From New Scientist #2357, 24th August 2002 [link]
Frances and Matthew are playing a game of cards. There are 30 cards in the game, numbered 1, 2, 3, …, 30 and each player has 15 [cards] at the start of the game. Frances has 5, 6, …, 16 and 28, 29, 30, while Matthew has 1, 2, 3, 4 and 17, 18, …, 27.
The game consists of 15 rounds. In each round the player who won the previous round goes first, except that in the first round Frances goes first. A round consists of the players alternately taking a card from their hand and putting it face up on the table. When all cards are on the table, the last two to be put on the table are compared and the player who put the higher of those two cards wins the round. The two cards that were compared are then discarded from the game and the players pick up their remaining cards; they then play the next round. Frances and Matthew are both superb players, playing as well as anyone could.
Question 1: At the end of the game, how many rounds had Frances won?
On another occasion they used 100 cards. Frances started with 28, 29, …, 37 and 61, 62, …, 100, and Matthew with the other fifty cards.
Question 2: At the end of the game, how many rounds had Frances won?
On a third occasion they used 200 cards. Frances started with 76, 77, …, 130 and 156, 157, …, 200, and Matthew with the other 100 cards.
Question 3: At the end of the game, how many rounds had Frances won?
Enigma 1252 is also called “Cards on the table”.