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OlympiadBench / 2040 / Let k be a positive integer. The organising committee of a tennis tournament…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Expression

is multiple answer

false

language

English

question

Let

k

be a positive integer. The organising committee of a tennis tournament is to schedule the matches for

2 k

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.

Plain-text mathematical notation (without MathML)

Let k be a positive integer. The organising committee 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 committee of a tennis tournament is to schedule the matches for $2 k$ 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.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2040
task_id: 1ae7525e-5684-524a-b691-a69576b2a0bd
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2040
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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