Using the standard Gregorian calendar, on which day of the week did 31st December 2011 fall?

Introduction / Context:
Finding the day of the week for a specific past date is a classic calendar aptitude problem. Here, you are asked for the weekday corresponding to 31st December 2011. You can approach this either by using a known reference date and counting forwards or backwards, or by using a known algorithm such as odd days or Zeller’s congruence.

Given Data / Assumptions:

• Date required: 31st December 2011.
• Calendar used: standard Gregorian calendar.
• We know that 2011 is not a leap year (2011 is not divisible by 4).
• We will work with standard month lengths:
  • January: 31 days
  • February: 28 days in 2011
  • March: 31 days
  • April: 30 days
  • May: 31 days
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
  • November: 30 days
  • December: 31 days

Concept / Approach:
One reliable method is to start from a known reference date whose weekday is well remembered, then count the number of days forward to 31st December 2011, reducing by modulo 7 to get the weekday shift. Another structured approach is to use the concept of odd days: every complete week contributes zero odd days, and the remainder mod 7 determines the weekday shift from a known base (like 1st January 1900 or 1st January 2001). For explanation simplicity, we will rely on known reference dates and confirm the weekday.

Step-by-Step Solution:
Step 1: It is known (and can be verified using standard algorithms) that 1st January 2011 fell on a Saturday. Step 2: Since 2011 is not a leap year, it has 365 days, corresponding to 52 weeks and 1 extra day. Step 3: That means that 1st January 2012 must fall one weekday ahead of 1st January 2011, i.e., on a Sunday. Step 4: Because 2011 starts on a Saturday, the pattern of weekdays over the year leads to 31st December 2011 also falling on a Saturday (the same as 1st January for a non-leap year). Step 5: More formally, counting days or using standard calendar tables confirms that 31st December 2011 is a Saturday.

Verification / Alternative check:
Another way is to use a trusted perpetual calendar or an algorithm such as Zeller's congruence to compute the weekday directly from the date (31, 12, 2011). Applying such an algorithm also produces Saturday as the weekday. Spot-checking known days in 2011, such as 25th December 2011 (Sunday), shows that 31st December 2011 must be the next Saturday in that sequence.

Why Other Options Are Wrong:
Monday, Sunday, Friday and Thursday all contradict the established pattern of the 2011 calendar. In a non-leap year, if 1st January is Saturday, 31st December falls on the same weekday, not one of the others listed. Any other weekday choice fails when checked against the counts of days and known date-weekday pairs.

Common Pitfalls:
Learners sometimes misapply the rule for leap years when checking the relationship between the first and last days of the year. Others miscount days by forgetting that the year starts on a specific weekday. Using a systematic algorithm or memorising some key reference years helps prevent such mistakes and speeds up calendar calculations.

Final Answer:
31st December 2011 fell on Saturday.