The maximum possible number of Sundays in 3 consecutive calendar months is:

Question

Accepted Answer

To determine the maximum possible number of Sundays in three consecutive calendar months, we need to consider the structure of the calendar and how days are distributed across months.

1. **Explanation for Option 1 (14 Sundays):**
   - A month can have a maximum of 31 days. If we consider three consecutive months, the maximum number of days they can collectively have is 31 + 31 + 31 = 93 days.
   - A week consists of 7 days. Therefore, in 93 days, there are 93 ÷ 7 = 13 full weeks and 2 extra days.
   - If the first of these three months starts on a Sunday, then every 7th day thereafter will also be a Sunday. This means there will be 13 Sundays from the full weeks.
   - Additionally, the two extra days can also include a Sunday if the sequence of days starts on a Sunday. Thus, there can be one more Sunday, making it a total of 14 Sundays.
   - Therefore, the maximum possible number of Sundays in three consecutive months is 14, which supports Option 1 as the correct answer.

2. **Explanation for why other options are incorrect:**
   - **Option 2 (15 Sundays):** It is not possible to have 15 Sundays in three consecutive months because the maximum number of days (93) only allows for 13 full weeks and 2 extra days. Even with the most favorable alignment of days, only one additional Sunday can occur beyond the 13 Sundays from full weeks, totaling 14 Sundays.
   - **Option 3 (13 Sundays):** While 13 Sundays are possible, this is not the maximum number. As explained, with the right alignment of days, an additional Sunday can occur, making 14 Sundays possible.
   - **Option 4 (12 Sundays):** This is fewer than the maximum possible number. Even with less favorable alignment, more than 12 Sundays can occur in three consecutive months.

In conclusion, the maximum possible number of Sundays in three consecutive calendar months is 14, making Option 1 the correct answer.