On 24 November 2007 it is given that Thursday falls on this date; based on this information, what day of the week was it on 10 November 2006?

Introduction / Context:
This problem involves working backward and forward with days of the week over a span of more than one year. You are given the weekday for a particular date in 2007 and asked to determine the weekday for an earlier date in 2006. Such questions test your ability to manage long gaps of days using the idea that every 7 days the calendar repeats its weekday pattern.

Given Data / Assumptions:

• 24 November 2007 is given as a Thursday.
• We need to find the day of the week on 10 November 2006.
• We assume the Gregorian calendar with February 2007 as a non leap month of 28 days.
• The day of the week repeats every 7 days.

Concept / Approach:
The key idea is to calculate how many days lie between 10 November 2006 and 24 November 2007, then use the remainder when that number is divided by 7 to shift weekdays backward. Since the target date is earlier than the reference date, we will move backwards in time from the known Thursday by the appropriate number of days modulo 7 to determine the weekday for 10 November 2006.

Step-by-Step Solution:
Step 1: Count the number of days between 10 November 2006 and 24 November 2007. Step 2: The exact difference is 379 days between these two dates. Step 3: Since weekdays repeat every 7 days, find 379 mod 7, which is 1. Step 4: A remainder of 1 means that 10 November 2006 falls one day earlier in the week compared to 24 November 2007. Step 5: The given day on 24 November 2007 is Thursday. Step 6: One day before Thursday is Wednesday. Step 7: Therefore, 10 November 2006 was a Wednesday.

Verification / Alternative check:
Instead of computing the full 379 days directly, you can break the interval into manageable pieces. For example, count days from 10 November 2006 to 10 November 2007, then from 10 November 2007 to 24 November 2007. The one year span from 10 November 2006 to 10 November 2007 contains 365 days, because 2007 is not a leap year affecting February. Then from 10 November 2007 to 24 November 2007 there are 14 days. Adding 365 and 14 again gives 379 days, and 379 mod 7 equals 1. This reconfirms that the weekday shifts by one day when moving between the two dates.

Why Other Options Are Wrong:
Tuesday would be two days earlier than Thursday, but we only require a shift of one day. Friday is one day after Thursday, which corresponds to moving forward instead of backward. Another Thursday would correspond to a shift of a multiple of 7 days, but our remainder is 1, not 0, so that cannot be correct. Therefore only Wednesday matches the computed backward shift of one day from the known Thursday.

Common Pitfalls:
A common source of error is confusing whether you should move forward or backward in time when the target date is earlier than the reference date. Another frequent mistake is ignoring the modulus operation and attempting to track the full number of days, which is unnecessary and can cause arithmetic slips. Students may also miscount the number of days between the two dates by forgetting that year 2007 is not a leap year or by making month length errors. Always remember that only the remainder upon division by 7 matters for the weekday.

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