If 4 December 1999 is given to be a Monday, then what day of the week will it be on 3 January 2000?

Introduction / Context:
This question asks you to cross a year boundary from late in one year to early in the next year and determine the change in weekday. We are told that 4 December 1999 is a Monday, and we must find the day of the week on 3 January 2000. This type of calendar problem reinforces counting days across months and years and then reducing modulo 7 to adjust for the cyclic nature of weekdays.

Given Data / Assumptions:

• 4 December 1999 is a Monday.
• We need the weekday on 3 January 2000.
• We treat 1999 as an ordinary year with 365 days.
• December 1999 has 31 days and January 2000 has 31 days.

Concept / Approach:
The general approach is to count how many days lie between 4 December 1999 and 3 January 2000, then compute this number modulo 7. The remainder tells us how many steps to move forward from the starting weekday, Monday. Because the period is less than a month and a half, the counting is manageable and can be done by breaking it into December and January portions.

Step-by-Step Solution:
Step 1: Count days remaining in December after 4 December 1999. Step 2: December has 31 days, so days from 5 December to 31 December are 31 − 4 = 27 days. Step 3: From 1 January 2000 to 3 January 2000 inclusive, there are 3 days. Step 4: Total days from 4 December 1999 to 3 January 2000 are 27 (end of December) + 3 (up to 3 January) = 30 days. Step 5: Compute 30 mod 7. Since 28 is divisible by 7, the remainder is 2. Step 6: A remainder of 2 means we move two weekdays forward from Monday. Step 7: Two days after Monday are Tuesday and then Wednesday, so 3 January 2000 is a Wednesday.

Verification / Alternative check:
An alternative view is to group the 30 days as four weeks (28 days) plus 2 days. The four full weeks do not change the weekday, so the net shift comes only from the extra two days. Starting on Monday and moving two steps forward yields Wednesday. You can also quickly sketch the last few days of December and the first few days of January, marking Mondays, and confirm that the alignment at 3 January is consistent with Wednesday.

Why Other Options Are Wrong:
If we had no remainder, we would remain on Monday, which does not match the 30 day difference. A remainder of 1 would give Tuesday, and a remainder of 3 would give Thursday, neither of which aligns with the correct modulo 7 result. Sunday would correspond to moving backward rather than forward from Monday. Thus, only Wednesday fits the two day forward shift implied by the calculated total of 30 days.

Common Pitfalls:
Students sometimes miscount by including the starting day incorrectly or by forgetting that the interval covers both the end of December and the beginning of January. Confusing inclusive and exclusive counting of 4 December or 3 January can lead to a one day error in the final result. Another common problem is not taking the modulus, instead trying to track the weekday after every single day, which increases the chance of mistakes. Always compress the total into weeks and a remainder and apply the shift only to the remainder.

Final Answer:
Therefore, the day of the week on 3 January 2000 is Wednesday.