Three players agree that the loser will owe the winners as much as the amount of money each winner has. After three games, each player has lost once. How much did they start with, if at the end of the game each had 104 crowns?
At the beginning of the game, the card players had $x, y$ and $z$ crowns. Based on the given conditions:

$$
x+y+z=312
$$

$$
x-y-z=26
$$

$$
3 y-x-z=52
$$

Adding (1) and (2) yields $x=169$, and adding (1) and (3) gives $y=91$; therefore, $z=52$.

Number of solutions: 54.