If 1 January 2006 was a Sunday, what was the day of the week on 1 January 2010?

Introduction / Context:
This question spans several years and asks for the weekday on 1 January 2010 given that 1 January 2006 was a Sunday. It tests your understanding of how weekdays shift over multiple years, especially when some of those years are leap years and others are normal years.

Given Data / Assumptions:

• 1 January 2006 was a Sunday.
• We must find the weekday on 1 January 2010.
• Years in between: 2006, 2007, 2008, and 2009.
• Among these, 2008 is a leap year, while 2006, 2007, and 2009 are normal years.

Concept / Approach:
Between 1 January of one year and 1 January of the next year, the weekday moves forward by one day for a normal year and by two days for a leap year, because normal years contribute 1 odd day and leap years contribute 2 odd days. We accumulate the odd days over the years from 2006 to 2009 and then apply the net shift to the weekday of 1 January 2006.

Step-by-Step Solution:
Step 1: From 1 January 2006 to 1 January 2007, there is a normal year 2006 with 1 odd day. Step 2: From 1 January 2007 to 1 January 2008, year 2007 is also a normal year, adding another 1 odd day. Step 3: From 1 January 2008 to 1 January 2009, year 2008 is a leap year, contributing 2 odd days. Step 4: From 1 January 2009 to 1 January 2010, year 2009 is a normal year, contributing 1 odd day. Step 5: Total odd days = 1 + 1 + 2 + 1 = 5. Step 6: Starting from Sunday on 1 January 2006, move forward 5 days: Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5). Hence, 1 January 2010 is Friday.

Verification / Alternative check:
You can double check by noting that 4 years correspond to 1461 days when one of them is a leap year and three are normal years. Dividing 1461 by 7 gives 208 full weeks and 5 odd days, which matches the previous calculation. This confirms that the net shift is 5 weekdays forward from Sunday.

Why Other Options Are Wrong:
Sunday: This would require zero or a multiple of seven odd days, not 5.

Saturday: This is 6 days ahead of Sunday and would correspond to 6 odd days, not 5.

Wednesday: This is 3 days ahead of Sunday, and would match only if the total odd days were 3 instead of 5.

Common Pitfalls:
Students sometimes forget to treat leap years differently and count them as having only one odd day. Another common error is misidentifying which years in the range are leap years. Always check divisibility by 4 and apply the century rules when necessary, and then sum the odd days carefully.

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