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:
(Sun, Oct 10, 2010 10:04:54 AM)
@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:
(Wed, Nov 3, 2010 03:27:18 PM)
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:
(Tue, Jan 11, 2011 12:18:47 AM)
How did you calculate number of odd days for 97 years?.
Dinesh said:
(Tue, Jan 11, 2011 03:37:27 AM)
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:
(Wed, Jan 26, 2011 08:32:56 AM)
How to calculate odd days in a year ?
Rajesh said:
(Fri, Feb 4, 2011 02:38:52 PM)
17th june 1998
year 98+
year code 24+
month code 05+
day 17+
144%7
140+4
wednesday is the answer
Sandeep said:
(Fri, Feb 18, 2011 04:40:56 AM)
Mr. Rajesh how you know year code.
Praveen said:
(Sat, Feb 19, 2011 02:13:08 AM)
Please tell me how 0 odd days for 400 years ?
Praveen said:
(Sat, Feb 19, 2011 02:17:34 AM)
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:
(Thu, Mar 3, 2011 05:22:06 AM)
I am not understand problem correctly. Please anybody explain me.
Vaibhav said:
(Wed, Mar 16, 2011 06:40:03 AM)
Nice one rajesh.
Nitin said:
(Wed, Apr 20, 2011 08:32:52 AM)
How can I find no leap year in 97 year.
Aishu said:
(Fri, Apr 29, 2011 07:06:23 AM)
How to find the month code rajesh ?
Inshan said:
(Sat, May 14, 2011 10:52:05 AM)
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:
(Sun, May 15, 2011 01:26:42 AM)
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:
(Tue, May 17, 2011 03:16:19 AM)
How to calculate this sum?
Ranjith said:
(Thu, Jul 7, 2011 04:19:32 AM)
How could you tell that 1600 has 0 odd days?
Anupama said:
(Sun, Jul 10, 2011 01:23:44 AM)
Wy we are 300 years and why we are calculating odd days for 300 ?
Arya said:
(Wed, Jul 20, 2011 01:37:01 PM)
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:
(Mon, Jul 25, 2011 03:16:18 PM)
Pls tell me ....why did you add 1 in the calculation of odd days in 400 years???
Vanita said:
(Wed, Jul 27, 2011 10:53:30 AM)
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:
(Mon, Aug 22, 2011 12:41:09 PM)
To Nitin:
Here we have 97 yrs
97/4=24 leap yrs
97-24=73 ordinary yrs
Ekta said:
(Fri, Sep 16, 2011 08:25:46 PM)
Thank you Arya. I can understand properly your solution.
Sri Harsha. P said:
(Sat, Sep 17, 2011 02:14:14 PM)
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:
(Tue, Sep 27, 2011 11:48:34 AM)
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:
(Fri, Oct 21, 2011 03:39:33 PM)
How you got ordinary days? could you explain?
Hdx said:
(Wed, Nov 9, 2011 10:18:30 AM)
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:
(Sat, Nov 12, 2011 11:48:27 AM)
How to calculate odd days for 300 years? I don't understand this only.
Rishi said:
(Fri, Nov 18, 2011 11:22:40 PM)
Ishan , Arya and Raviteja
Thanks to all u for ur such a explanation
Praveen Kumar said:
(Tue, Nov 22, 2011 03:58:09 PM)
How we gat an idea to take 1600 years and 300 years in above problem.
Muthaiyan said:
(Tue, Dec 27, 2011 02:25:05 PM)
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
1
168 days = 24 weeks = 0 odd day.