If 4th December 1999 was a Monday, then what day of the week was 3rd January 2000?

Introduction / Context:
This calendar problem links dates across two consecutive years. You are told the weekday for 4 December 1999 and must determine the weekday for 3 January 2000. The key idea is to find the number of days between these two dates and then adjust the weekday accordingly using modulo 7 arithmetic.

Given Data / Assumptions:

4 December 1999 is given as a Monday.

We need the weekday for 3 January 2000.

1999 is not a leap year (since 1999 is not divisible by 4), and 2000 is a leap year, but the leap day in 2000 (29 February) occurs after 3 January and does not affect this calculation.

Concept / Approach:
We count the days from 4 December 1999 to 3 January 2000. Each elapsed day moves the weekday forward by one. After finding the total number of days, we take this number modulo 7 to find the effective weekday shift, then move that many days forward from Monday to get the weekday for 3 January 2000.

Step-by-Step Solution:
Step 1: Count days remaining in December 1999 after 4 December. December has 31 days. Days from 5 December to 31 December = 31 - 4 = 27 days. Step 2: Count days in January 2000 up to 3 January. Days from 1 January to 3 January 2000 = 3 days. Step 3: Total number of days between the two dates. From 4 December 1999 to 3 January 2000 inclusive of movement is 27 (end of December) + 3 (start of January) = 30 days. So, the weekday will shift forward by 30 days. Step 4: Reduce this shift modulo 7. 30 divided by 7 gives 4 full weeks (28 days) and a remainder of 2 days. So the effective weekday shift is 2 days forward. Step 5: Move 2 days forward from Monday. Starting at Monday: Tuesday is 1 day forward, Wednesday is 2 days forward. Therefore, 3 January 2000 was a Wednesday.

Verification / Alternative check:
You can also check by listing a short sequence: 4 Dec (Mon), 11 Dec (Mon), 18 Dec (Mon), 25 Dec (Mon), then 1 Jan (Mon), and finally 3 Jan is two days later, Wednesday. This quick weekly stepping confirms the modulo 7 result without full-day counting.

Why Other Options Are Wrong:
Sunday would be one day before Monday, not two days after; Monday would require no net shift, and Tuesday would imply a 1-day shift. The arithmetic clearly shows a 2-day shift, which leads uniquely to Wednesday.

Common Pitfalls:
Typical mistakes include miscounting the days remaining in December or incorrectly including or excluding one of the endpoints. Another common slip is forgetting to reduce the total day count modulo 7 and instead shifting the weekday by the full number of days, which is unnecessary. Careful counting and the use of modulo 7 make the process straightforward.

Final Answer:
3 January 2000 fell on a Wednesday.