Aptitude - Calendar - Discussion

Discussion :: Calendar - General Questions (Q.No.3)

3. 

What was the day of the week on 17th June, 1998?

[A]. Monday
[B]. Tuesday
[C]. Wednesday
[D]. Thursday

Answer: Option C

Explanation:

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan.  Feb.   March    April    May      June 
(31 +  28  +  31   +   30   +   31   +   17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.


Shruthi said: (Aug 17, 2010)  
How to calculate odd days for 300 years?

Bhupendra said: (Aug 18, 2010)  
499*2=899 = no of odd day in leap(for understand)
1996-499=1497 odd day in remaining year (for understand)
odd day 899+1497= 2396 total odd day (for understand)
2396/7= 342+ 2/7=> 2odd day (actual odd day till 1996)
2+1= 3 odd day till 1997 (actual odd day till 1997)
then 1 Jan 1998= thursday
Jan 31
Feb 28
mar 31
april 30
may 31
june 17= wedenesday

Nitesh Nandwana said: (Oct 10, 2010)  
@Hi Shruthi,.

It is measured that each 100year has 5 odd days OK ?.

(remember it always don't ask why because this is not our main problem).

So, for 300years 5*3=15 odd days.

But 15 days are convert-able in weeks.

So, 15/7 = 2 weeks + 1 odd days.

(leave days for week, now they are not odd).

That's why 300years = 1 odd day.

Srinivas said: (Nov 3, 2010)  
We can caluclate the number of leap years by dividing the given two digit nuber with 4.

Supose we will take the above problem if 98 is divided by the 4 then we will get the no. Of leap years which nothing but the multiple of four i.e. 24.

Then 97 - 24 = 73.

73 ordinary years and 24 leap years.

Venkatesh said: (Jan 11, 2011)  
How did you calculate number of odd days for 97 years?.

Dinesh said: (Jan 11, 2011)  
What's odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) 1

97 years has 24 leap years + 73 ordinary years.

Sathi said: (Jan 26, 2011)  
How to calculate odd days in a year ?

Rajesh said: (Feb 4, 2011)  
17th june 1998
year 98+
year code 24+
month code 05+
day 17+
144%7
140+4
wednesday is the answer

Sandeep said: (Feb 18, 2011)  
Mr. Rajesh how you know year code.

Praveen said: (Feb 19, 2011)  
Please tell me how 0 odd days for 400 years ?

Praveen said: (Feb 19, 2011)  
If 5 odd days for 100 years, then for 400 years it will be 5x4=20 means 20%7 = 6 odd days no...? bit confused about this calculation....anybody help me please..

Chetan said: (Mar 3, 2011)  
I am not understand problem correctly. Please anybody explain me.

Vaibhav said: (Mar 16, 2011)  
Nice one rajesh.

Nitin said: (Apr 20, 2011)  
How can I find no leap year in 97 year.

Aishu said: (Apr 29, 2011)  
How to find the month code rajesh ?

Inshan said: (May 14, 2011)  
Think it like this!!
Maybe year 0 A.D. is included as an ordinary year rather than as a leap year.
So,
2000 yrs = 499 leap years. (Year: 0 A.D. is be included.)
= 1501 ordinary years
But, 1997 yrs = 498 leap yrs
= 1499 ordinary years
(Year 1998 is not taken because it is of this year's day of 17th of June that we have to figure out.)

1.) Leap years = 366 days (per year)/ 7 = Remainder is 2. Therefore, 2 odd days for every leap year, i.e. to say,
Total odd days = 2 * 498 = 996 odd days
2.) Ordinary years = 365 days (per year)/7 = Remainder is 1. Therefore, 1 odd day for every ordinary year, i.e. to say,
Total odd days = 1 * 1499 = 1499 odd days.

Therefore, total odd days altogether = 2495 days / 7 = 3 odd days.

April and June, & September and November: 30 days each.
Rest of the month: 31 days.
So, for 17th June = 31+28+31+30+31+17 = 168/7 = 0 odd days.

Total odd days = 3 + 0 = 3 odd days.
If 3 odd days:
Start at Sun: Then, 1st is Mon, 2nd is Tues and 3rd is Wednesday.

Inshan said: (May 15, 2011)  
Sorry for mistake!
What I said was that 0 A.D. is not included as either years!
But, I surmise that it is better to take into account every 100 yrs to understand such problems better.
For this, we need to figure out how many ordinary years and leap years are there altogether in a century (100 yrs). If we find this, we will go to heaven!!! :)))

C.Paththira Selvi said: (May 17, 2011)  
How to calculate this sum?

Ranjith said: (Jul 7, 2011)  
How could you tell that 1600 has 0 odd days?

Anupama said: (Jul 10, 2011)  
Wy we are 300 years and why we are calculating odd days for 300 ?

Arya said: (Jul 20, 2011)  
Counting of Odd Days:

1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 1 + 24 x 2) odd days = 124 odd days.

= (17 weeks + days) 5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Rinki said: (Jul 25, 2011)  
Pls tell me ....why did you add 1 in the calculation of odd days in 400 years???

Vanita said: (Jul 27, 2011)  
Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Why, (Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.) in this 1 is added ,

please clarify

Steffy said: (Aug 22, 2011)  
To Nitin:

Here we have 97 yrs

97/4=24 leap yrs

97-24=73 ordinary yrs

Ekta said: (Sep 16, 2011)  
Thank you Arya. I can understand properly your solution.

Sri Harsha. P said: (Sep 17, 2011)  
There is another way...

Remember the code FOR ALL PROBLEMS ABOUT CALENDER


MONTH : J F M A M J J A S O N D
CODE . : 0 3 3 6 1 4 6 2 5 0 3 5

and

CODE FOR THE YEAR
1700 -- 1799 = 4
1800 -- 1899 = 2
1900 -- 1999 = 0
2000 -- 2099 = 6
2100 -- 2199 = 4

AT FINAL EX: FOR 17 JUNE 1998

take the last two numbers in the year for ex. In 1998 take 98 and divide them by 4 and take only the quotient and leave the reminder

ex: 4)98(24
8
----
18
16
----
2
leave that reminder 2 and take only quotient 24.

add the following

month code for JUNE 4
year code for 1998 0
left quotient while
divided by 4 24
finally add the last
two numbers in year
1998 and date17(98+17) 115

------------
143

divide the amount by 7 i.e., 143/7
here take only the reminder and left the quotient.

ex: 7)143(2
14
----
03
take the value of reminder 3.


WEEK S M T W T F S
CODE 0 1 2 3 4 5 6

IN THE ABOVE PROBLEM ANSWER IS 3 THEN DAY IS W-Wednesday


ANOTHER EXAMPLE: 15 AUGUST 1947

ADD

month code 2
year code 0
quotient divided by 4 11
(47+15) 62
----
75
75/7 take only reminder 5
Answer is 5-F-Friday.

Raviteja said: (Sep 27, 2011)  
For those who did not understand this problem,let me try to explain you.

The first thing to be cleared is that for every 400 years there are 0 odd days.

This is because,in 400 years,there are 97 leap years and 303 ordinary years(remember that 100,200,300 are not leap years but 400 is a leap year.Because any year ending with 00,that year should be divisible by 400 in order to become a leap year)

So the number of odd days at the end of 400 years will be [(97*2)+(303*1)]=497 days.Convert this into weeks,we get 71weeks + 0odd days=totally 0 odd days

Now coming to the problem,
1997=1600+397
for 1600 years 0 odd days
therefore 397 years can be classified as
1601-1700-->24 leap years + 76 ordinary years=[(24*2)+(76*1)]=
124 odd days
1701-1800-->24 leap years + 76 ordinary years=124 odd days
1801-1900-->24 leap years + 76 ordinary years=124 odd days
1901-1997-->24 leap years + 73 ordinary years=121 odd days
totally we have 124*3 + 121=493 odd days
convert this into weeks=70weeks +3 odd days
Hence at the end of the year 1997,we have 3 odd days

Now coming to the year 1998,
the number of odd days=31+28+31+30+31+17=168 odd days(jan,feb,...jun17th)
Convert this into weeks=24weeks +0 odd days
Hence the total odd days=3+0=3 odd days
therefore 17th june 1998=Wednesday

Janvi said: (Oct 21, 2011)  
How you got ordinary days? could you explain?

Hdx said: (Nov 9, 2011)  
Here is complete solution, the year is 1998
16+3=19
See from 0 A.D
1600yr+300yr =1900yr
We are calling the odd days from the 0 A.D. So 1600 yr has 0 odd days
But the remaing 300 year has 15 odd days and rest you can do.

Arun said: (Nov 12, 2011)  
How to calculate odd days for 300 years? I don't understand this only.

Rishi said: (Nov 18, 2011)  
Ishan , Arya and Raviteja

Thanks to all u for ur such a explanation

Praveen Kumar said: (Nov 22, 2011)  
How we gat an idea to take 1600 years and 300 years in above problem.

Muthaiyan said: (Dec 27, 2011)  
Step 1:[1997+1.1.1998to17.6.1998]
step2: 1997=1600+300+97=> 1600 is 0 odd days, 300 is 1 odd day
step3: calculate 97
step4:97/4= 24,=> [24-97=73]
step5:24leap year +73 ordinary year=>(24*2)+(73*1)=127
step6:127/7=17,=>17week+2 odd days
step7:1998 is an ordinary year therefore [31+28+31+30+31+17=168]
ste8:168/7=24weeks+0 odd days
step9:add all odd days we get 3 is an wednesday

Ravihans said: (Jan 10, 2012)  
Good explanation rajesh.

Saurabh said: (Feb 3, 2012)  
Muthaiyan good way of explanation.

Chitaranjan said: (Mar 7, 2012)  
1998=1600+300+98
1600-->0 odd days
300-->1 odd day
98 years= 24 leap yr +73 normal year

= 24*2+73*1=121 odd =121/7=2odd

Jan to June 17 =168 days =168/7= 0 odds
Total odd days=0+1+2+0=3, so its Wednesday.

Mickey said: (Apr 16, 2012)  
A simple trick to solve calender problems for those who don't wana go for tidious concepts.

Just memorize these codes for months.

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.
Where x = the year we have to calculate.

Eg.

17 june 1998.

Req day = 17+5+ (1998-1900) + (1998-1900) /4.
=17 + 5 + 98 + 98/4.
=17 + 5 + 98 + 24 (here do not take the digits after decimal).
=144.

Now. Devide 144 by 7.
we'll get quotient=20 and remainder=4.
So 4th day is wednesday.

This is the simplest trick. We just have to memorize the codes for months.

Ravi said: (May 8, 2012)  
Thank you harsha

But tell me in case of any case if date is of 16 jan 2002. becoz here we will divide 02 by 4 which gives 0. thn code for jan =0, year code =6, adding 02+16=18.

Hence total gives=0(quotient)+0(month code)+6(year code)+18(addition of last two digits and date)=24

24/7 gives quotient gives remainder as 3 i.e tuesday. but on this date it is saturday... plz explain..

Sruthi said: (May 26, 2012)  
How to know how many odd days to 121 days?

Shail said: (Aug 19, 2012)  
Hi every one,

Here is the best solution for this for Arun and all those who want to know about concepts of using 1600 and then 300 years.


Basics :
odd days are calculated on weeks. If given 8 days, we can have 7 in a week. so here odd days=1 , where as if we have 13 days then this no will be 5.
for 121 days. 121/7=17weeks +2 days. here 2 days are odd days.

now for a year we have total of 365 day .
for leap year 366.

Step1: every ordinary year(365 days)=1 odd
Step 2: Every leap = 2 odd days.
Step 3: 100 years= 76ordinary + 24 leap year.=76+ 48=124 :: 5 odd
Step 4: year 4th century is leap year. means 100,200,300 years will have 5 odd days and 400th year will have 6 odd days.
thats coz. 400th year=25 leap +75 ordinary years=125:: 6 odd days.

Step 5: for 300 years odd days= 5+5+5=15:: 1 odd
Step 6: and for 400 years odd days =5+5+5+6=21= 0 odd days.

Step 7: Rest is explained clearly.

Radhika said: (Sep 2, 2012)  
How do we calculate for 75years it is 18 leap years +57 ordinary years ?

Roxy said: (Dec 5, 2012)  
17 June 2000. What is the day, can any one explain the solution. Please calculate using odd days method? The answer is Saturday.

Ramya said: (Dec 9, 2012)  
How to calculate no.of leap years in given years? Ex. 87 years.

Shilpa said: (Dec 11, 2012)  
How many odd days are there in 500 years?

Vicky said: (Dec 31, 2012)  
Leap year comes for every four years

The basic rule to know about leap year is that the year should be divisible by 4

For Eg: 4, 8, 12, 16, 20................100, 104 etc.,

Then here as per my knowldeged 25 leap years should exists for every 100 years.

why all are considering 24yrs in 100 years?

Need clarity on this.

Juhi said: (Jul 15, 2013)  
According to my thinking:

97 years has 23 leap years not 24
because if in 100 years 24 leap years.

Then in this case from 1901 to 2000 the last one is leap is 2000, which we are not counting because we want to count from 1901 to 1997.

So please justify your answer.

Keya said: (Jul 19, 2013)  
@Juhi.

The centuries divisible by 400, like 400, 800, 1200, 1600, 2000...etc have 25 leap year and 75 ordinary years.

In given question we have to calculate from 1900 to 1997 therefore.

1998 - ordinary year.
1999 - ordinary year.
2000 - leap year.

So from 1901 to 1997 - ordinary years will be = 75-2 = 73.

And leap year will be = 25-1 = 24.

Priya Singh said: (Sep 21, 2013)  
300 years 5*3 = 15 odd days.

What is 5 and 3. Please tell me ?

Abhi said: (Oct 1, 2013)  
Guys, Could help me, what would be the day on 13th-july-1992 ?

Need answer with procedure. Please?

Goms said: (Oct 14, 2013)  
The basic rule to know about leap year is that the year should be divisible by 4.

For Eg: 4, 8, 12, 16, 20................100, 104 etc.,

Then here as per my knowledged 25 leap years should exists for every 100 years.

why all are considering 24 yrs in 100 years?

Vikram said: (Nov 29, 2013)  
Month codes:

Jan- 1, Feb- 4, Mar- 4, Apr- 0, May- 2, June- 5.

July- 0, Aug- 3, Sep- 6, Oct- 1, Nov- 4, Dec- 6.

Year codes:

1500-99: 0
1600-99: 6
1700-99: 4
1800-99: 2
1900-99: 0
:
:
:
So on.......

Day codes:

Sat- 0, Sun- 1, Mon- 2, Tue- 3, Wed- 4, Thu- 5, Fri- 6.

Here,

17+05+98+24+00 = 144.

144/7 = 20+ 4 days.

Which is wednesday

Ravi said: (Dec 12, 2013)  
Why you taken 300 years ? why not 400 years please explain in detail.

Naresh said: (Dec 17, 2013)  
Hello Everyone.
The simple answer is:

1996+2 = 1996(leap year)+1 ordinary year+Jan to june 17th.
= 2 odd days +1 odd day+168 days.
= 2+1+0 odd days.
= 3 odd days.

i.e Wednesday.

Vishnu said: (Jan 1, 2014)  
The question is what is day of 17 june 1998?

If the year is 1998 that is mean in 100 year gets total 25 leap years if getting 25 leap in 100 year then why using 24 leap year in above comments.

Calculating leap year.
On every 4 years gets 1 leap year.
1901 to 1904 = 1 leap year.
1905 to 1908 = 1 leap year ....

Calculating odd days
I am calculating odd days from 1 jan to 17 june 1998

in jan = 31 days
feb = 28 days
march = 31 days
april = 30 days
may = 31 days
june = 17 days
------
168 days

Dividing by 7 to 168 days (7 mean 7 days in week).

168/7= 24 = 24 weeks + 0 odd days (there is any more days).

If eg., 170 /7 = 24 weeks + 2 odd days.

Only this not understood.

In above discuss why used 1900, 300, 400.

If the year is 1998.

We should have take in 1998 years.

1901 to 2000 years = total 100 years.

1901 to 1997 years = 97 years.

24 leap year + 52 weeks + 1 odd days.

Gayatri said: (Jan 27, 2014)  
We can calculate the day of week based on current date and day.

Whenever we got back one year on the same date the day of week will be one less than today's day of week.

For example today is 27th january 2014 Monday means 27th january 2013 was one day behind of Monday i.e Sunday.

If the year is leap year the day of week goes back 2 days for examples if 27th january 2013 is Sunday and the previous year 2012 is leap year so 27th january 2012 will be two day behind sunday i.e friday. If like this we calculate we have :

27th january 2013 - Sunday.
2012 - Friday 2011 - thur 2010 - wed 2009 - tue 2008 - sun.
2007 - sat 2006 - fri 2005 - thur 2004 - tue 2003 - mon .
2002 - sun 2001 - sat 2000 - thur 1999 - wed 1998 - tues.

SO now 27th January 1998 was tuesday.
To calculate : 17th june 1998 what day?

Jan Feb Mar Apr May june
5 days 28days 31d 30d 31d 17d Total = 142d
(31-27
including 27)

Now total = 142 days between 27th january 1998(Tuesday) and 17th june 1998 .

To calculate the day divide total no of days by 7 and check the remainder. If remainder is 0 it would be previous day of week. If remainder is 1 it would be same day of week. If remainder 2 it would be next day of week and so on.

So here 142/7 = 20 and remainder 2 so the day of week would be Wednesday(Next day of Tuesday).

Gayatri said: (Jan 27, 2014)  
Use doomsday algorithm :

Remember that last day of feb , 4th april, 6th july , 8th august , 10th october and 12th december will have the same day of week which is known as doomsday and we need to calculate it in the following way :

For 1900-1999 always take the anchor day as wednesday.
For 2000-2099 always take base anchor day as tuesday.

So now formula for calculating the doomsday:

Doomsday = anchor(wed for 1900-99 tue for 2000-2099) + Y/12(ignore decimal) + remainder(Y/12) + {remainder(Y/12)/4}.

Take only last two digits of the Year.

Based on the formula we have for 17th june 1998 we have:

Doomsday = wednesday + 98/12 + Remainder(98/12) + Remainder(98/12)/4.

Wednesday + 8 + 2 + 2/4.
Wednesday + 8 + 2 + 0 = wednesday + 10 = saturday.

So from the above list mentioned for the nearest doomsday we can see that 6th june is the nearest doomsday.

So 6th june will have the day Saturday.

17th june - wednesday.

Avishek said: (Feb 17, 2014)  
Number of odd days in 97 years (24 x 2 + 73) = 121 = 2 odd days.

Can't understand this part. Can anybody explain me this part ?

Riya said: (Feb 25, 2014)  
How we got 24 leap year in 100 year.

It should be 100/4 = 25.

Why not 25? but 24.

Ritesh said: (Apr 17, 2014)  
Why 400 years have 0 odd day?

Narayan Das said: (May 16, 2014)  
To find out any day of any year of date we have to go through a formula.

Always remember Code:

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
31 (28/29) 31 30 31 30 31 31 30 31 30 31
3 (0/1) 3 2 3 2 3 3 2 3 2 3

So now today is 17/05/2014 is Saturday.(today's date)
Calculate 17/05/1998.

Now leap year(the year which is divisible by 4 or 400) coming between 1998 and 2014 is 2000,2004,2018,2012 means 4.

And year gap between 1998 to 2014 is 16.

Now add 16 to 4 and then divide with 7(days in a week)
the result gives (16+4)/7= 6

So if today is Saturday then 17/05/1998 will be Saturday - 6 = Sunday.(since we are coming to back year so we should differentiate)
Now calculate days between 17/05/1998 to 17/06/1998 is 31 day.

Now divide 7 in 31, result is 3

So if 17/05/1998 is Sunday then 17/06/1998 will be Sunday + 3= Wednesday.(Since we are going forward year we should add)

Harish said: (Jun 26, 2014)  
Solution:

First we calculate upto 1997.
1998 = 1600+300+97.

For 1600 0odd days because 1600 is divisible by 4 so it is 0.
For 300 is 1 odd days.
For 97 we have 24 leap year and 73 ordinary year.
Calculate if leap year*2 so 24*2 = 48+73.
=121.

While dividing 121 by 7 we get remainder as 2 that is 2 odd days.
Still we have to calculate from jan 1998 to 17th june 1998 we have 168 days if We divided by 7 remainder is zero.
Totally we have 3 odd days.

Sun Mon Tue Wed Thu Fri Sat
0 1 2 3 4 5 6
So answer is wed.

Dharsinipriya said: (Jul 18, 2014)  
How to calculate leap year and ordinary year between 200 years?

Pragati said: (Jul 26, 2014)  
First divide that no by 4.
200/4 = 50 is the leap year.
And 200-50 = 150 is the ordinary year.

Vinod Zala said: (Aug 14, 2014)  
Friends it's so simple, Remember only code:

Year Code:

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

Month Code:

Jan = 0
Feb = 3
Mar = 3
April = 6
May = 1
June = 4
July = 6
Aug = 2
Sep = 5
Oct = 0
Nov = 3
Dec = 5

Day Code:

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

Steps to solve:

What was day on 17/8/1998 ?

Step:1 (add day + last two digit of years).

(17+98=115).

Step:2 (divide last two digit of years by 4).

98/4 == 24.

Step:3 (add code value)

115
+24
+04 --- month code.
+00 --- year code.
-----
143.

Step: 4 (divide result step 3 by 7).

143/7 = 3.

Step:5 (match with day code).

3 === Wednesday.

Sahithi said: (Sep 15, 2014)  
Please any one explain how to find 11th oct 1993 - day?

But above explained rules are not giving exact day what it is.

Deepak said: (Sep 17, 2014)  
How to calculate odd day in 1600 years?

Maheshmydo said: (Oct 17, 2014)  
How did you arrive at MONTH CODES?

Prince said: (Dec 18, 2014)  
We can solve this problem by going back from 2000 to 17 June 1998.

= 2000-2 odd days (leap year).

= 1999-1 odd day.

= 1988 (197 days i.e 1 odd day) (31 dec+30 nov. 17 june).

Total 4 odd days.

Since we have reversely calculated it.

Sat, Fri, Thurs, Wed.

John said: (Jan 9, 2015)  
@Mickey.

Now divide 144 by 7.

We'll get quotient = 20 and remainder = 4.

So 4th day is Wednesday.

Here remainder is wrong. We will get it as 5.

How you get remainder as 4?

Monu said: (Feb 3, 2015)  
If 15 august 1993 is Friday then what would be the day of 6th march of same year? Anybody please answer this.

Kavya said: (Feb 21, 2015)  
Is there any shortcut? Its very complicated, confusing, odd days, why there is a need to take 1600, 400, it will take more time in competitive exams. Please tell easy way to solve if have.

Mamta said: (Jun 23, 2015)  
Can anybody explain me? I can't understand.

Prateek said: (Jul 9, 2015)  
How come 100 years have 76 ordinary and 24 lap years ? And how it is calculated for any number of years?

Saikumar said: (Jul 12, 2015)  
Formula = (Date+No of normal year+No of leap year+Month code+Century code)/7.

(17+98+24+4+0)/7 = 143/7.

And remainder is 3 code of week is Wednesday.

Santhosh said: (Aug 2, 2015)  
How to calculate number of odd days for 2008, 2009, 2010?

Surya said: (Aug 10, 2015)  
I can understand that problem. So please explain simple to way?

Surya said: (Aug 10, 2015)  
I cannot understand our calculation so please say simple way.

Ravi said: (Aug 13, 2015)  
Hey dude, its simply easy.

97/4 gives 24 and remaining 3.

So, 76-3=73.

So 97 =73 ordinary year and 24 leap year.

Khan said: (Aug 22, 2015)  
But why we are calculating odd days of 300? And what the role of it? Please make me understand.

Suraj Singh said: (Sep 2, 2015)  
Before asking questions, you guys should have clear concept on leap year.

A leap year is a year, which is divisible by 400, or which is divisible by 4 and not divisible by 100.

So 100, 200, 300 is not a leap year.

So in 100 years, only 24 leap years, and so on.

Saurabh said: (Sep 4, 2015)  
1998 was the leap year so the February month of 1998 has 1 odd day?

Likitha said: (Sep 20, 2015)  
Why should we consider 1600 and 300 years of odd days here?

Yatindra Umrane said: (Sep 29, 2015)  
What is odd days in 1600 years = 0 and odd days in 300 years = (5 x 3)1?

Why we calculate 1600 years and 300 years?

Gurasheesh Singh said: (Oct 8, 2015)  
What are the number of odd days in 99 years?

Krocy said: (Nov 1, 2015)  
3 odd days = Wednesday.

Gyanendra Vaishya said: (Nov 1, 2015)  
Q. How to find number of odd days in 300 years?

Solution:

First number of odd days in 100 years = 98 ordinary years + 2 leap years (2 leap years means: 2*2 = 4 odd days).

1+4 = 5 odd days.

100 years had 5 odd days.

300 years had = 5 odd days*3.

= 15 odd days = 7*2 +1.

= 0+1 (7 days = 0 odd days so, 7+7= 0+0 = 0 odd days = days).

= 1 odd days.

Deepika said: (Dec 18, 2015)  
How can we calculate in a 100 years there are 76 ordinary years and 24 leap years?

Raju said: (Jan 18, 2016)  
How can calculate in a week?

Asif Syed said: (Mar 2, 2016)  
How can we calculate in a 100 years there are 76 ordinary years and 24 leap years?

100/4 = 25; then we should have 25 leap years, but why 24 please anyone clarify this.

Rajesh said: (Mar 27, 2016)  
Is there is any shortcut way and simple way to resolve the above query?

Madhukumar M S said: (Mar 29, 2016)  
Today is 29th March 2016, Tuesday. But if I calculate as your procedure, I'm getting Wednesday as the answer. Because 2016 is a leap year, should count February as 29 days. Please clarify.

Sathesh said: (Apr 19, 2016)  
100 years are not coming Tuesday or Thursday or Saturday.

Pratik Chudasama said: (May 20, 2016)  
The answer should be Tuesday. Please check it again.

Akshay said: (Jun 28, 2016)  
Yeah. The answer should be Tuesday. Because in 100 years there are 24 leap years. But in 97 years there are 23 leap years. I think so. Where I m wrong tell me, please.

Akshay said: (Jun 28, 2016)  
@Deepika and @Asif, Just listen.

100/4 = 25, but the first year is not divisible by 4. (note that)

For example from 2001 to 2100 ....... 2001 is not leap year. That's why 25 - 1 = 24 leap years in 100 years.

Krishnoshakawat said: (Jul 7, 2016)  
Why will we calculate from 1600?

Anybody, please help me.

Vissu said: (Jul 7, 2016)  
Please explain everything ones how has come to Wednesday.

Karan said: (Jul 15, 2016)  
Can you help me in calculating? How many odd days in 50 years? Need it asap!

Srimant said: (Jul 15, 2016)  
How month code comes like;

J0, F3, M3, A6, -----, O0, N3, D5?

Bidhya said: (Jul 22, 2016)  
What is odd day? I don't understand to find this.

Priyanka Agrawal said: (Jul 30, 2016)  
@ Bidhya.

When no.of days are divided by 7 we get reminder, the reminder is called odd days.

Eg. In one year [non-leap year] there are 365 days,

So 365/7 = 1[reminder].

Then there is 1 Odd day in one year.

Simply no.of days/7 = reminder means odd days.

Vidya said: (Aug 13, 2016)  
Please explain calculation 76 ordinary years in 100 years, because I got it as 75 ordinary years.

Shyni said: (Aug 26, 2016)  
How to calculate the number of odd days in 300 years?

Sonali said: (Aug 30, 2016)  
How did you know that Feb has 28 days regarding above example?

Sathiyaraj said: (Sep 5, 2016)  
1998/4 = 499 leap years + 2 days,

499/7 = 71 weeks + 2 days,

So, 01-01-1998 falls on Wednesday(4th day of week),

Jan 31 + Feb 28 + Mar 31 + Apr 30 + May 31 + Jun 17 = 168 /7 = 24 weeks + 0 day,

So, 17 jun 1998 falls on Wednesday.

Sreejith S S said: (Sep 21, 2016)  
Read important formula of calendar problem, that time you will be realized.

Mohit said: (Oct 11, 2016)  
@ Sri Harsha.

Can you apply that trick on example Like 2002, 2014?

Karthik Babu said: (Oct 31, 2016)  
It should be 23 leap years know because 2000 is also leap year.

Khushi said: (Nov 6, 2016)  
Why we are considering odd days for 300 years? Can we consider 400 year instead of 300 year than odd days also changes.

Manoj Kumar Majhi said: (Jan 3, 2017)  
Find out the day in the date of 25 .5.1975.

Sayali said: (Jan 5, 2017)  
@Vikram.

How did you find month codes?

Ekowseegar said: (Jan 10, 2017)  
How do find the odd days in 1999?

Akash Anand said: (Jan 22, 2017)  
The answer should be Thursday not Wednesday because there are 3 odd days.

If there had been 2 odd days then answer would have been Wednesday.
Monday + 3 odd days = Thursday.

Ramya said: (Feb 5, 2017)  
@Ekowseegar.

1999 can be written as 1600+300+99.
No. of odd days in 1600 years is 0.
No. of odd days in 300 years is 1.
Now, no.of leap years in 99 years is 99/4 = 24.
No. of non leap years is 99 - 24 is 75.

Extra days=(24 * 2 + 75)
= 48 + 75 = 123.

Odd days in 123 is the reminder of 123/7 that is 4.

Therefore total no of odd days = 0 + 1 + 4 = 5.

Kavitha said: (Feb 25, 2017)  
How 1600 and 300 come? Please give me the suggestion to solve it.

Abhi said: (May 9, 2017)  
One other way of Finding the Answer is :

Just remember that 1st Jan 2000 was Saturday.

1999 (not leap year so 365 days) = 52 weeks + 1 day.
So to go to 1st Jan 1999 just have to subtract that 1 Extra day which is bringing the change.

Gardas Anusha said: (May 18, 2017)  
In 100 years isn't this correct:

25 leap years + 75 ordinary years?

4*1=4 .. 4*2=8.. 4*3=12.. ......... 4*25=100 and so 25 leap years.

Hemant said: (Jul 17, 2017)  
Sir, how you concluded 2 odd days from 121? Please explain me.

Nitin Gupta said: (Aug 15, 2017)  
Anyone explain why 144025036146 is the codes for month explain how 1 arrives for January for ordinary year and 4 for feb again 4 for March I know 31/7=3 is code for feb leap year but why 144 for jan feb march.

Kunal More said: (Nov 1, 2017)  
How to calculate leap year in 100 years?

Zemanian said: (Dec 15, 2017)  
There's a better way to solve this:

We know that for 2000 years, the number of odd days is 0.
Consider 17 June, 2001.

for the previous 2000 years, there are 0 odd days.
for the year of 2001, starting from Jan
31+28+31+30+31+17 = 168

which means there are 0 odd days.

now the day of the week for 17 June 2001 is Sunday.

now we need the day for 17 June 1998. Simply subtract the odd days of the preceding three years.

2000 is a leap year, whereas 1999 and 1998 are ordinary years.

So 0 - 2 - 1 - 1 = -4.

Go back 4 days from Sunday and you get Wednesday.

Ayesha said: (Dec 26, 2017)  
Why it's needed to calculate odd days for 1600 and 300?

Anuradha said: (Feb 15, 2018)  
How to calculate ordinary year and leap years in one century?

Please explain?

Joy said: (Apr 22, 2018)  
Simple , leap year = 100 / 4 = 25.
Ordinary year = 100 - 25 = 75.

Savanth said: (May 2, 2018)  
If you want to find number of odd days in 100 years, then 100/4=25.(Only. Quotient) Now,( 100 +25)/7=6(remainder).
So, there are 6 odd days in 100 no of Years.

Pratit said: (May 24, 2018)  
How many odd days in between 1901 to 2000? Please tell me the answer with the explanation.

Deepak Padmule said: (Jun 28, 2018)  
In 1998.

i.e, 98 is a leap year so you should have to consider 29 days in Feb month but you hadn't considered it.

Bharathi said: (Jul 21, 2018)  
Can anybody derive and say 15th June 1998 is what day? Please

Shreya said: (Jul 22, 2018)  
How to calculate 1 odd day in 300years?

Roja St said: (Jul 31, 2018)  
Thanks @Sri Harsha.

Akshatha said: (Sep 26, 2018)  
Thanks for your answer @Sri Harsha.

Sreeja said: (Sep 26, 2018)  
Why should we take 1600 and 300 here? Please explain.

Suhel said: (Nov 1, 2018)  
@Rajesh.

Can you please explain how get the year code.

Akshakumar said: (Feb 21, 2019)  
1600 + 300 + 97 + (J to March)+17.

0 + 1 + {24(leap year)+73(ordinary y)}+(3+0+3+2+3) + 17.
1 + (24 * 2 + 73 * 1) + 17.
150/7.
21 week + 4 odd days.
Then the Ans is Thursday.

Prabhu said: (May 7, 2019)  
Take 1996 is a leap yera so it has 2 odd days.

Then 1997 has 1 odd day so total odd day till 1997 is;
(2+1)= 3.

Then,
Add the date till 01-01-1998 to 17- 06- 1997 so the total,
The day is 168 days divided it by 7, 168%7 = 0 odd days so total odd says from 1996 to 17-06-1998 is 3 only do that the day is WEDNESDAY.

Mim said: (Jun 1, 2019)  
@Akshay.

1st year to 10th year= 2 Leap year(LY) + 8 ordinary year(OY)
11th to 20th= 3 LY+7 OY.
21st to 30th= 2 LY+ 8 OY.
31st to 40th= 3 LY+ 7 OY.
41st to 50th= 2 LY+ 8 OY.
51st to 60th= 3 LY+ 7 OY.
61st to 70th= 2 LY+ 8 OY.
1st to 80th= 3 LY+ 7 OY.
81st to 90th= 2LY + 8 OY.
91st to 100th year= 3 LY+ 7 OY.

In total 25 leap year and 75 ordinary years in 100 years. Here we don't count 1st year as leap year. We've counted 1st year as OY.


Then how 24 LY + 76 OY in 100 year? Please explain to me.

R G said: (Jul 1, 2019)  
Here, for calculation of 1997, they have said 1600 yrs + 300 yrs.

So the odd day obtained is 1. But instead, if we do 1700 yrs + 200 yrs than odd days obtained will be different. How to understand this? Please explain to me.

Ashok said: (Jul 6, 2019)  
@All.

First we need to know about century codes;
1600-1699=6
1700-1799=4
1800-1899=2
1900-1999=0
2000-2999=6

Then we need to know month codes.

jan =0,feb=3, mar=3, apr=6, may=1, jun=4, july=6, aug=2, spt=5, oct=0, nvm=3, dec=5 afterv knowing this..
The finding procedure is;
Given date=28
Last two digits of the year=06
Last two digits divided by 4=1(taking the only quotient)
Century code =6.

AFTER, ADD ALL THE VALUES WE GET 42 SINCE WE HAVE 7 DAYS DIVIDE THE NUMBER 42/7=0.
Answer is SUNDAY.

Shruthi said: (Aug 6, 2019)  
How we got 5*3? Please tell me.

Suchitra said: (Sep 15, 2019)  
Thanks for the clear explanation @Prabhu.

Sharath said: (Sep 21, 2019)  
400 years = (5 x 4 + 1).

Here 1 is added because of leap year !

Yashu said: (Sep 26, 2019)  
Anyone tell why we consider 300 & 1600 years only. Why don't we consider 400 or other than that?

Shweta said: (Oct 1, 2019)  
Thank you @Arya, @Inshan, @Nitesh.

Kirtan said: (Oct 13, 2019)  
How many leap years are there between1701 and 1900 (both included) ?

Dream Boy said: (Nov 6, 2019)  
How to know a day of a particular date?

Dream Boy said: (Nov 6, 2019)  
How to know a day of a particular date?

Kavi said: (Nov 28, 2019)  
Which day of 21 July 1997. Describe below.

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