To determine the day of the week on 29 November 2017, given that 29 November 2010 was a Monday, we need to calculate the number of 'odd days' between these two dates. Odd days are the extra days left after forming complete weeks.

Understanding Odd Days and Leap Years for Calendar Calculations

A standard year has 365 days, which is exactly 52 weeks and 1 day. This extra day is called an odd day.

A leap year has 366 days (because of the extra day in February), which is 52 weeks and 2 days. These extra 2 days are the odd days in a leap year.

Leap years occur every 4 years, except for years divisible by 100 but not by 400.

Calculating the Time Period

The period we are considering is from 29 November 2010 to 29 November 2017. This spans exactly 7 years.

Identifying Leap Years in the Period (2011-2017)

We need to find the number of leap years between 29 November 2010 and 29 November 2017. The years in this period are 2011, 2012, 2013, 2014, 2015, 2016, and 2017.

We check which of these years are leap years:

• 2011: Not divisible by 4, so not a leap year.
• 2012: Divisible by 4, so it is a leap year. Since 29 November is after February, the extra day (Feb 29) is included.
• 2013: Not divisible by 4, so not a leap year.
• 2014: Not divisible by 4, so not a leap year.
• 2015: Not divisible by 4, so not a leap year.
• 2016: Divisible by 4, so it is a leap year. Since 29 November is after February, the extra day (Feb 29) is included.
• 2017: Not divisible by 4, so not a leap year.

Thus, there are 2 leap years (2012 and 2016) in the period from 29 November 2010 to 29 November 2017.

Calculating Total Odd Days

In the 7-year period:

• Number of leap years = 2
• Number of normal years = Total years - Leap years = $7 - 2 = 5$

Total odd days contributed by these years:

• Odd days from normal years = \(5 \text{ years} \times 1 \text{ odd day/year} = 5 \text{ odd days}\)
• Odd days from leap years = \(2 \text{ years} \times 2 \text{ odd days/year} = 4 \text{ odd days}\)

Total odd days = \(5 + 4 = 9 \text{ odd days}\)

Finding the Equivalent Day Shift

To find the shift in the day of the week, we find the remainder when the total odd days are divided by 7 (since there are 7 days in a week).

Equivalent odd days = \(9 \pmod{7} = 2\)

This means the day of the week will shift forward by 2 days from the starting day.

Determining the Day on 29 November 2017

The day on 29 November 2010 was Monday.

The day on 29 November 2017 will be Monday + 2 days.

Monday + 1 day = Tuesday

Tuesday + 1 day = Wednesday

So, the day of the week on 29 November 2017 was Wednesday.

Summary of Day Calculation

Starting Day: Monday

Shift: +2 days

Resulting Day: Wednesday

Revision Table: Calendar Concepts

Additional Information on Calendar Reasoning

Calendar problems often involve calculating odd days over periods spanning years or months. Key points to remember:

• Every period of 7 odd days completes a week and brings you back to the same day.
• When calculating odd days across years, accurately identifying leap years within the period is crucial. Remember the rule for century years (divisible by 400).
• When calculating odd days across months within the same year, sum the odd days for each month in the period (Jan=3, Feb=0 or 1, Mar=3, Apr=2, May=3, Jun=2, Jul=3, Aug=3, Sep=2, Oct=3, Nov=2, Dec=3).
• Adding the net odd days to the starting day gives the final day. If the odd days are $n$, the day shifts forward by $n$ days. If $n$ is negative (e.g., calculating backward), the day shifts backward.

This problem is a straightforward application of identifying leap years and calculating total odd days over a multi-year period with the same start and end date (Nov 29) each year.