Aptitude - Calendar - Discussion

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.

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.

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.

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.

@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.

@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.

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

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..

@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.

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