Using the Gregorian calendar, what day of the week fell on 25 January 1981?

Introduction / Context:
Finding the weekday for a given historical date is a common type of calendar problem. Here we are asked for the day of the week on 25 January 1981. Solving this demands careful application of day counting or a standard formula to transform the date into a weekday using modular arithmetic with respect to seven day weeks.

Given Data / Assumptions:
- Target date = 25 January 1981. - Calendar system = Gregorian calendar. - Leap year rule: divisible by 4, with century corrections for divisibility by 400. - We only need the weekday name for this date.

Concept / Approach:
One systematic approach is to take a known base date with a known weekday and then count the number of days between that base and the target date. Once the number of days is known, we divide by 7 and use the remainder to adjust the weekday. Another robust approach is to employ a known day of week algorithm that accounts for the century, year within the century, month, and day and returns the weekday directly via modular arithmetic.

Step-by-Step Solution:
Step 1: Note that 1981 itself is not a leap year because it is not divisible by 4. Step 2: Consider the fact that 1 January 1981 falls on a known weekday according to standard references or by computation from a base year. Using a day of week algorithm gives 1 January 1981 as Thursday. Step 3: From 1 January to 25 January there are 24 days in between. Step 4: Total days to add to Thursday are 24. Step 5: Divide 24 by 7 to find the remainder. 7 times 3 equals 21, leaving remainder 3. Step 6: Advance the weekday 3 steps from Thursday: Thursday to Friday (1), Saturday (2), Sunday (3). Step 7: Hence 25 January 1981 falls on Sunday.

Verification / Alternative check:
Verification can be done using Zellers type congruence or another text book formula that uses the components of the date directly. Substituting day 25, month code for January, year code for 1981, and the appropriate century code yields a numeric value which corresponds to Sunday in the mapping of numbers to weekdays. A cross check using a reliable calendar source confirms that 25 January 1981 was indeed a Sunday.

Why Other Options Are Wrong:
- Monday, Friday, Tuesday, and Thursday correspond to different remainders when converting date differences into weekdays. - These alternative answers typically arise from small mistakes in either the base weekday for 1 January 1981 or from miscounting the number of days up to 25 January.

Common Pitfalls:
Students often miscalculate day counts when moving from 1 January to a later date, especially regarding whether to include or exclude the starting day in the count. Others use approximate rules without accounting for the correct century code in the formula, leading to weekday shifts. Consistent use of a single, well understood method and checking remainders carefully helps avoid these errors.

Final Answer:
The day of the week on 25 January 1981 was Sunday.