathML)
Mattis is hosting a badminton tournament for 40 players on 20 courts numbered from 1 to 20. The players are distributed with 2 players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court 1, and the player who won on court 20 stay in place. For the remaining 38 players, the winner on court i moves to court i+1 and the loser moves to court i−1. The tournament continues until every player has played every other player at least once. What is the minimal number of rounds the tournament can last?
Original LaTeX notation
Mattis is hosting a badminton tournament for $40$ players on $20$ courts numbered from $1$ to $20$. The players are distributed with $2$ players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court $1$, and the player who won on court $20$ stay in place. For the remaining $38$ players, the winner on court $i$ moves to court $i + 1$ and the loser moves to court $i - 1$. The tournament continues until every player has played every other player at least once. What is the minimal number of rounds the tournament can last?

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Source and history

task_id
9a261c61-52d0-5693-9b64-ce8a01f07c35
task_key
test--9a261c61-52d0-5693-9b64-ce8a01f07c35
task_revision_id
1
config / split
/ test

Official source

initial import