MathDB
Card game with np cards in p rounds

Source: Romanian TST 2002

February 5, 2011
combinatorics proposedcombinatorics

Problem Statement

There are nn players, n≥2n\ge 2, which are playing a card game with npnp cards in pp rounds. The cards are coloured in nn colours and each colour is labelled with the numbers 1,2,…,p1,2,\ldots ,p. The game submits to the following rules: each player receives pp cards. the player who begins the first round throws a card and each player has to discard a card of the same colour, if he has one; otherwise they can give an arbitrary card. the winner of the round is the player who has put the greatest card of the same colour as the first one. the winner of the round starts the next round with a card that he selects and the play continues with the same rules. the played cards are out of the game. Show that if all cards labelled with number 11 are winners, then p≥2np\ge 2n.
Barbu Berceanu
Back to ProblemsView on AoPS