Workout for the day of week on the given date:

(1) 15th August 1947

(2) 22nd November 2025

(3) 21st September 2080

(4) 18th October 2100

Question

Workout for the day of week on the given date:

(1) 15th August 1947

(2) 22nd November 2025

(3) 21st September 2080

(4) 18th October 2100

Accepted Answer

> [!TLDR]
> Using the odd-days method (with century blocks, leap-year corrections, and the day-count within the year): 15 Aug 1947 = Friday, 22 Nov 2025 = Saturday, 21 Sep 2080 = Saturday, 18 Oct 2100 = Monday.

> [!FORMULA]
> **Odd-days method.** Reduce the number of days elapsed since a fixed reference modulo $7$; the remainder ("odd days") gives the weekday via the code $0=	ext{Sun},1=	ext{Mon},2=	ext{Tue},3=	ext{Wed},4=	ext{Thu},5=	ext{Fri},6=	ext{Sat}$.
> - Every complete $400$-year block contributes $0$ odd days (the Gregorian calendar repeats every 400 years); $100$ years $	o5$, $200	o3$, $300	o1$ odd days.
> - Each ordinary year among the remaining years contributes $1$ odd day, each leap year contributes $2$.
> - Add the number of days elapsed *within* the target year up to (and including) the given date, then reduce mod 7.
> - A year is leap if divisible by 4, except century years, which must be divisible by 400.

**(1) 15 August 1947**
1. Split $1946$ complete years $=1900+46$. For $1900$ years ($=4	imes400+300$): odd days $=0+1=1$.
2. For the next $46$ years (1901–1946): leap years $=1904,\dots,1944\Rightarrow11$ leap, $35$ ordinary. Odd days $=35(1)+11(2)=35+22=57\equiv57\bmod7=1$.
3. Odd days from complete years $=1+1=2$.
4. Days elapsed in 1947 (non-leap) to 15 Aug: $31+28+31+30+31+30+31+15=227\equiv227\bmod7=3$.
5. Total $=2+3=5\Rightarrow$ code $5=$**Friday**.

**(2) 22 November 2025**
1. $2024$ complete years $=2000+24$. $2000$ years ($5	imes400$): odd days $=0$.
2. Next $24$ years (2001–2024): leap $=2004,\dots,2024\Rightarrow6$ leap, $18$ ordinary. Odd days $=18+12=30\equiv2$.
3. Odd days from complete years $=0+2=2$.
4. Days elapsed in 2025 (non-leap) to 22 Nov: $31+28+31+30+31+30+31+31+30+31+22=326\equiv326\bmod7=4$.
5. Total $=2+4=6\Rightarrow$ code $6=$**Saturday**.

**(3) 21 September 2080**
1. $2079$ complete years $=2000+79$. $2000$ years: odd days $=0$.
2. Next $79$ years (2001–2079): leap $=2004,\dots,2076\Rightarrow19$ leap,

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Q.Workout for the day of week on the given date:

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