On 1st January 2005, Saturday falls. What day of the week was 1st January 2006?

Introduction / Context:
This is a straightforward calendar problem that links the first day of one year to the first day of the next year. It checks whether you understand how ordinary and leap years shift weekdays from one year to another.

Given Data / Assumptions:

• 1st January 2005 was a Saturday.
• We must determine the day of the week on 1st January 2006.
• 2005 is a non-leap year (not divisible by 4).
• We use standard Gregorian calendar rules.

Concept / Approach:
A non-leap year has 365 days. Since 365 = 52 * 7 + 1, a non-leap year contains 52 full weeks and 1 extra day. Therefore, the weekday on 1st January of the next year will be one day ahead of the weekday on 1st January of the current year. For a leap year (366 days), the shift would be 2 days.

Step-by-Step Solution:
Step 1: Recognise that 2005 is not divisible by 4, so it is an ordinary (non-leap) year. Step 2: A non-leap year has 365 days, which equals 52 weeks plus 1 day. Step 3: Because of the extra 1 day, the weekday on 1st January of the next year moves forward by exactly one day. Step 4: Given that 1st January 2005 is Saturday, we move one day forward. Step 5: The day after Saturday is Sunday. Step 6: Therefore, 1st January 2006 must fall on Sunday.

Verification / Alternative check:
You can verify this by observing any actual 2005–2006 calendar pair. All reliable calendars show that 1st January 2006 was indeed a Sunday. Additionally, the general rule that the first day of an ordinary year moves forward by one day for the following year is widely used and matches this result perfectly.

Why Other Options Are Wrong:
Saturday: This would imply no shift at all, which would only be possible if the year had exactly 364 days (52 weeks), not 365.

Friday: This would imply a shift of 6 days backward or 1 day forward in the opposite direction, inconsistent with the structure of a 365-day year.

Monday: This corresponds to a 2-day forward shift, which occurs after a leap year with 366 days, not after a non-leap year.

Tuesday: This would imply an even larger shift that is not supported by a single-year difference.

Common Pitfalls:
Students sometimes mistakenly treat every year as if it added two days of shift, confusing the rule for leap years with that for ordinary years. Another common error is to misremember whether a particular year is leap or ordinary. Always recall that only years divisible by 4 (and not century years, unless divisible by 400) are leap years, and check the year in question carefully.

Final Answer:
1st January 2006 fell on a Sunday.