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Omni-MATH / There are 2018 players sitting around a round table. At the beginning of the game we arbitrarily deal all the cards from a deck of K cards to the players (some players may receive …

Problem

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problem

There are 20182018 players sitting around a round table. At the beginning of the game we arbitrarily deal all the cards from a deck of KK cards to the players (some players may receive no cards). In each turn we choose a player who draws one card from each of the two neighbors. It is only allowed to choose a player whose each neighbor holds a nonzero number of cards. The game terminates when there is no such player. Determine the largest possible value of KK such that, no matter how we deal the cards and how we choose the players, the game always terminates after a finite number of turns.
Plain-text mathematical notation (without MathML)
There are 2018 players sitting around a round table. At the beginning of the game we arbitrarily deal all the cards from a deck of K cards to the players (some players may receive no cards). In each turn we choose a player who draws one card from each of the two neighbors. It is only allowed to choose a player whose each neighbor holds a nonzero number of cards. The game terminates when there is no such player. Determine the largest possible value of K such that, no matter how we deal the cards and how we choose the players, the game always terminates after a finite number of turns.
Original LaTeX notation
There are $2018$ players sitting around a round table. At the beginning of the game we arbitrarily deal all the cards from a deck of $K$ cards to the players (some players may receive no cards). In each turn we choose a player who draws one card from each of the two neighbors. It is only allowed to choose a player whose each neighbor holds a nonzero number of cards. The game terminates when there is no such player. Determine the largest possible value of $K$ such that, no matter how we deal the cards and how we choose the players, the game always terminates after a finite number of turns.

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Source and history

task_id
c76d7b40-3457-5ecb-8c79-98ffe0e1a5d9
task_key
test--c76d7b40-3457-5ecb-8c79-98ffe0e1a5d9
task_revision_id
1
config / split
/ test

Official source

initial import