10 people collected a total of 46 mushrooms in a forest. It is known that no two people collected the same number of mushrooms. How many mushrooms did each person collect?
Prove that the equation \(\frac {x}{y} + \frac {y}{z} + \frac {z}{x} = 1\) is unsolvable using positive integers.
On each of four cards there is written a natural number. Take two cards at random and add the numbers on them. With equal probability, this amount can be less than 9, equal to 9 or more 9. What numbers can be written on the cards?
In the first term of the year Daniel received five grades in mathematics with each of them being on a scale of 1 to 5, and the most common grade among them was a 5 . In this case it turned out that the median of all his grades was 4, and the arithmetic mean was 3.8. What grades could Daniel have?