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Omni-MATH / Let k be a positive integer. The organising commitee of a tennis tournament is to schedule the matches for 2k players so that every two players play once, each day exactly one matc…

Problem

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problem

Let kk be a positive integer. The organising commitee of a tennis tournament is to schedule the matches for 2k2k players so that every two players play once, each day exactly one match is played, and each player arrives to the tournament site the day of his first match, and departs the day of his last match. For every day a player is present on the tournament, the committee has to pay 11 coin to the hotel. The organisers want to design the schedule so as to minimise the total cost of all players' stays. Determine this minimum cost.
Plain-text mathematical notation (without MathML)
Let k be a positive integer. The organising commitee of a tennis tournament is to schedule the matches for 2k players so that every two players play once, each day exactly one match is played, and each player arrives to the tournament site the day of his first match, and departs the day of his last match. For every day a player is present on the tournament, the committee has to pay 1 coin to the hotel. The organisers want to design the schedule so as to minimise the total cost of all players' stays. Determine this minimum cost.
Original LaTeX notation
Let $k$ be a positive integer. The organising commitee of a tennis tournament is to schedule the matches for $2k$ players so that every two players play once, each day exactly one match is played, and each player arrives to the tournament site the day of his first match, and departs the day of his last match. For every day a player is present on the tournament, the committee has to pay $1$ coin to the hotel. The organisers want to design the schedule so as to minimise the total cost of all players' stays. Determine this minimum cost.

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Source and history

task_id
95e34ce8-4f33-52ba-8686-0819166c511c
task_key
test--95e34ce8-4f33-52ba-8686-0819166c511c
task_revision_id
1
config / split
/ test

Official source

initial import