Aptitude - Calendar - Discussion

Discussion :: Calendar - General Questions (Q.No.1)

1. 

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

[A]. Sunday
[B]. Saturday
[C]. Friday
[D]. Wednesday

Answer: Option C

Explanation:

On 31st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31st December 2009, it was Thursday.

Thus, on 1st Jan, 2010 it is Friday.


Goutham said: (Jul 14, 2010)  
What is odd days?

Alaguvel.C said: (Jul 27, 2010)  
How to find odd days?

Sundar said: (Jul 27, 2010)  
Hi Friends,

Odd days of a year X = Remainder of [No. of days in the year X / 7].

[Where 7 --> For every 7 days, the day will be repeated, thats why we are dividing the total number of days of an year by 7. If it has any remainder then it will be considered as an odd day for that year.]


The required remainders (odd days) for the different years are given below:

For 2006: 365/7 = 1 (Total no. of days in 2006 is 365)
For 2007: 365/7 = 1
For 2008: 366/7 = 2 (Leap year, hence Feb month has 29 days)
For 2009: 365/7 = 1

Therefore, total number of odd days = 5.

Given day is 'Sunday' and total no of odd days is '5'.

The required date = Sunday + 5

= (The 5th day next to Sunday)

= Sunday + 1-Monday + 2-Tuesday + 3-Wednesday + 4-Thursday + 5-Friday.

= Friday (Required answer).

Rajeswari said: (Aug 13, 2010)  
Nice Sundar.

Bhupendra said: (Aug 18, 2010)  
31 dec 2005 = Saturday
365/7 = 52+1/7
2006= 1 odd day
2007= 1 odd day
2008=> 366/7 = 52+ 2/7=> 2 odd day
then 31 Dec 2008= Thursday
and 1 Jan 2009 = Friday.

Nilesh said: (Aug 28, 2010)  
How do we know leap year of that specific year?

Vijaya said: (Sep 14, 2010)  
Given :.

Jan 1, 2006 is sunday.

Jan 1, 2010 =?.

Consider completed year before 2010 i.e 2009 (since 2010 was starting).

2009=2000+9.

2009=0+9 (since 400, 800, 1200, 1600. Contains '0' odd days).

9/4=2 (2 leap years are there. Here it is divided by 4 because for every 4 years we get leap year).

Leap year=2*2=4.

Non leap =7*1=7.

Total = 11.

Jan 1st=1 day.

11+1=12.

12/7 = 5.

Friday.

Veer Singh Pal said: (Sep 30, 2010)  
If any year divided by 4 with out reminder its year known as leep year.

E.g: 2008/4 = 502 (no reminder)

And in this year were 29 days in Feb.

Basavaraj said: (Oct 23, 2010)  
I want clear method to calculate odd days.

Manu said: (Nov 12, 2010)  
Everytime the odd days are considered from sunday onwards i.e.,if there are are 0 odd days then we take the day as sunday and the count follows likewise

Shaunak said: (Nov 28, 2010)  
@veer singh pal:your answer is partially correct.for years like 1600,1700,1800,1900,2000 etc,we need to divide by 400.for other nos.,it needs to be a multiple of 4.

Arun Anoop M said: (Dec 7, 2010)  
Thanks vijaya

100=24 leap yr+[100-24]ordinary days
=[24*2]+76
=124
my way is
124=17weeks+5 ordinary days
So answer is 5.

But your way is very easy
124/7=5(remainder).

Priyavel said: (Dec 15, 2010)  
Hai Nilesh.

We divide year by 400. If remainder comes 0 means that year is leap year.

Dhanagopal said: (Dec 16, 2010)  
I want briefly to find odd days.

Boomathi said: (Dec 23, 2010)  
Please tell how do we know the leap year?

Latha said: (Dec 29, 2010)  
@Boomathi.

We know the given year is leap year or not, that year is divided by 4. That number (year) does not give any remainder that year is called leap year.

Saamy said: (Jan 5, 2011)  
How there are 24 leaf years there in 100 years.

Anyone please explain.

Pavithra said: (Jan 8, 2011)  
Hi there is a formula for this type of problem.

Plz memorize this

jan=1
feb=4
mar=4
apr=0
may=2
jun=5
jul=0
aug=3
sep=6
oct=1
nov=4
dec=6

days:
s=1
m=2
t=3
w=4
th=5
f=6
sat=7 or 0

formula=day+mon no.+(x-1900)+(x-1900)/4
x= the year we have to calculate

Eg:
16-may-2011

for=16+2+(2011-1900)+(2011-1900)/4
=16+2+111+111/4
=16+2+111+27
  (here we should not take the no behind decimal i.e 111/4=27.75)
=156

156/7=2(reminder)

mon =2

Seetharaman said: (Jan 17, 2011)  
Thanks pavithra.

Suman said: (Jan 31, 2011)  
Many many thanx...Pavithra

Kamal said: (Feb 4, 2011)  
Vijay can we do the same calculations for years like 2000, 1990, 1980 ?

Kamal said: (Feb 4, 2011)  
Pavithra can you apply you are concept for this date?.

1st Jan 2008.

If please explain it with steps.

Sonu Navgotri said: (Feb 17, 2011)  
For non-leap year odd number = 1 .

For leap year odd number = 2.

Dg1234 said: (Mar 3, 2011)  
This formula does not work on leap year. Pavithra..I am so sorry

Akhtar said: (Mar 8, 2011)  
I think sundar gave perfect ans.

Priya said: (Mar 22, 2011)  
Multiples of 4 and multiples of 400 are leap years but multiples of 100 not a leap year

Priyanka said: (Mar 24, 2011)  
Guys give a simple and easy method to find the leap year like pavithra has given to find the week day of a certain date.

Siddharth said: (Apr 4, 2011)  
Well done sundar.

Let me know that simple method to find leap year.

Rajellam said: (Apr 29, 2011)  
Thank you sunder. Actually I don't know how to calculate. But now I can do with help of you. Thak you.

Deena said: (May 17, 2011)  
Pavithra your formula is perfect and easy method. Thank you.

Some X said: (May 19, 2011)  
Vijaya please don't confuse students with your typical explanation. Sunder's explanation is pretty simple when compared to yours. Don't make students to give up their effort in learning something by giving these type of difficult explanations.

Sidhu said: (Jun 14, 2011)  
Pavithra. Thanks for your approach. Can u please say me why 1900 is used there (possibly some concept behind)?

Revathi said: (Jun 29, 2011)  
Hi pavithra, tell me if they asked for the year with below 1900. Because the value will be gone to minus so what to do?

Vallinath said: (Jul 25, 2011)  
Pavithra you said sat code 7 or 0 when we use 7 and when we use 0 please tell me.

Faiza said: (Jul 28, 2011)  
1 ordinary year = 365days = 52weeks + 1day
so, each ordinary year has 1 odd day.

1 leap year = 366 days = 52 weeks + 2 days (since 52 weeks=364days so, in leap year , to get 366 days we add 2 in 364)
so, each leap year has 2 odd days


100 years = 76 ordinary years + 24 leap years
= 76 multiply with its odd day i.e 1 + 24 multiply with its odd days i.e 2
= 76 + 48
=124 odd days

This means that every 100 years contain 124 odd days.

Aparna said: (Aug 3, 2011)  
Pavithra very wrong method. How can you calculate 16th july 1776 ?

Sonakshi said: (Aug 6, 2011)  
Yes Arpana Pavithra's formula is somewhere wrong.

Sasi said: (Aug 7, 2011)  
Nice sundar.

Gowthami.S said: (Aug 12, 2011)  
We want what day is jan 1,2010 for that

2000+9+jan1;
0+(9/4)+1
=(2+7)+1(2=leap year,7=non leap year)
=(2*2+7*1)+1
=4+7+1=12/7=5 odd days
= Friday

Pranay Goud said: (Aug 13, 2011)  
Thanks pavithra and sundar.

Priya said: (Sep 2, 2011)  
I would like to know , how many leap years are there in 99 years and 100 years.

i.e How to calculate number of leap years from 'n' number of years ?

I too want to know the same.

Sridhar said: (Sep 9, 2011)  
Centuries Table

1700-1799 4
1800-1899 2
1900-1999 0
2000-2099 6
2100-2199 4
2200-2299 2
2300-2399 0
2400-2499 6
2500-2599 4
2600-2699 2

Months Table:

January 0 (in leap year 6)
February 3 (in leap year 2)
March 3
April 6
May 1
June 4
July 6
August 2
September 5
October 0
November 3
December 5
Days Table:

Sunday 0
Monday 1
Tuesday 2
Wednesday 3
Thursday 4
Friday 5
Saturday 6


For example

April 24,1982.

1. Look up the 1900s in the centuries table: 0
2. Note the last two digits of the year: 82
3. Divide the 82 by 4: 82/4 = 20.5 and drop the fractionalpart: 20
4. Look up April in the months table: 6
5. Add all numbers from steps 1-4 to the day of the month (in this case, 24): 0+82+20+6+24=132.
6. Divide the sum from step 5 by 7 and find the remainder: 132/7=18 remainder 6
7. Find the remainder in the days table: 6=Saturday.

Sekhar said: (Oct 22, 2011)  
Thanks pavithra

Girija said: (Oct 28, 2011)  
Sridhar my quetion for you how you wrote century table we have to remember that or else is there any calculation but your expalanation so nice I have that doubt only, so please clarify that and before 1700 how you know value ?

Vijay said: (Nov 1, 2011)  
365 day = 1 year, day364/7days = 54weeks, balance 1 day that will be conce considered as ODD days.

If it is leap year total no of days for = 366, 364/7 = 54 weeks balnce 2 days.

Satishmohan said: (Nov 7, 2011)  
Sridhar my quetion for you how you wrote century table we have to remember that or else is there any calculation but your expalanation so nice I have that doubt only, so please clarify that and before 1700 how you know value ?

Abhinav said: (Nov 7, 2011)  
It is Thursday on 25th of September. What day will it be on the 25th of October in the same year?

Subhashree said: (Nov 10, 2011)  
@Sridhar, how we know the centuries table value or months table value?

Vipanchi said: (Nov 21, 2011)  
Hi could you please explain clearly formula to find the day of the week.

Kundan K said: (Nov 26, 2011)  
Hi friends,

There are 52 weeks in a year.And there are 7 days a week.So, the closest factor of 7 is 49.And 52-49=3.So after 49 days again there will be Sunday.So,add 3 days to Sunday that is Wednesday.Now similarly continuously add 3 days for 4 times as there is difference of 4 years between 2010 & 2006.

Therefore the ans is "FRIDAY".

Chandu said: (Nov 26, 2011)  
Thanks sundar

Intaj said: (Dec 3, 2011)  
Hi, you can do it easily follow my shortcut rule :-

jan = (1) = 3 jan = 31/7 = remain = 3
feb = (2)= 0 feb= 28/7 = remain = 0
march = (3)= 3
april = (4)= 2 april = 30/7 = reminder = 2
may = (5) = 3
june = (6) = 2
july = (7) =3 ====================================
aug = (8)= 3 (1 , 3, 5, 7, 8, 10, 12) = 3
sept = (9)= 2 ( 4, 6, 9, 11) = 2
oct = (10)= 3 2= 0 (Feb)
nov = (11) = 2
dec = (12) = 3 JUST REMEMBER ABOVE

Arkright said: (Dec 15, 2011)  
Why do you divide with is it 4 or 7 to get a leap /ordinary year am confused some of you using 7 while others 4. Please explain?

Manish Tiwari said: (Dec 16, 2011)  
Thanks pavitra. Really good dear.

Sreehitha said: (Jan 7, 2012)  
Pavitra, can you please explain for 1st jan 2008 as it is a leap year how to approach it. The example 16 may 2011 which you have given is for non leap year right.

Nallathambim said: (Jan 12, 2012)  
Please explain it with more details.

Shashi said: (Feb 1, 2012)  
Nice one Sundar & Pavitra.

Mamatha said: (Feb 1, 2012)  
Thanks Pavithra.

Kayal said: (Feb 24, 2012)  
First we take the previous century why because every 4th century is leap year.

Then take the finding year with substract 1.

So 2009-2000=9.

Now find the how many leap year and how many ordinary year in this 9. So we divide.

9/4=2. So 2 leap year and 7 ordinary year.

= (2*2+7*1) =4.

Now take the months table what they ask to find out here jan 1.

So no months is there as to take 1.

=4+1.

=5 (friday).

Weeks table.

0-sunday.

1-monday.

2-tuesday.

3-wednesday.

4-thursday.

5-friday.

6-saturday.

Thats all.

K.Velmurugan said: (Mar 27, 2012)  
odd days
1-jan
4-feb
4-mar
0-apr
2-may
5-jun
0-july
3-agu
6-sep
1-oct
4-nov
6-dec
0-sunday.

1-monday.

2-tuesday.

3-wednesday.

4-thursday.

5-friday.

6-saturday.
20--=6 odddays
19--=0 oddays

ex : 27/03/2012
day=27 total=day+month+20--+ year
month=4
20--=6 =27+4+6+17=54/7
(year=--12/7= 5remainter) remainder=5
year=12+5=17
ans: friday

Prasant said: (Apr 9, 2012)  
Let's take a simple way:
1 Jan 2006 - Sunday (given)
1 Jan 2006 to 1 Jan 2007: 1 odd day
1 Jan 2007 to 1 Jan 2008: 1 odd day
1 Jan 2008 to 1 Jan 2009: 2 odd day
1 Jan 2009 to 1 Jan 2010: 1 odd day
Total odd days = 5 (i.e. 5th no. odd day is 1 Jan 2010)
Since given day is sunday, consider it as '0', then 1 for monday, 2 for tuesday....5 for Friday.

Pinto said: (Apr 9, 2012)  
2010=1600+400+10
1600=0 add days
400 =0 add days
10 =10/4=2 leap year + 8 ordinary year
=2*2 + 8*1
=4+8=12
=12/7(no days in a week)
=5 (Friday)

Rajesham said: (May 16, 2012)  
Normalyear-365days (365/7) 56weeks&1odd day.

Leapyear-366days (366/7) 56weeks&2odddays.

Narendra said: (Jun 16, 2012)  
In each next year day will come next day.

2006 Sunday.
2007 Monday.
2008 Tuesday+Wednesday (leap year).
2009 Thursday.
2010 Friday.

Somu said: (Jun 26, 2012)  
Odd days in 2000 years = 0.

Odd days in 9 years = (2*2+7x1) Since (2 leap+7 ordinary)

= 4+7 = 11.

In 2010 January,

1 = 1 odd days.

Total odd days = 11+1 = 12.

Odd days = 12/7.

= 5.

5 mentions Fridays.

Mahesh said: (Jun 30, 2012)  
Hi Guys,

I don't know why guys are giving so much pressure to your brain its too simple what I know in my method, please check below logic and let me know its simple or complicate feel free to feedback on my answer.

i.e.,

1 Jan 2006 is Sunday.

1 Jan 2007 is Monday.

1 Jan 2008 is Tuesday.

1 Jan 2009 is Thursday (extra day for the 2008 FEB 29).

1 Jan 2010 is Friday.

Solution:

Add next day for the next year.

Ex: 1 Jan 2006 is Sunday in next year it will come on Monday.

In 2008 Feb 29 will come extra day for the year.

Kamatchi said: (Aug 2, 2012)  
Will give a clear explain to find odd day ?

Raj said: (Aug 16, 2012)  
@Mahesh your method is nice but if there is large variation in years we want to go for concept based solution for ex 15 aug 2012 is wednesday then what is the day of 15th aug 1935

Raaj said: (Aug 16, 2012)  
@kamatchi the answer for ur question is( to find number of odd days )
be clear for every 7 days a cyle(week) wii be compleated so just divide the number of days with 7 the remainder will be the number of odd days for example number of odd days in leap year 366 divided by 7 so the remainder will be 2 days which is the number of odd days in a leap year

Saheb Ali said: (Aug 24, 2012)  
According to pavitra formula
15 aug 1947

=15+3+(1947-1900)+(1947-1900)/4

=18+47+47/4

=76/7
remainder 6

its friday!

Satishkumar said: (Aug 27, 2012)  
Nice mahesh. , keep it up!

Keepsmiling said: (Sep 18, 2012)  
Nice mahesh. Its helpful.

Sangeeta said: (Oct 13, 2012)  
But pavitra if I have to solve for 16th july 1776 which is less than 1900. Please tell me the solution.

Meethi said: (Oct 14, 2012)  
//
How many times does the 29th days of the month occur in 400 consecutive years
1) 97 times 2) 4400 times 3) 4497 times 4) none
Sol: In 400 consecutive years there are 97 leap years. Hence in 400 consecutive years, February has the 29th day 97 times, and the remaining 11 months have the 29th day 400 x 11 or 4400 times.
Therefore, 29th day of the month occurs (4400 + 97) or 4497 times.
//

How to calculate leap years in 400 consecutive years ?

Krishna said: (Feb 3, 2013)  
How 100 years having 24 leap years ?, If we divide by 4 it will be 25 leap years ! can anyone clarify my doubt?

Gayathri said: (Jun 12, 2013)  
Given info is :
1.01.2006 --- Sunday.

Since 2006 is non leap year. 1 odd day
i.e 1 day extra for the next year.
1.01.2007 --- Monday.

similarly for 2007 .
1.01.2008 -- Tuesday.

2008 is a leap year. So 2 days extra.
1.01.2009 -- Thursday(2 days gap).

1.01.2010 -- Friday.

So Friday is answer.

Bipin said: (Jul 11, 2013)  
Pavithra You told us a very good way to solve the calendar question but only few things you left i.e related to leap year, this formula doesn't work for leap year, it works only for non-leap year.

@Dg1234.

You can solve leap year by this formula as told by Pavithra but only few things I have changed. Check out.

Formula For Leap Year:

0 - Apr, jul 0 - Sat
1 - Jan 1 - Sun
2 - May 2 - Mon
3 - Aug 3 - Tue
4 - Feb, mar, nov 4 - Wed
5 - Jun 5 - Thu
6 - Sep, dec 6 - Fri
7 - Sat

Note:- To find the odd days for leap year we have to add 6 only with this formula.

Formula: 6 + Day + Month + (Year-1900) + (year-1900)/4.

Eg. 4-feb-2004.

= 6+4+4+(2004-1900)+(2004-1900)/4.
= 6+8+104+(104/4).
= 118+26.
= 144.

= 144/7.

= Remainder = 4.
= Wednesday.

Ayu said: (Aug 30, 2013)  
I don't understand how to calculate leap year and odd day?

Ram said: (Aug 31, 2013)  
There is a another Method of to calculate this.

We memorize this,

Jan-0
Feb-3
mar-3
Apr-6
May-1
Jun-2
Jul-6
Aug-2
Sept-5
Oct-0
Nov-3
Dec-5

Given 1 Jan 2010.

Add date and year of the last 2 digits.

1+10=11 this is the equation (1).

Divide by 4 last 2 digits of the year.

10/4=2 equation(2).

Here we take only coefficient. Don't take reminder.

In 1st the codes to take the code and add equation 1 & 2.and divide by 7.

11+2+0/7=5.

Here we take reminder.

Answer is Friday.

Prathyusha said: (Sep 16, 2013)  
To remember month codes small tips for you guys.

Janactober-0 (jan, oct).

Dwagust-2 (aug, dwa=2).

Mayday-1 (may day is on may 1).

Femano-3 (feb, mar, nov).

Saydec-5 (sept, dec).

Julapril-6 (july, april).

June-4.

Try to remember like this guys.

Kaveri said: (Nov 14, 2013)  
Hi friends,

2005 1st Jan is sunday,
31st Dec 2005 is Saturday,
2006, 2007, 2008 (Leap Year), 2009.

2008 is leap year- add 2 No.

Other is 3 No(2006, 2007, 2009).

So you add + 5 days.

That mean Its day is Friday

Ramesh said: (Dec 29, 2013)  
What was the day of the week Jan 1, 2014?

Sejal Maru said: (Dec 30, 2013)  
How the 365/7=1 answer was came?

Naman Rai said: (Jan 22, 2014)  
Odd days came as 5 so it should be Friday not Thursday. We take Sunday as 0. So if we start it from Sunday then till the counting of 5 it should come as Friday.

Sri said: (Jan 22, 2014)  
How you got 24 leap years in 100 years ?

Prabhuchandu said: (Jan 22, 2014)  
Centuries can be remembered like this :

1600-1699->6.
1700-1799->4.
1800-1899->2.
1900-1999->0.
2000-2099->6.
2100-2199->4.
2200-2299->2.
2300-2399->0.
.
.
.
.
.
.
This will continue.

Pawan Bejawada said: (Jan 30, 2014)  
365/7 In this you have to consider reminder.

Venkatesh said: (Jan 30, 2014)  
How to find 31st December 2005 is Saturday?

Neha said: (Feb 8, 2014)  
How to calculate odd days?

Vinodh Guvalla said: (Mar 11, 2014)  
This is easy explanation by @Narendra.

Sri said: (May 15, 2014)  
If 1st Jan is a Sunday then find the number of Sundays in that year?

Jenny said: (Jun 18, 2014)  
2006/4, 2007/4, 2008/4, 2009/4 if remainder will zero that is the leap year.

Mustaq said: (Jul 12, 2014)  
1 year = 365 days and 8 hours.

So after 3 year = 3*8 = 24 hours = 1 days.

Priya Gaikwad said: (Jul 14, 2014)  
1 jan 2006 = Sunday count 1 .
1 jan 2007 = Monday count 1.
1 jan 2008 = Tuesday count 1.
1 jan 2009 = Thursday count 2 because 2008 is leap year(2008/4=0).
1 jan 2010 = Friday. Req. answer.

Prabu said: (Jul 28, 2014)  
If any shortcut to solve this problem with in 1 min.

Sameera Keerthana Best Frnds Forever said: (Aug 18, 2014)  
Don't confuse yaar just calculate.

Jan 1 2010 = (jan+2009)odd day calculation.

For 2009 no.of odd days are (2000+1+2+3+4+5+6+7+8+9)
(0+1+1+1+2+1+1+1+2+1) = 11/7 = 4 odd days.

For 1 Jan no.of odd days = 1 odd day.
So totally = (4+1) = 5 odd days.

5->Friday.

Shiva said: (Aug 21, 2014)  
How do find leap years?

Dhara said: (Aug 28, 2014)  
Easy style to calculate this question.

jan 1, 2006 sunday.
jan 1, 2007 monday (+1 in day because 2007 is not leap year) .
jan 1, 2008 wendsay (+2 in day because 2008 is divisible by 4).
jan 1, 2009 Thursday (+1 in day because it is not leap year).
jan 1, 2010 Friday (+1 because it is not leap year).

If leap year then add 2 days otherwise 1 day will be add if and only if year is only changed and date will be same.

Himanshu said: (Sep 16, 2014)  
Method to find the leap year:

If any year divided by 4 without reminder its year known as leap year.
Example-: 2008/4 = 502(no reminder).

And in this year were 29 days in Feb.
And a year consist 366 days.

Susi said: (Sep 16, 2014)  
How to find the day for any given date?

Vasim Ghanchi said: (Sep 16, 2014)  
1-jan-2006 sunday.
1-jan-2007 Monday.
1-jan-2008 Wednesday (if year is leap year then left one day and next day will be used).
1-jan-2009 thursday.
1-jan-2010 Friday.

Darkkites said: (Sep 23, 2014)  
Divide 4 to any year. If reminder is 0 then it is leap year.

Kasinath @Hyd said: (Oct 7, 2014)  
From 2010..... 2000 is a factor of 400.(A/C to leap year Formula).
Therefore Year 2000 is Leap year hence we get 0 odd days.

From remaining 10 Years we have,
8 Ordinary years and 2 leap years i.e.,(4th & 8th year).

=> 8*1 + 2*2 = 12 days.
12/7 = 1 week + 5 odd days.

A/C to formula 5th day represent Friday.

Mounika said: (Oct 10, 2014)  
How we can find same day of another year?

Sunidhi said: (Nov 18, 2014)  
Hey friends please help me please give me another formula to solve problems because by above condition all problems are not solved. Please help me.

Sumit said: (Dec 3, 2014)  
Please just tell me how to find out leap year, and odd days?

Prabhas said: (Jan 31, 2015)  
What is the day of 8-oct-1996?

Sohan Bansal said: (Mar 24, 2015)  
What is the even day?

Akshay Dixit said: (May 12, 2015)  
Yes, still I have doubt. Can any one give easy and clear method?

Manoj said: (May 29, 2015)  
I am little confused with this particular question. Could you please explain in detail?

M Rajeswari said: (Jul 8, 2015)  
Simple in question we have 2006 Jan 1 to 2010 Jan 1.

Here 2006, 2007, 2008, 2009, 2010.

In this number of odd days in each year is 1 but 2008 is is the leap year. So we can take extra one day so it is 2.

Then now total number of odd days is 6.

Now from Jan 1 2006 Sunday to 6th day of Jan 1 2010 is Friday.

I think it is helpful.

Ashwini said: (Jul 27, 2015)  
Lot of confusion is there in calendar problems. Please give me clarity on finding odd days of leap and ordinary year and days also.

Sumanth Geras said: (Aug 5, 2015)  
Hello guys according to the formula.

Jan=1.
Feb=4.
Mar=4.
Apr=0.
May=2.
Jun=5.
Jul=0.
Aug=3.
Sep=6.
Oct=1.
Nov=4.
Dec=6.

Days:

S=1.
M=2.
T=3.
W=4.
Th=5.
F=6.
Sat=7 or 0.

Formula = Day+month no. + (x-1900) + (x-1900) /4.

X = The year we have to calculate.

Answer/7 = Day we require. We can calculate it for leap year also.

If the given date is before 1st mar' of leap year. The obtained answer is given date if it is. On and after 1st march leap year you should subtract 1 from answer.

Girish said: (Aug 12, 2015)  
Is above formula is applicable to leap year?

Akki said: (Aug 25, 2015)  
In 100 year they found 76 odd & 24 leap year.

I cannot understand please any body help me?

Ram said: (Sep 5, 2015)  
Please briefly explain who to find out the leap year.

Mahesh said: (Sep 6, 2015)  
Please explain that ''2004 august 15'' which day with explanation, I'm getting little bit confusion.

Amaranth Reddy said: (Sep 15, 2015)  
Month code:

January -1.
February -4.
March -4.
April -0.
May -2.
June -5.
July -0.
August -3.
September-6.
October -1.
November -4.
December -6.

Days:

Saturday -0.
Sunday -1.
Monday -2.
Tuesday -3.
Wednesday -4.
Thursday -5.
Friday -6.

Century code:

1500-1599=0.
1600-1699=6.
1700-1799=4.
1800-1899=2.
1900-1999=0.
2000-2099=6.
2100-2199=4.

Formula:

Date+Month code+No. of years+No. of leap years+century code/7.

Problem:

That ''2004 august 15'' which day?

Solution:

15+3+4+1+6/7.

=>7) 29 (4.
28.
_.
1 = Sunday.

Answer is Sunday.

Note:

No. of leap year calculation is.

4) 4 (1=quotation value can be taken.
4.
-.
0.

Maradon said: (Sep 21, 2015)  
If instead of every fourth year, every third year is a leap year, then what day will it be on the 1st January 2020, of year 2013 is a leap year and 1st January 2013 is a Friday.

Navaj said: (Oct 6, 2015)  
2015-Feb-14-Saturday.

What is the day of 2020-Feb-18?

Give me full explanation to this question?

Jai said: (Oct 6, 2015)  
Can Anybody Explain how to find odd days in months.

January -1.
February -4.
March -4.
April -0.
May -2.
June -5.
July -0.
August -3.
September-6.
October -1.
November -4.
December -6.

@Sumanth Geras, @Pavithra, @Amaranth Reddy can you explain how to get code?

Vivek said: (Nov 3, 2015)  
Hi Friends,

The concept is after every year the 1st day will be next day of previous year for example if on 1st January, 2007 the day is Monday then on 1st January, 2008 the day will be Tuesday.

But for year after leap year, the day is next of next day for example for 1st January, 2009 the day will be Thursday. You can verify it from calendar.

Simanchala Panda said: (Nov 7, 2015)  
In a 100 year there should be 25 leap year when that century year is divisible by 4 00 otherwise century year is not a leap year so there are only 24 leap year.

Ramya said: (Jan 6, 2016)  
How to find the exact day?

Visu said: (Jan 10, 2016)  
Miss @Pavithra.

Your calculation is wrong. Please correct your mistake.

Karan said: (Jan 14, 2016)  
How many odd days are there till 1947?

Shivaram said: (Feb 5, 2016)  
Its simple:

2007-1 odd day (leap year).
2008-2 odd days (non leap).
2009-1 odd day (leap year).

= 1 + 1 + 2 + 1 (Jan 1= 1 day) = 5 = Friday.

Vinay said: (Feb 17, 2016)  
How to solve the problem method or what was the day on the 15th August 1947?

Bharathi said: (Feb 27, 2016)  
I need the correct answer. Which is very simple to understand?

Rajesh said: (Mar 14, 2016)  
In 100 year they found 76 odd & 24 leap year.

I cannot understand please any body help me?

Soubhagya said: (Mar 20, 2016)  
In 100 year we find leap year & non leap year first.
We take 99 years because 100th years is continues.

In 100/4 we get 24 leap year & 99-24=76 is normal yard.

In leap year we get 2 odd days,
In non-leap yard we get 1 odd day, Like this we can find leap the non leap years.

Praveen Kumar said: (Mar 24, 2016)  
How to solve the problem method or what was the day on the 16 JULY 1988.

Vijendra said: (Apr 1, 2016)  
It is helpful. Good question with good explanation. Thank you all.

Revathi said: (Apr 14, 2016)  
How can we know 2008 is leap year?

Dipesh said: (Apr 16, 2016)  
@Revathi. Divide by 4 is Leap Year.

This is Simple. Example 1st January 2014 is Sunday, then next year same date 1st january 2015 will be Monday.

Similarly, 1st January 2016 will be Tuesday.
Now, 2016 is leap year. So if the question asks what was the day on 1st January 2017 then it will increase by two days i.e Thursday.

Ranjeet Singh Saini said: (Apr 29, 2016)  
Why we say that 100 is a leap year?

Saikiran said: (May 4, 2016)  
@Pavithra.

Using your formula solve the below problem and give explanation:

What will be the day of the week 15th August 2010?

Surehh said: (May 15, 2016)  
Big thank for everyone it's more helpful for solving this type of problems and I understand easy to this solving methods.

Subhash said: (Jun 4, 2016)  
Thank you all for explaining it in different way.

Mishi said: (Jun 6, 2016)  
Good and clear explanation @Sundar.

Divya said: (Jun 24, 2016)  
Hi, I had calculated the day for 23 Jan 1988 and got the answer as Sunday which was wrong in actual calendar. It was Saturday. Could anyone help me to solve this?

Anand said: (Jul 5, 2016)  
1st Jan 2006 - Sunday.
Next, 1/1/07- Monday.

2008 is a leap year so here we have 2 days extra, so 01/01/08 - Wednesday.

Next 01/01/2009 - Thursday.
so then,
01/01/2010 - Friday.

Naveenamargam said: (Jul 6, 2016)  
Codes for the calendar.

DAYCODES.

Sun = 0.
Mon = 1.
Tue = 2.
Wed = 3.
Thurs = 4.
Fri = 5.
Sat = 6.

CENTURY CODE.
1600-1699 = 6.
1700-1799 = 4.
1800-1899 = 2.
1900-1999 = 0.
2000-2099 = 6.
2100-2199 = 4.
-
-
Repeats.

MONTH CODE:.
Jan = 0.
Feb = 3.
Mar = 3.
April = 6.
May = 1.
June = 4.
July = 6.
Aug = 2.
Sept = 5.
Oct = 0.
Nov = 3.
Dec = 5.

A leap year January code=-1 and Feb = 2.

For example:- Find the day of the week on 26-jan-1956.

Solution:-.

Date + last two digits of the year + (last two digits/4) + monthcode + centuarycode.

= 26 + 56 + (56/4) + (-1) + 0 (since, 56/4 remainder is' 0' it is a leap year) (when leap year comes above).
=26 + 56 + 14 - 1 + 0 codes we said that jan=-1).
= 95 (we should divide by 7 because we have to find the day of the week).
= 95/7 (remainder '4').
= 4 (Thursday).

You can also check the calendar on this date.

Aishu said: (Jul 13, 2016)  
How everyone is calculating month codes? Can anyone explain?

Jose Kappani said: (Jul 24, 2016)  
@Divya.

When you calculated leap year 88/4 you got 22 but the date is in January, so any day before February 28 there will be this problem.

Sai Krishna Chari said: (Jul 31, 2016)  
Your solution is very nice. Thank you @Pavithra.

Rajiv Ranjan Kumar said: (Aug 12, 2016)  
Sir, I want to general method for the year 1800 - 1900 and 1900 - 2000 and 2000 and above.

How can find if 30 Sept 1853 was Monday then what day will be on 18 March 1803 and 23 April 1879?

Bhavya said: (Aug 17, 2016)  
How can you guess the leap year? Please teach me.

Sheela said: (Aug 18, 2016)  
Please help me to solve in a simple way.

Moon said: (Aug 21, 2016)  
How two same calendar are found? please help me.

Sathiyaraj said: (Sep 5, 2016)  
Here, 2010-2006 = 4 days.

2008 is a leap year, so we get one more day => 5 days.

1-Jan-2006 is Sunday.

So 1-Jan-2010 = Sunday + 5 days = Friday.

Sonali said: (Oct 10, 2016)  
Hello. Please solve my problem. I am a new learner to reasoning. If october1 is Sunday then 1st November will be what date? Solve this and tell the tricks.

Rishika said: (Nov 5, 2016)  
If Thursday falls on 1st January 2015, what day of the week will be on 1st January 2016?

Give me the clear solution.

Srijita Biswas said: (Nov 10, 2016)  
Hi please solve this question.

If 2nd July 216 is Wednesday then find out the day of 4th June 2019.

Vinod said: (Dec 22, 2016)  
15 June 1987 how I can found which day of the week? Please let me know the solution.

Harsh said: (Jan 5, 2017)  
Nice explanation @Sundar.

Kundan said: (Jan 10, 2017)  
Hi,
A simple technique is;
2010 - 2006 + no. of leap year between them = 4 + 1 = 5.
[There is only a leap year between 2006 to 2010 is 2008]
Now,
Sunday + 5 = Friday.

Abhishek said: (Mar 17, 2017)  
It is very helpful, Thanks @Mahesh.

Prashant D said: (Apr 15, 2017)  
Really helpful. Thanks to all.

Shubham Gupta said: (May 15, 2017)  
Hi Friends,

Odd days of a year X = Remainder of [No. of days in the year X / 7].

[Where 7 --> For every 7 days, the day will be repeated, thats why we are dividing the total number of days of an year by 7. If it has any remainder then it will be considered as an odd day for that year.]

The required remainders (odd days) for the different years are given below:

For 2006: 365/7 = 1 (Total no. of days in 2006 is 365)
For 2007: 365/7 = 1
For 2008: 366/7 = 2 (Leap year, hence Feb month has 29 days)
For 2009: 365/7 = 1

Therefore, total number of odd days = 5.

Given day is 'Sunday' and total no of odd days is '5'.

The required date = Sunday + 5.

= (The 5th day next to Sunday).
= Sunday + 1-Monday + 2-Tuesday + 3-Wednesday + 4-Thursday + 5-Friday.
= Friday (Required answer).

Jyoti said: (May 26, 2017)  
Please, memorise this.

Jan=1
Feb=4
Mar=4
Apr=0
May=2
Jun=5
Jul=0
Aug=3
Sep=6
Oct=1
Nov=4
Dec=6

Days:
S=1
M=2
T=3
W=4
Th=5
F=6
Sat=7 or 0

Formula = day + mon no . + (x-1900) + (x-1900)/4.
x = the year we have to calculate.

Eg:
16-may-2011.

for = 16 + 2 + (2011-1900) + (2011-1900)/4,
= 16+2+111+111/4.
= 16+2+111+27.

(here we should not take the no behind decimal i.e 111/4=27.75)
= 156.

156/7 = 2(reminder).

Mon = 2.

Ajit said: (May 29, 2017)  
Thanks @Pavithra.

Rohan Roy said: (Jun 2, 2017)  
Month code- 033614625035 or 144025036146?

Please explain it.

Ragu said: (Jun 17, 2017)  
Ans :-
Step 1 ; how many years we have between 2006 to 2010 = 2006 - 2010 =4.
Step 2 ; per year 365 so if we divide by weeks = 365/7 = 52.1 that means 52weeks 1ood days.
Step 3 ; So every 4th year we have an extra day that we call leap year means 366 days again if we divide by weeks = 366/7 = 52.2 in this 2 ood days we have.
Step 4; 2006 = 1.
For 2007 = 1.
For 2008 = 1.
For 2009 = 2 (1+1+1+2 = 5days).
Step 5;
1 jan 2006 = Sunday count 1 .
1 jan 2007 = Monday count 1.
1 jan 2008 = Tuesday count 1.
1 jan 2009 = Wednesday & Thursday count 2 because as per our count it is leap year(2days extra).
1 jan 2010 = answer is Friday.

Tarun said: (Jun 27, 2017)  
How to find an leap year by seeing an year. Ex. 2006 is which year?is it leap year or ordinary year. If it is leap year how can we say it is leap year. If not how can we say not?

Sai said: (Jul 4, 2017)  
Good @Sundar.

Minhaz said: (Jul 12, 2017)  
Thanks @Sundar.

Vinay said: (Jul 18, 2017)  
If a month has 31 days, Then we have 3 ODD DAYS.

If a month has 30 days, Then we have 2 ODD DAYS.

Suresh said: (Jul 19, 2017)  
In 2007 -one odd day,
In 2008 -two odd days,
In 2009 -one odd day,
So 2010-(add 4 days to sunday).

ANS: Friday.

Pooja said: (Jul 25, 2017)  
What was the day of the week 28 feb 1995?

Can anyone please explain?

Sachin said: (Aug 7, 2017)  
In this question, we can apply formula.

f = k + (13 * m-1)/5+D D/4+C/4-2C.

Yilkunna Benedict said: (Aug 8, 2017)  
A question was asked that how can you calculate a no of leap year in 100 years but answers provided does not give a clear solution to the question. Please, tell me how can I know that 100 is the beginning of the year? Thanks.

Benino said: (Aug 8, 2017)  
In 400 consecutive years, there are 97 leap years. Hence in 400 consecutive years, February has the 29th day 97 times. How was 97 leap year gotten?

Mangesh said: (Aug 21, 2017)  
Odd days -consider no of weeks in 15 days=15/7=2 week plus1additional day
This additional day is an odd day.
To solve given Q : ordinary yr =52
weeks plus 1 odd day=365 days
Leap yr=52 plus 2 odd days=366 days
2006 ordinary-1 odd
2007 ordinary-1 odd
2008 (leap bcoz divided by 4)-2 odd
2009 ordinary-1 odd
2010 ordinary-1 odd
Total odd days=1+1+2+1+1=6.

Go six day ahead of Sunday there is Friday.
Leap yr concerned with Feb month ordinary month 28 days.
Leap Feb 29 days.

Shubham Aragade said: (Sep 8, 2017)  
What is the day on second July 1984?

Srikanth said: (Oct 6, 2017)  
It's Monday @Shubham Aragade.

Mangesh V Upare said: (Oct 10, 2017)  
There are 5 no of odd days in between Jan 1 2006 to Jan 2010.

Add 5 days in Sunday.

Shiva said: (Nov 11, 2017)  
Thank you @Pavitra for your concept. And the only thing I found this for leap year. Especially if we calculate the month of Feb in any leap year. We have to use (answer-1) as the real answer. If I am wrong please let me know.

Chithra said: (Dec 1, 2017)  
Can anyone tell me the formula to find the day of the week for a year less than 1900?

Yogini said: (Dec 6, 2017)  
12th may 2016 was Wednesday then on what day will be the independence day in the same year?

Please solve this?

Jaimin said: (Dec 12, 2017)  
@Yogini.

If 12th may 2016-wed....(may 31 days={28}+3 so add 3 days)
12th June 2016-sat......(June 30 days={28}+2 so add 2 days)
12th July 2016-mon.....(July 31 days so add 3 days)
12th August 2016-thurs... and adding (3) we get 15th August Sunday.

Gajendra Singh said: (Dec 16, 2017)  
Can someone help to me for this question?

If 31st July, 1993 was Friday, then what will be the day on 31st July, 2001?

Pravin Kumar. S said: (Dec 23, 2017)  
If 2nd February 2004 fells on Monday, then what was the day on the 10th November 2004? Explain the answer.

Raju Verma said: (Dec 25, 2017)  
What was the day on 1st February 1972? Please explain.

P.Venkatesh said: (Dec 28, 2017)  
Thank you friends.

Sagar said: (Jan 3, 2018)  
If in a month fourth day after 21st was saturday then what was the day on 3rd of the month?

Yogini said: (Jan 10, 2018)  
Thank you @Jaimin.

Kummari Hemanth said: (Jan 25, 2018)  
1600+400=6odd days.
10 =2+8
=4+8=12
=4odd days
Total=4+6/7=10/7=3odd days.
Jan=2.

All odd days =3+2=5=Friday.

Amar said: (Jan 31, 2018)  
2006 jan 1 Sunday
2010 jan 1 ?

Here,
Jan 1 ana jan1 cut
then,
(2010-2006)
=4
leap year = 1
=4+1
=1

So, given day is sunday+5
= Friday is the answer.

Prashanth said: (Feb 15, 2018)  
If 1932 December 21st is a Sunday then which day is 2018 December 21st?

Can anyone solve this?

Indrani said: (Mar 6, 2018)  
If 18th may is a Sunday, then which day will fall on 5th September of the same year?

Can you please find the answer?

I am not getting it.

Pujaa said: (Mar 22, 2018)  
How to find leap year? Please explain.

Naren said: (Jun 25, 2018)  
Divide the years last two digits by 4 if the remainder is 0 then it's a leap year.

Atharva said: (Jul 12, 2018)  
What are the odd days how to find it? Please tell me.

Ramesh said: (Jul 13, 2018)  
Formula:day + month code + no of years(last 2 digits) + no of leap years + century code.

Month code :1 4 4 0 2 5 0 3 6 1 4 6.

Centuty code: 1900-1999=0.
2000-2099=6.
2100-2199=4.
2200-2299=2.

Day code: Sat-0,Sun-1,Mon-2,Tue-3,wed-4, Thu-5, Fri-6.

Lokesh said: (Jul 17, 2018)  
Hi guys.

I just want to know how to find a leap year. Is there any tips to remember? Please tell me.

Pavan Kalyan said: (Jul 26, 2018)  
Take any particular year and divide that year with 4.

If youu get the exact division, then, such year is a leap year.
Eg:- 2012 divide with 4 = 503.
2016/4 = 504,
2014/4 = 503.5. ( this is not a leap year. you shouldn't get decimals at the end.)

Sahithisundararao said: (Jul 30, 2018)  
Can anybody tell me how to calculate; what is the day on June 15, 1998?

Yogesh said: (Aug 24, 2018)  
How to find day on 1 Jan 1900?

Umasankar said: (Aug 25, 2018)  
No of odd days =5 on December 31, 2009, it comes on Friday.
Jan 1, 2010, it comes on Saturday.

Sayyam said: (Oct 2, 2018)  
If on 15th Jan 1993 its Monday then what day of the week will be on 17 Aug 2004?

Please explain.

Nivedhitha said: (Oct 7, 2018)  
On which day of the week does 3rd March, 2005 falls?

Aryan said: (Oct 11, 2018)  
If Friday is on 15 September 2000 then what would be the day on 15 September 2001?

Please explain me.

Vanisha Nagar said: (Oct 16, 2018)  
If it was Tuesday on 24 March 2018 then what was the day on 26 January 1950? Please explain.

Salini said: (Oct 16, 2018)  
Hi guys.

For this 1/1/2006 Sunday then 1/1/2010 ___day.

For this, from 2006 to 2009 the odd days will be 1+1+2+1.
So, 5 days.
Sunday - 0, Monday - 1, Tuesday - 2, Wednesday - 3,Thursday - 4, Friday - 5.
So, till 31st December. We counted.

And my doubt is 1/1/2010 is another day which we have not counted. And it will be Saturday. Please, anyone, clear my doubt.

Sam said: (Oct 27, 2018)  
If 21st November falls five days before Wednesday then what will be the day on 25th December?

Can anyone answer this?

Balu said: (Dec 26, 2018)  
@Vijaya.

Nice explanation. Thanks.

Sowndharya said: (Feb 1, 2019)  
What was the day in 14 August 2008? Can anyone answer this?

Abhi said: (Feb 8, 2019)  
@Sowndhrya.

It will be Thursday.

Abhi said: (Feb 8, 2019)  
@Sowndharya
It will be Thursday

P Shobha said: (Mar 2, 2019)  
@Sundar.

How you take Jan 1, 2006 is Sunday?

Jason Roy said: (Mar 29, 2019)  
Thank you all for explaining.

Shivani said: (Apr 13, 2019)  
2006 - Sunday.
2007 - Monday.
2008(leap year) - wednesday.
2009 - Thursday.
2010 - Friday.

Roopchandrayadav said: (Apr 15, 2019)  
Only takes a remainder number of year.

As 2006-1
2007-1
2008-2
2009-1.
Total remainders number=5.
Then, Sunday from 5 days next Friday.

Ash said: (May 17, 2019)  
If 15 August 1947- Friday.

Then what will be 7 May 2019? Anyone solve this.

Soumya said: (May 22, 2019)  
6th day of August 1989 falls on Thursday.

Then the number of Sunday in that month are? Can anyone explain to me?

Pradyumna Kumar Tiwari said: (Jul 1, 2019)  
@Soumya.

6th Aug is Thursday it means 2nd Aug is Sunday.
After every 7 days, the same day will fall.
2nd Aug, 9th Aug,16th Aug, 23th Aug, 30th Aug are Sunday. It means a total of 5 Sunday in Aug.

Sooraj Mahato said: (Jul 22, 2019)  
It is very simple remeber these 2 basic terms:

1)whenever we go from general year to general year or leap year then add 1.
2)whenever we go from leap year to general year then add 2.

Now come to question:

Given Jan 1 , 2006 was Sunday then;
Jan 1, 2010 = ?.

So here we go;

2006(general year) to 2007(general year)=1
2007(general year) to 2008(leap year)=1
2008(leap year) to 2009(general year)=2
2009(general year) to 2010(general year)=1

Adding them=1+1+2+1=5.
now Jan 1, 2010 = sunday+5= Friday.

Hope you guys got it. It's very simple method.

Kiranbaladora said: (Aug 2, 2019)  
Hi,

Jan 1 2006 is sun.

Jan 1 2010 is ---date is same, year is different so if you are going general year to leap year add +1 days (leap to general add +2 days).

So 2007 is mon, 2008 is a leap year (divisible by 4) so add 2 days i.e. wed, 2009 is thus, 2010 is Friday.

Jyo said: (Aug 13, 2019)  
If 3-March-2018 is Thursday.

Then 03-March-2008 which day will come?

Desu said: (Aug 17, 2019)  
On a fix particular date, as the year increases by one unit, the day also increases by one unit, Except for leap year where the day is increased by two units.

So coming to the problem:

On particular date 1 Jan.
Day- sun and year-2006.

So on increasing year by one unit.
Year - Day
2007 -.Monday.
2008. - Tuesday.
2009 - Thursday (when leap year is increased by one unit days Will be increased by two units)
2010 - Friday.

Sandip Manware said: (Oct 14, 2019)  
Month code for ordinary year 144 025 036 146.

Formula to find day = date + month code + last 2 digit of year + last 2 digit/4 ......note- take only whole number not after decimal.

Ex.. 15 Aug 1989.

15 + 3 + 89+ (89/4).
15 +3+ 89+22..........89/4=22.xxxx
= 129.

Divide 129 by 7.
129/7 = The remainder will be 3.

Then sunday =1
Monday=2
Tuesday=3
Wednesday=4
Thursday=5
Friday=6
Saturday=00
Aur remainder is 3 then answer will be Tuesday.

Pls, remember.

For 1900 series add in addition = 00
For series 2000 add +6
For series 2100 add +4
For series 2200 add +2
For series 2300 add +00
For series 1800 add +02
For series 1700 add +04
For series 1600 add +06

Srinivas said: (Nov 20, 2019)  
2006 = 1(odd day).
2007 = 1(odd day).
2008 = 2(odd days-it is a leap year).
2009 = 1(odd day).

Total = 5(odd days).

Monday=1
Tuesday=2
Wednesday=3
Thursday=4
Friday=5
Saturday=6
Sunday=7/0

So now we consider 5 as Friday.

Saket said: (Dec 10, 2019)  
3 April 2005.
6 August 2010.
5 December 2013.
15 August ?

Rashi Thakur said: (Dec 11, 2019)  
How can we find that 1996 is a leap year?

Monika said: (Dec 25, 2019)  
How many Sundays are there in year if 1st December in that year is on Sunday?

Ganesh said: (Feb 21, 2020)  
November 25, 1950 was Saturday what day was November 2016?

Deepika said: (Mar 3, 2020)  
If the first day of 1987 is Thursday, then what will be the last day of the year 1987?

Ivan said: (Mar 14, 2020)  
@Deepika.

If the given year is a non-leap year then the first day is the same as the last day of the year.

For leap year last day will be the next day of the starting day of the year.

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