Consider years from 2001 to 2017. Out of
these 17 years, the following 4 are leap years: 2004, 2008, 2012, 2016
Exceptions:
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’1^{st} to Feb’28^{th}
and the other scenario is for the dates from Mar’1^{st} to Dec’31^{st}.
These two scenarios result in two different patterns. In brief, scenarioI set of dates is (Jan’1^{st} to Feb’28^{th}) and scenarioII set of dates is (Mar’1^{st} to Dec’31^{st}).
For example, let us consider a year 2007.
How many days are there from Jan’1^{st} of 2006 to Jan’1^{st}
of 2007? It is 365. Reason is simple.
Being a nonleap year, '2006' has 365 days. Similarly, there are 365
days from Jan’1^{st} of 2007 to Jan’1^{st} of 2008 (here again,
being a nonleap year '2007' consists of 365 days). So here, any day (taken
from scenarioI 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 scenarioI set
of dates are considered.
PatternI
Here we consider a date from Jan’1^{st}
to Feb’28^{th} 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 'NonEquidistant'.
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
PatternII
Here we consider a date from scenarioII
set of dates ie., from Mar’1^{st} to Dec’31^{st} 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.
If it is to be defined
mathematically, Leap year is a number which
must be a multiple of 4 and
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: can be a multiple of 400
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.
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:
PatternI
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
PatternII
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
PatternI 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 PatternII, 1899
and 1900 would have been N and N respectively and also it would have been in a
perfect pattern.
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