If 5 January 2011 was a Thursday, then on which day of the week did 1 January 2013 fall?

Introduction / Context:
Here we are not directly given the weekday of 1 January 2013. Instead, we are given a reference date, 5 January 2011, and its weekday. The task is to move from that reference date across multiple years to reach 1 January 2013. This type of question checks your ability to handle odd days over several years, including leap years.

Given Data / Assumptions:

• 5 January 2011 was a Thursday.
• We must find the day of the week on 1 January 2013.
• Years involved: 2011 and 2012, followed by the start of 2013.
• 2012 is a leap year, while 2011 is a normal year.

Concept / Approach:
We calculate how many days lie between 5 January 2011 and 1 January 2013. Then we find how many odd days that distance represents by dividing by 7. Finally we shift the weekday of 5 January 2011 forward by that many odd days. Careful handling of leap year 2012 and the partial months at the beginning and end is important.

Step-by-Step Solution:
Step 1: Count days remaining in 2011 after 5 January. There are 31 days in January, so remaining January days = 31 - 5 = 26. Step 2: Add days in the rest of 2011 from February to December. Total days from 6 January to 31 December 2011 is 365 - 5 = 360 days. Step 3: Full year 2012 is a leap year, so it has 366 days. Step 4: From 1 January 2013 back to 31 December 2012 is 1 day. So total days between 5 January 2011 and 1 January 2013 is 365 (for 2011 from 5 January to 5 January 2012) plus 366 minus 4 days adjustment. A direct calculation gives 727 days between the two dates. Step 5: Compute odd days: 727 / 7 gives remainder 6. Step 6: Starting from Thursday, move 6 days forward: Friday (1), Saturday (2), Sunday (3), Monday (4), Tuesday (5), Wednesday (6). Therefore 1 January 2013 was a Wednesday.

Verification / Alternative check:
You can also compute directly with a date difference approach: from 5 January 2011 to 5 January 2012 is 365 days, from 5 January 2012 to 5 January 2013 is 366 days, and then adjust backwards to 1 January 2013 by subtracting 4 days. This again results in 727 days and confirms the same weekday shift. Any reliable calendar method will agree that the result is Wednesday.

Why Other Options Are Wrong:
Thursday: This would imply 0 or 7 odd days, which does not match the remainder 6.
Tuesday: This is one day behind the correct weekday and would correspond to 5 odd days only.
Monday: This would correspond to 4 odd days and is inconsistent with the calculated 6 odd days.

Common Pitfalls:
A major source of error is miscounting the number of days when crossing a leap year. Some students forget that 2012 has 366 days. Another pitfall is miscalculating the exact day difference between the given date and the target date. Always convert the total number of days into odd days and apply those to the known weekday.

Final Answer:
Thus, the day of the week on 1 January 2013 was Wednesday.