Maths about number cards - IMO problem

Logic Level 4

3 people: \(A, B, C\) participate in a cards game. There are 3 cards, and there is positive integer number on each card (the numbers are different). After each draw, each player will receive randomly one card from these cards, and the number on the cards are the score of them after each draw. After 2 or more draws, A receives 20 points in total, B receives 10 points, C receives 9 points.

If in the last draw, B received the card with highest score. So in the first draw, who receive the card with the score in the middle? Give the answer as the product of b and the number of the person who received this card in the first draw of \A, B, C \(A=1,B=2,C=3\).


If \(a, b, c\) are the numbers on each card, and \(a<b<c\), the score in the middle is \(b\).

For example, if \(B\) received the \(\text{b-point-card}\), your answer is the product of 2 and \(b\).


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