It was Sunday on 1st January 2006. What was the day of the week on 1st January 2010?

Introduction / Context:
This question asks you to move from one known date with its weekday to another date several years later. The main idea is to count how many days the calendar shifts due to ordinary years and leap years between 2006 and 2010.

Given Data / Assumptions:
• 1 January 2006 was a Sunday.• We want the weekday on 1 January 2010.• Years between: 2006, 2007, 2008, 2009.• Leap year rule: A year divisible by 4 is a leap year, except century years not divisible by 400.

Concept / Approach:
From 1 January of one year to 1 January of the next, the day of the week advances by 1 day for a normal year and by 2 days for a leap year (because a leap year has one extra day: 366 days ≡ 2 mod 7).

Step-by-Step Solution:
Step 1: Identify which years among 2006–2009 are leap years.• 2006: not divisible by 4 ⇒ normal year.• 2007: normal year.• 2008: divisible by 4 ⇒ leap year.• 2009: normal year.Step 2: Count total day shifts:• 2006 → 2007: +1 day.• 2007 → 2008: +1 day.• 2008 → 2009: +2 days (leap year).• 2009 → 2010: +1 day.Step 3: Total shift = 1 + 1 + 2 + 1 = 5 days forward.Step 4: Starting from Sunday, move 5 days ahead:Sunday → Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5).

Verification / Alternative check:
Because the total shift is 5 mod 7, and Sunday + 5 = Friday, any alternative counting method (for example, counting total days directly) must give the same weekday if done correctly.

Why Other Options Are Wrong:
Monday, Sunday, Tuesday: These correspond to shifts of 1, 0, or 2 days rather than 5. They would be obtained only if leap years were ignored or counted incorrectly.

Common Pitfalls:
The usual mistake is to forget the extra day in a leap year, or to think that 2009 is a leap year. Miscounting the number of years in the interval also shifts the result.

Final Answer:
1st January 2010 was a Friday.