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Omni-MATH / In a game, N people are in a room. Each of them simultaneously writes down an integer between 0 and 100 inclusive. A person wins the game if their number is exactly two-thirds of t…

Problem

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problem

In a game, NN people are in a room. Each of them simultaneously writes down an integer between 0 and 100 inclusive. A person wins the game if their number is exactly two-thirds of the average of all the numbers written down. There can be multiple winners or no winners in this game. Let mm be the maximum possible number such that it is possible to win the game by writing down mm. Find the smallest possible value of NN for which it is possible to win the game by writing down mm in a room of NN people.
Plain-text mathematical notation (without MathML)
In a game, N people are in a room. Each of them simultaneously writes down an integer between 0 and 100 inclusive. A person wins the game if their number is exactly two-thirds of the average of all the numbers written down. There can be multiple winners or no winners in this game. Let m be the maximum possible number such that it is possible to win the game by writing down m. Find the smallest possible value of N for which it is possible to win the game by writing down m in a room of N people.
Original LaTeX notation
In a game, \(N\) people are in a room. Each of them simultaneously writes down an integer between 0 and 100 inclusive. A person wins the game if their number is exactly two-thirds of the average of all the numbers written down. There can be multiple winners or no winners in this game. Let \(m\) be the maximum possible number such that it is possible to win the game by writing down \(m\). Find the smallest possible value of \(N\) for which it is possible to win the game by writing down \(m\) in a room of \(N\) people.

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Source and history

task_id
ee1a7ce1-e14b-537d-a83f-6b1b95b21b19
task_key
test--ee1a7ce1-e14b-537d-a83f-6b1b95b21b19
task_revision_id
1
config / split
/ test

Official source

initial import