Question 50
Four players $A_{1}$, $A_{2}$, $A_{3}$ and $A_{4}$ have the same amounts of money and play the following game with seven dices: $A_{1}$ throws the seven dices and then pays to each of the other three players $\frac{1}{k}$ of the money that the corresponding player has at the moment, where $k$ is the sum of the points on the seven dices. Then the same action is performed consecutively by $A_{2}$, $A_{3}$ and $A_{4}$ and the game is over. Find the sums of the points on the dices thrown by each player if after the game their money are in ratio $3: 3: 2: 2$ (the money of $A_{1}$ to the money of $A_{2}$ to the money of $A_{3}$ to the money of $A_{4}$ ).