It was Sunday on 1st January 2006. On which day of the week did 1st January 2010 fall?

Introduction / Context:
This question spans several years and asks you to determine how the weekday of 1st January shifts from 2006 to 2010. It combines knowledge of leap years and ordinary years over a multi-year period, which is common in competitive exams.

Given Data / Assumptions:

• 1st January 2006 was a Sunday.
• We must find the day of the week on 1st January 2010.
• We use standard Gregorian rules where:
  • Ordinary year (365 days) adds 1 odd day.
  • Leap year (366 days) adds 2 odd days.
• We must consider the years 2006, 2007, 2008, and 2009.

Concept / Approach:
We track the shift in weekdays year by year:

• From 1st January of one year to 1st January of the next, add 1 day if the year is ordinary, or 2 days if it is a leap year.
• We then sum the total odd days and apply modulo 7 to find the net shift from Sunday in 2006 to the weekday in 2010.

We must correctly identify which of the intervening years are leap years.

Step-by-Step Solution:
Step 1: Identify leap and ordinary years between 2006 and 2010: 2006 (ordinary), 2007 (ordinary), 2008 (leap), 2009 (ordinary). Step 2: From 2006 to 2007, add 1 odd day (ordinary year). Step 3: From 2007 to 2008, add 1 odd day (ordinary year). Step 4: From 2008 to 2009, add 2 odd days (leap year). Step 5: From 2009 to 2010, add 1 odd day (ordinary year). Step 6: Total odd days from 1st January 2006 to 1st January 2010 = 1 + 1 + 2 + 1 = 5 days. Step 7: Starting from Sunday (for 1st January 2006), move forward 5 days: Sunday → Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5). Step 8: Therefore, 1st January 2010 falls on a Friday.

Verification / Alternative check:
You can verify this by consulting actual calendars for 2006 to 2010. They show that 1st January 2010 is indeed a Friday. Another way is to check 1st January 2008 and 1st January 2009 as intermediate steps, confirming that the progressive shifts match the leap-year and ordinary-year contributions.

Why Other Options Are Wrong:
Sunday: This would imply a full multiple-of-7-day shift (0 net odd days), which is not the case here.

Saturday: This would be 6 days ahead of Sunday, not 5, and would require an additional odd day.

Wednesday: Only 3 days ahead of Sunday, inconsistent with the total of 5 odd days.

Monday: Only 1 day ahead of Sunday, which would be true after a single ordinary year, not after four years with a leap year in between.

Common Pitfalls:
A frequent mistake is misclassifying leap years or forgetting to assign 2 odd days for a leap year. Candidates also sometimes count the years incorrectly (including 2010 itself when they should stop at 2009, or vice versa). Carefully listing each year and its type (leap or ordinary) before summing odd days helps prevent errors.

Final Answer:
1st January 2010 fell on a Friday.