Determining the number of marriage anniversaries falling on Sunday

To determine how many marriage anniversaries would fall on a Sunday in the next 15 years after the couple's wedding date of 18.09.1977, we need to consider a few factors.

1. Identifying the day of the week for the wedding date

To find out the day of the week for the wedding date, we can use the Zeller's Congruence formula. This formula calculates the day of the week for any given date. Zeller's Congruence is as follows:

h = (q + [(13(m+1))/5] + K + [K/4] + [J/4] - 2J) mod 7

Where:
- h is the day of the week (0 = Saturday, 1 = Sunday, ..., 6 = Friday)
- q is the day of the month
- m is the month (3 = March, 4 = April, ..., 12 = December, January and February are counted as months 13 and 14 of the previous year)
- K is the year of the century (year % 100)
- J is the zero-based century (actually ⌊ year/100 ⌋)

For the given wedding date, 18.09.1977:
- q = 18
- m = 13 (since January is counted as month 13 of the previous year)
- K = 77
- J = 19

Plugging these values into the formula:
h = (18 + [(13(14))/5] + 77 + [77/4] + [19/4] - 2*19) mod 7
h = (18 + 35 + 77 + 19 + 4 - 38) mod 7
h = 115 mod 7
h = 2

The day of the week for the wedding date, 18.09.1977, is Sunday (h = 2).

2. Calculating the number of marriage anniversaries falling on Sunday

Since the wedding date falls on a Sunday, the couple's first marriage anniversary will also fall on a Sunday. From there, we can determine the subsequent marriage anniversaries that fall on a Sunday by adding multiples of 7 to the original wedding date.

Given that we need to find the number of anniversaries that fall within the next 15 years, we can calculate the number of Sundays by dividing the total number of days (15 years * 365 days) by 7 (the number of days in a week) and rounding down to the nearest whole number.

Number of Sundays = floor((15 years * 365 days) / 7 days)

Number of Sundays = floor(5475 days / 7 days)

Number of Sundays = floor(782.14)

Number of Sundays = 782

Since the couple's first anniversary falls on a Sunday, and there are a total of 782 Sundays within the next 15 years, the number of marriage anniversaries that fall on a Sunday is 2 (option B).

Therefore, the correct answer is option B) 2.