If 24th November 2007 was a Thursday, then what day of the week was 10th November 2006?

Introduction / Context:
This type of calendar question asks you to move between two dates in different years and determine the weekday at one date, given the weekday at another. The key is to find the number of days between the two dates and then shift the weekday accordingly using modular arithmetic with base 7.

Given Data / Assumptions:

24 November 2007 is given as a Thursday.
We need to find the day of the week on 10 November 2006.
Both 2006 and 2007 are common (non-leap) years.
We use the Gregorian calendar month lengths.

Concept / Approach:
We calculate the number of days between 10 November 2006 and 24 November 2007. The weekday moves forward by one step for each day. Since we are going backward (to an earlier date), we will effectively subtract this shift. Only the remainder modulo 7 matters because the weekday cycle repeats every 7 days.

Step-by-Step Solution:
Step 1: Count the days from 10 November 2006 to 24 November 2007. There are 20 days from 10 November 2006 to 30 November 2006 inclusive of the end, or 20 days to move from 10 November to 30 November if counting carefully. December 2006 contributes 31 days. January to October 2007 contributes 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 = 304 days. From 1 November 2007 to 24 November 2007 adds 24 days. Total days = 20 + 31 + 304 + 24 = 379 days between the two dates. Step 2: Reduce the day difference modulo 7. 379 divided by 7 gives 54 weeks and a remainder of 1 (since 379 = 54 * 7 + 1). So the weekday shift is effectively 1 day. Step 3: Move backward by 1 weekday from 24 November 2007. 24 November 2007 is Thursday. One day earlier than Thursday is Wednesday. Therefore, 10 November 2006 was a Wednesday.

Verification / Alternative check:
Instead of summing month lengths, you could note that 365 days (one common year) is equivalent to a shift of 1 weekday, and check the remaining days separately. From 10 November 2006 to 10 November 2007 is 365 days (shift of 1 day). From 10 November 2007 to 24 November 2007 is 14 days (another full 2 weeks), so no additional effective shift. Thus, the total effective shift is still 1 day, leading from Wednesday to Thursday when moving forward, and from Thursday back to Wednesday when moving backwards, which agrees with our result.

Why Other Options Are Wrong:
Tuesday or Friday would require a shift of 2 days instead of 1 in either direction, and Thursday would imply no shift at all. The precise calculation shows a net shift of exactly 1 weekday, making those options inconsistent with the data.

Common Pitfalls:
Common mistakes include miscounting the number of days between the dates, especially across year boundaries, or forgetting to account for the 365-day shift between the two years. Another pitfall is moving in the wrong direction when converting the shift into weekdays. Always decide whether you are moving to an earlier or later date and adjust the weekday accordingly.

Final Answer:
The day of the week on 10 November 2006 was Wednesday.