IMO Shortlist 1974 problem 1
Three players and play a game with three cards and on each of these cards it is written a positive integer, all numbers are different. A game consists of shuffling the cards, giving each player a card and each player is attributed a number of points equal to the number written on the card and then they give the cards back. After a number of games we find out that A has points, has points and has points. We also know that in the last game B had the card with the biggest number. Who had in the first game the card with the second value (this means the middle card concerning its value).