If 29 December 1956 was a Saturday, then what was the day of the week on 16 January 1967?

The correct option is Monday.

To find the day of the week on 16 January 1967 given that 29 December 1956 was a Saturday, we can calculate the total number of odd days between the two dates.

Step 1: Calculate odd days from 29 December 1956 to 29 December 1966

The number of full years between 29 December 1956 and 29 December 1966 is 10 years (from 1957 to 1966 inclusive).

During these 10 years, we identify the leap years and ordinary years:

- Leap years have 366 days (2 odd days): 1960 and 1964 (2 leap years).

- Ordinary years have 365 days (1 odd day): 10 - 2 = 8 ordinary years.

Total odd days from these 10 years:

$\text{Total odd days}=(2\times 2)+(8\times 1)=4+8=12\text{odd days}$

$12÷7=1\text{week and}5\text{odd days}$

So, on 29 December 1966, the day was Saturday + 5 days = Thursday.

Step 2: Calculate odd days from 29 December 1966 to 16 January 1967

- Remaining days in December 1966: 31 - 29 = 2 days.

- Days in January 1967: 16 days.

Total additional days = 2 + 16 = 18 days.

$18÷7=2\text{weeks and}4\text{odd days}$

Step 3: Find the total number of odd days

Total odd days = 5 (from step 1) + 4 (from step 2) = 9 odd days.

$9÷7=1\text{week and}2\text{odd days}$

Step 4: Determine the final day of the week

Adding 2 odd days to Saturday:

- Saturday + 1 day = Sunday

- Saturday + 2 days = Monday

Therefore, 16 January 1967 was a Monday.