Alignment of Number of Days in a Month

Alignments

Alignment of Number of Days in a Month:

All know that

1. Certain months have 31 days, 
2. and some have 30 days. 
3. Feb has 28 in Non Leap Years
4. and 29 in Leap Years.

	# of Days	Months
Common	31	1 (Jan)	3 (Mar	5 (May	7 (Jul)	8 (Aug)	10 (Oct)	12 (Dec)
	30		4 (Apr)	6 (Jun)		9 (Sep)	11 (Nov)
Leap Year	29	2 (Feb)
Non Leap Year	28

There is a small trick to differentiate between those that have 31 and those that have lesser.
On our knuckles, the month that falls on high is 31 days, while those that fall on low are 30 days or lesser. We have to count to Jul and start again the first which makes Jul and Aug both 31 days.
Isn't it simple?

Alignment of First Day/Weeks in a Month

Alignments

Alignment of First Day/Weeks in a Month:

Like "Alignment of Number of Days in a Month" certain months align. In the following table, 

1. Common Alignment is for the all years
2. Leap Alignment 
• can combine (like 1,4,7) 
• or can be unique (like (2,8)
3. Non Leap Alignment
• can combine (like 2,3,11) 
• or can be unique (like (1,10)
4. Some Months Standout in All Years (like 5 and 6).

Non Leap Alignment	Leap Alignment	Common Alignment
	1	4, 7
1, 10
2		3, 11
	2,8
		9, 12

Alignment of WeekDays and Months in a Year

Alignments

Alignment of WeekDays and Months in a Year:

Like "Alignment of Number of Days in a Month" and "First Day/Weeks in a Month"
we can align Years based on the above.

Months							Years
Range ->							1973-1999			2001-2027			2029-2055
1, 10	5	8	2, 3, 11	6	9, 12	4, 7	1978	1989	1995	2006	2017	2023	2034	2045	2051
4, 7	1, 10	5	8	2, 3, 11	6	9, 12	1973	1979	1990	2001	2007	2018	2029	2035	2046
9, 12	4, 7	1, 10	5	8	2, 3, 11	6	1974	1985	1991	2002	2013	2019	2030	2041	2047
6	9, 12	4, 7	1, 10	5	8	2, 3, 11	1975	1986	1997	2003	2014	2025	2031	2042	2053
2, 3, 11	6	9, 12	4, 7	1, 10	5	8	1981	1987	1998	2009	2015	2026	2037	2043	2054
8	2, 3, 11	6	9, 12	4, 7	1, 10	5	1982	1993	1999	2010	2021	2027	2038	2049	2055
5	8	2, 3, 11	6	9, 12	4, 7	1, 10	1977	1983	1994	2005	2011	2022	2033	2039	2050
Sun	Mon	Tue	Wed	Thu	Fri	Sat	<- Weekday
1, 4, 7	10	5	2, 8	3, 11	6	9, 12	1984	2012	2040
9, 12	1, 4, 7	10	5	2, 8	3, 11	6	1996	2024	2052
6	9, 12	1, 4, 7	10	5	2, 8	3, 11	1980	2008	2036
3, 11	6	9, 12	1, 4, 7	10	5	2, 8	1992	2020	2048
2, 8	3, 11	6	9, 12	1, 4, 7	10	5	1976	2004	2032
5	2, 8	3, 11	6	9, 12	1, 4, 7	10	1988	2016	2044
10	5	2, 8	3, 11	6	9, 12	1, 4, 7	1972	2000	2028
Range ->							72-96	00-24	28-52
Months							Leap Years
1							Sun
2	1						Mon
3	2	1					Tue
4	3	2	1				Wed
5	4	3	2	1			Thu
6	5	4	3	2	1		Fri
7	6	5	4	3	2	1	Sat
8	7	6	5	4	3	2	Sun
9	8	7	6	5	4	3	Mon
10	9	8	7	6	5	4	Tue
11	10	9	8	7	6	5	Wed
12	11	10	9	8	7	6	Thu
13	12	11	10	9	8	7	Fri
14	13	12	11	10	9	8	Sat
15	14	13	12	11	10	9	Sun
16	15	14	13	12	11	10	Mon
17	16	15	14	13	12	11	Tue
18	17	16	15	14	13	12	Wed
19	18	17	16	15	14	13	Thu
20	19	18	17	16	15	14	Fri
21	20	19	18	17	16	15	Sat
22	21	20	19	18	17	16	Sun
23	22	21	20	19	18	17	Mon
24	23	22	21	20	19	18	Tue
25	24	23	22	21	20	19	Wed
26	25	24	23	22	21	20	Thu
27	26	25	24	23	22	21	Fri
28	27	26	25	24	23	22	Sat
29	28	27	26	25	24	23	Sun
30	29	28	27	26	25	24	Mon
31	30	29	28	27	26	25	Tue
	31	30	29	28	27	26	Wed
		31	30	29	28	27	Thu
			31	30	29	28	Fri
				31	30	29	Sat
					31	30	Sun
						31	Mon

In the above table, the numbers below the Months Column show which Month of which year have which day as the first day of that month.
For Eg.,

1. For Non Leap Years
• For Years 78, 89, 95, etc, Months Jan and Oct have Monday as the First Day of the month.
• For Years 73, 79, 90, etc, Months Jan and Oct have Tuesday as the First Day of the month.
2. For Leap Years
• For years 1984, 2012, 2040, Months Jan, Apr and Jul have Monday as the First Day of the month.
• For years 1996, 2024, 2052, Months Jan, Apr and Jul have Tuesday as the First Day of the month.

One can observe that the combination of Month Slides to the left every next line.
Non Leap Years tend to have a similar Month Week Combination every 6th, 11th or 17th years, but for sure on every 28th year.
Leap Years have same calendar every 28th year.

Based on this, any one can calculate for more years not mentioned in the above table, by simply deducting or adding 28 from the Year they want and to match it in the Years in the table.