Regarding Days and Week in Calendar

Question

How to find the Particular day for 27 -1-1932, can anyone solve the Problem, how to study the Day for particular calendar events

Answer 1

There is a method deduced from congruencies and having into account some facts concerning Leap-years.

The day is given by
$$A+B+C+D+E \equiv x\pmod 7$$ where the digit $x$ gives the required day according to the correspondence $1,2,3,4,5,6,0$ to Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, respectively. This is very easy to remember (why?).

In this formula, $A,B,C,D,E$ are as follows.

$A$ is the century affected by the following procedure: Giving to the century $2000-2099$ the value $0$, future centuries are valued successively increasing by the terms of an arithmetic progression of common difference and first term equal to $-2$ and past centuries, successively decreasing, the term of an arithmetic progression of common difference equal to 2 and first term equal to $1$; so one has, for example: $$1700—1799\to 5\\1800—1899\to 3\\1900—1999\to 1\\2000—2099\to 0\\2100—2199\to -2\\2200—2299\to -4\\2300-2399\to -6$$

$B=$ {last two digits, say $ab$, of the year plus the floor function of $\frac{ab}{4}$}, in other words if $abcd$ is the year then $$B=ab+ \left[\frac{ab}{4}\right]$$ $C$ is the month. You have the following table assigning to each month a fixed number: $$\begin{cases}6\text{ to January } \\2\text{ to February } \\2\text{ to March } \\ 5\text{ to April } \\ 0 \text{ to May } \\3\text{ to June } \\5\text{ to July } \\ 1\text{ to August } \\ 4\text{ to September } \\ 6\text{ to October } \\2\text{ to November } \\ 4 \text{ to December }\end{cases} $$ $D$ is the day- number of the date.

$E$ concerns the Leap-years and its value is $-1$ or $0$.

►►Leap-years are those whose last two digits are multiples of $4$ (say your 1932) and when the number of the year is multiple of $400$. To these special years you assign the variable $E$ with two possible values, $$\begin{cases}E=-1 \text{ when the month is January or February }\\E=0 \text { otherwise }◄◄ \end{cases}$$ Example: For your $1-27-1932$ you have $$A=1$$ $$B= 32+8=40$$ $$C=6\text{ according to the given table for the variable } C$$ $$D=27$$ $$E=-1$$ hence $$1+40+6+27-1=73\equiv3\pmod7$$ and this $3$ corresponds to the third day of the week (see the beginning).

Your day is $\color{red}{ Wednesday }$.