IMO Shortlist 1974 problem 1

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Dodao/la: arhiva
2. travnja 2012.
Three players A,B and C play a game with three cards and on each of these 3 cards it is written a positive integer, all 3 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 (\geq 2) of games we find out that A has 20 points, B has 10 points and C has 9 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).
Izvor: Međunarodna matematička olimpijada, shortlist 1974