In the month of April 2001, on which dates did Wednesday occur?

Introduction / Context:
This is a calendar pattern question that asks on which dates of April 2001 Wednesday fell. Knowing the weekday of one date in a month allows you to list all other dates with the same weekday by repeatedly adding 7 days. The challenge is to identify the correct starting date and then apply this weekly pattern accurately.

Given Data / Assumptions:
- Month and year concerned: April 2001. - April always has 30 days. - We are working with the Gregorian calendar. - We need all dates in April 2001 that were Wednesdays.

Concept / Approach:
The key idea is that weekday patterns repeat every 7 days. Once we know the weekday of 1 April 2001, we can determine the weekday of any date in April by adding the appropriate number of days and taking the resulting shift modulo 7. In practice, one can determine the weekday for 1 April 2001 using a standard day of week algorithm and then generate all dates on which Wednesday falls by moving in steps of 7 days from the first Wednesday.

Step-by-Step Solution:
Step 1: Use a known day of week algorithm or a trusted reference to find the weekday of 1 April 2001. This turns out to be Sunday. Step 2: List weekdays for the first few days of April 2001: - 1 April 2001: Sunday. - 2 April 2001: Monday. - 3 April 2001: Tuesday. - 4 April 2001: Wednesday. Step 3: Since 4 April is a Wednesday, all subsequent Wednesdays in April are found by adding 7 days each time. Step 4: Add 7 days to 4 April to get 11 April. This is also a Wednesday. Step 5: Add another 7 days to get 18 April. This is again a Wednesday. Step 6: Add another 7 days to get 25 April. This is also a Wednesday. Step 7: Adding 7 days to 25 April would give 2 May, which lies outside April, so we stop. Step 8: Therefore, Wednesdays in April 2001 occurred on 4th, 11th, 18th, and 25th.

Verification / Alternative check:
To verify, you can quickly check that the numeric difference between any two of these dates is a multiple of 7. For example, 11 minus 4 equals 7, 18 minus 11 equals 7, and 25 minus 18 equals 7. This confirms that they are indeed separated by whole weeks. Also, using another standard reference for the 2001 calendar confirms that these dates in April 2001 were Wednesdays.

Why Other Options Are Wrong:
- Options with dates starting on 1st, 2nd, 3rd, or 5th as Wednesday are inconsistent with 1 April 2001 being Sunday. - Dates listed in the wrong options do not maintain correct 7 day spacing from the known first Wednesday in that month. - Some options include dates like 30th which do not align as Wednesdays for April 2001.

Common Pitfalls:
Common mistakes include misidentifying the weekday of 1 April or miscounting the weekly intervals. Some students attempt to guess from patterns in other years, which does not work reliably. Always determine the weekday of an anchor date correctly and then use a strict 7 day stepping pattern to list all related dates in that month.

Final Answer:
In April 2001, Wednesday fell on the dates 4th, 11th, 18th, and 25th.