Petr and Karel played a series of chess games. They agreed that a player would add 3 points for a win, subtract 2 points for a loss, and no points would be awarded for a draw. Their friends wanted to know how many games Petr and Karel had played and who was currently leading, but they only found out that Petr won six times, drew twice, lost several times, and that Karel has exactly 9 points. How many games have the boys played, and who is currently leading?

(M. Volfová)
Karel had to win so many times that after subtracting 12 points for 6 losses, he still had 9 points left. Therefore, he must have earned $9+12=21$ points from his wins, which corresponds to 7 wins. Thus, Petr lost 7 times. From the problem, we also know that Petr drew twice and won six times, so he has a total of $6 \cdot 3 + 2 \cdot 0 - 7 \cdot 2 = 4$ points.

The boys played $6+2+7=15$ games, and Karel is in the lead.

Evaluation. 4 points for the correct reasoning about the number of Karel's wins; 1 point for the justified observation that Karel is in the lead; 1 point for determining the number of games played.

Note. Contestants do not have to determine Petr's score. The observation that Karel is in the lead can also be justified simply by comparing Karel's seven wins with Petr's six wins.