What is the maximum number of months in a year that can have five Sundays?
The number of days in a month varies between 28 and 31, meaning that every month has at least 4 Sundays, but no month has more than 5. A year consists of $365=52 \cdot 7+1$ days, or in a leap year, $366=52 \cdot 7+2$ days, so there are 52 or 53 Sundays in a year.

Each of the twelve months thus contains at least 4 Sundays. Beyond the 48 Sundays, the remaining 4 or 5 Sundays must fall in different months, as no month can have 6 Sundays.

This means that in a year, there can be at most five months with 5 Sundays. This occurs in years with 53 Sundays, i.e., when the first day of the year is a Sunday, or in a leap year when the first day is a Saturday or Sunday.

Sziveri János (Budapest, I. István Gymn., I. o. t.)