Problem 6.2. Petya and Vasya decided to get as many fives as possible on September 1 and 2.

- On September 1, they got a total of 10 fives, and Petya got more fives than Vasya;
- On September 2, Vasya got 3 fives, while Petya did not get any;
- By the end of these two days, Vasya had more fives than Petya.

How many fives did each of them get over these two days?
Answer: Petya got 6 fives, and Vasya got 7.

Solution. On the first of September, Petya got more fives than Vasya, so Petya got at least 6 fives, and Vasya got no more than 4 fives.

If we add the fives from the second day, then we get that Petya got at least 6 fives, and Vasya got no more than 7 fives.

Since Vasya got more fives over the two days, he got exactly 7 fives, and Petya got exactly 6 fives.