It was Sunday on 1 January 2006 in the Gregorian calendar. Using calendar reasoning, what was the day of the week on 1 January 2010?

Introduction / Context:
This question tests your understanding of how days of the week shift from year to year in the Gregorian calendar. You are given the weekday for 1 January 2006 and asked to find the weekday for 1 January 2010. This requires knowledge of how ordinary years and leap years contribute extra days when counting forward across several years.

Given Data / Assumptions:
- 1 January 2006 was a Sunday.
- We are working in the Gregorian calendar.
- We need the weekday on 1 January 2010.
- The years between 2006 and 2010 are: 2006, 2007, 2008, 2009.
- Among these, 2008 is a leap year, while 2006, 2007 and 2009 are ordinary years.

Concept / Approach:
Between one 1 January and the next, an ordinary year causes the weekday to move forward by 1 day (since 365 = 52 weeks + 1 day), and a leap year causes a shift of 2 days (since 366 = 52 weeks + 2 days). By summing these shifts across the years 2006 to 2009 and then applying the result modulo 7, we can determine the weekday on 1 January 2010 starting from the known Sunday in 2006.

Step-by-Step Solution:
Step 1: List the years from 2006 up to (but not including) 2010: these are 2006, 2007, 2008 and 2009.Step 2: Identify leap years in this range. Only 2008 is a leap year because it is divisible by 4 and not a century year.Step 3: Each ordinary year shifts the weekday by 1 day, and each leap year shifts it by 2 days.Step 4: Total shift = 1 (for 2006) + 1 (for 2007) + 2 (for 2008) + 1 (for 2009) = 5 days.Step 5: Starting from Sunday on 1 January 2006, move forward 5 days: Sunday (0), Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5).Step 6: Therefore, 1 January 2010 falls on a Friday.

Verification / Alternative check:
If you prefer, you can check year by year. 1 January 2007 is Monday, 1 January 2008 is Tuesday, 1 January 2009 is Thursday (because of the leap year 2008 adding an extra shift), and 1 January 2010 becomes Friday. This year by year confirmation matches the earlier cumulative shift calculation and helps to ensure no year was misclassified as leap or ordinary.

Why Other Options Are Wrong:
Sunday would imply no net shift at all, which is incorrect over four years with at least one leap year. Saturday and Wednesday correspond to total shifts of 6 or 3 days respectively, while Monday would mean a shift of 1 day. None of these match the correct cumulative shift of 5 days from the starting Sunday.

Common Pitfalls:
Common mistakes include forgetting to treat leap years differently, misidentifying which years are leap years, or accidentally including the final year in the shift count again. Always list the years carefully, mark leap years clearly, compute the total shift, and then apply it step by step from the known starting weekday.

Final Answer:
The day of the week on 1 January 2010 was Friday.