6.1. In February of a non-leap year, Kirill and Vova decided to eat ice cream according to certain rules. If the date was even and the day of the week was Wednesday or Thursday, they each ate seven portions of ice cream. If the day of the week was Monday or Tuesday and the date was odd, they each ate three portions of ice cream. If the day of the week was Friday, the number of portions each ate was equal to the date on the calendar. Ice cream was forbidden on all other days and under other conditions. What is the maximum number of portions of ice cream that Vova could have eaten in February under these conditions?
# Answer: 110

Solution. February has 28 days, which is exactly 4 Mondays, 4 Tuesdays, and so on. Moreover, if Monday falls on an even date in one week, the following Monday will fall on an odd date, and vice versa. This means that the same day of the week falls on an even date twice and an odd date twice, regardless of which day of the week the month starts. Therefore, for Mondays, Tuesdays, Wednesdays, and Thursdays, Kirill and Vova will eat $4 \cdot (7+3) = 40$ portions of ice cream. For the four Fridays, the number of portions eaten will be $x, x+7, x+14$, and $x+21$, where $x$ is the date on which the first Friday falls. The maximum number of portions will be eaten when the first Friday is on February 7. Then $x + x + 7 + x + 14 + x + 21 = 42 + 4x = 42 + 28 = 70$, and in total, Vova will eat $70 + 40 = 110$ portions of ice cream.