Question 115
There are $2008$ pieces each of red cards and white cards. These $4016$ cards are mixed and put on a pile. Then, each of the $2008$ participating players is dealt $2$ cards from the pile, and then all of the players are seated in a circular arrangement facing interior of the circle. At every turn of the game each player will perform the following act simultaneously:
If a player possesses at least one red card, he will pass one red card to the player sitting next to him on the left-side. If a player does not have any red card in his possession, then he will pass one white card to the player on his left.
Determine the maximum possible number of turns necessary to reach for the first time the situation where every player will have one each of red and white cards.
If a player possesses at least one red card, he will pass one red card to the player sitting next to him on the left-side. If a player does not have any red card in his possession, then he will pass one white card to the player on his left.
Determine the maximum possible number of turns necessary to reach for the first time the situation where every player will have one each of red and white cards.