Consider years from 2001 to 2017. Out of
these 17 years, the following 4 are leap years: 2004, 2008, 2012, 2016
Let us consider a property “Equidistant”
here. If any day of a year is equidistant from the corresponding day of the
previous and next years, then that year is called to exhibit the property
‘Equidistant’. But here, before considering a date, it should be taken care of
two scenarios. One scenario is for the dates from Jan’1st to Feb’28th
and the other scenario is for the dates from Mar’1st to Dec’31st.
These two scenarios result in two different patterns. In brief, scenario-I set of dates is (Jan’1st to Feb’28th) and scenario-II set of dates is (Mar’1st to Dec’31st).
For example, let us consider a year 2007.
How many days are there from Jan’1st of 2006 to Jan’1st
of 2007? It is 365. Reason is simple.
Being a non-leap year, '2006' has 365 days. Similarly, there are 365
days from Jan’1st of 2007 to Jan’1st of 2008 (here again,
being a non-leap year '2007' consists of 365 days). So here, any day (taken
from scenario-I set of dates) of
2007 is equidistant from the corresponding days of 2006 and 2008. And hence, we
can say that year 2007 possesses the property “Equidistant” if scenario-I set
of dates are considered.
Pattern-I
Here we consider a date from Jan’1st
to Feb’28th and the pattern looks like this:
To have some fun, fill out the tables on
your own...
From here onwards, 'E' stands for the
property 'Equidistant' and 'N' for 'Non-Equidistant'.
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
2010
|
N
|
E
|
E
|
N
|
N
|
E
|
E
|
N
|
N
|
E
|
2011
|
2012
|
2013
|
2014
|
2015
|
2016
|
2017
|
|
|
|
|
E
|
N
|
N
|
E
|
E
|
N
|
N
|
|
|
|
|
*Years in bold are leap years
Pattern-II
Here we consider a date from scenario-II
set of dates ie., from Mar’1st to Dec’31st and the
pattern looks like this:
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
2010
|
E
|
E
|
N
|
N
|
E
|
E
|
N
|
N
|
E
|
E
|
2011
|
2012
|
2013
|
2014
|
2015
|
2016
|
2017
|
|
|
|
|
N
|
N
|
E
|
E
|
N
|
N
|
E
|
|
|
|
|
*Years in bold are leap
years
The
point in common for the two patterns is, for every four
consecutive years, there exist two E’s and two N’s.
Exceptions:
If it is to be defined
mathematically, Leap year is a number which
-must be a multiple of 4 and
-must not be a multiple of 100 but
-can
be a multiple of 400
Sequence of Leap years is
not in a perfect pattern. For example, If I start writing down the list of leap
years for a period starting from 1895, it goes like this:
1896,1904,1908,1912,1916.....
There is an exception for it to be a perfect 'Arithmetic Progression
with a common difference of 4'. The break is between 1896 and 1904. Had 1900
been existing between these two, it would have been so.
As there exist exceptions
in the leap year sequence (I mean, it’s not a perfect Arithmetic Progression.
Every year which is a multiple of 4 is not a leap year. The exception is due to
a year which is being a multiple of 100 (but not a multiple of 400) (and
obviously it’s a multiple of 4) is not a leap year), there exist exceptions too
in our two patterns. There exist breaches in the pattern at any year which is a
multiple of 100 (but not a multiple of 400) and also at one of it’s two
adjacent years. To explain this I take an example set of the years from 1895 to
1911:
Pattern-I
for this set is:
1895
|
1896
|
1897
|
1898
|
1899
|
1900
|
1901
|
1902
|
1903
|
1904
|
E
|
N
|
N
|
E
|
E
|
E
|
E
|
E
|
E
|
N
|
1905
|
1906
|
1907
|
1908
|
1909
|
1910
|
1911
|
|
|
|
|
N
|
E
|
E
|
N
|
N
|
E
|
E
|
|
|
|
|
*Years in bold are leap
years
Pattern-II
for this set is:
1895
|
1896
|
1897
|
1898
|
1899
|
1900
|
1901
|
1902
|
1903
|
1904
|
N
|
N
|
E
|
E
|
E
|
E
|
E
|
E
|
N
|
N
|
1905
|
1906
|
1907
|
1908
|
1909
|
1910
|
1911
|
|
|
|
|
E
|
E
|
N
|
N
|
E
|
E
|
N
|
|
|
|
|
*Red marked ones are exceptions
*Years in bold are
leap years
Had 1900 been a leap year, then 1900 and 1901 of
Pattern-I would have been N and N respectively and it would have been in a
perfect pattern like two N's followed by two E's. Similarly, for Pattern-II, 1899
and 1900 would have been N and N respectively and also it would have been in a
perfect pattern.
