Křemílek and Vochomůrka found a treasure chest. Each of them took silver coins into one pocket and gold coins into the other. Křemílek had a hole in his right pocket and lost half of his gold coins on the way. Vochomůrka had a hole in his left pocket and lost half of his silver coins on the way home. At home, Vochomůrka gave one-third of his gold coins to Křemílek, and Křemílek gave one-quarter of his silver coins to Vochomůrka. Each then had exactly 12 gold coins and 18 silver coins. How many gold and silver coins did each of them take from the found treasure?

(M. Dillingerová)
Since the loss and donation of coins always concern only one type of coin (either gold coins or silver coins), we will count their quantities separately.

Gold Coins: Vochomůrka was left with 12 gold coins, which is $\frac{2}{3}$ of his original amount. He therefore brought 18 gold coins and gave 6 to Křemílek. This left Křemílek with 6 gold coins in his pocket upon returning home, which is $\frac{1}{2}$ of his original amount. He thus brought 12 gold coins.

Silver Coins: Křemílek was left with 18 silver coins, which is $\frac{3}{4}$ of his original amount. He therefore brought 24 silver coins and gave 6 to Vochomůrka. This left Vochomůrka with 12 silver coins in his pocket upon returning home, which is $\frac{1}{2}$ of his original amount. He thus brought 24 silver coins.

Křemílek took 12 gold coins and 24 silver coins from the treasure, while Vochomůrka took 18 gold coins and 24 silver coins.

Evaluation. For the calculation of the number of coins of the first type for each character, award 2 points, i.e., a total of 4 points; for the analogous calculation of the number of coins of the second type for each goblin, award 1 point, i.e., a total of 2 points.

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