MathDB

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.
Proposed by Peter Novotný, Slovakia

Problem Statement