Aptitude - Calendar - Discussion

Can doomsday method be applied here?

Hello Budz.

This is not my technique but I am just explaining the technique, which they explained here. It is only for those who do not understand the technique.

Caution: This can only be used for years above 1900.

So let me start.

If you have to find the day 31st October 1984. 1600 and 300 will give you 1900.

Just remember 1600 has 0 odd day and 300 has 1 odd day. Take the year before 1984 which is 1983.

Then calculate 1983-1900=83; Divide 83 by 4 then you will get quotient as 20, so there will be 20 leap.

Years and 83-20=63 ordinary years will be there. So in leap years there will be 2 odd days and in ordinary years there will be 1 odd day.

So calculate 20*2+63*1 = 103;

Divide 103 by 7 you will get 5 odd days.

Then calculate total no of days from January to October 31. 305 days will be there. Then divide 305 by 7 you will get 4 as result.

Then add 4+5+1+0=10;

Then again divide 10 by 7 will get result as 3;

0-Sunday.
1-Monday.
2-Tuesday.
3-Wednesday.

So answer will be Wednesday.

If you have any doubt regarding this you may please post here I will check out regularly.

Can we say that 1972 year has no odd days?

400 years is called one century so its value is 0.
Next 2000 year also is value 0.

2005 have one leap year and 4 ordinary year.
1 leap year have 2 odd days 4+2=6.

2006.

Jan-31.
Feb-28.
March-31.
April-30.
May-28 (days only giving).

31+28+31+30+28 = 148.

148/7 days it have 21 weeks 1 odd day.

0 century (2000)+6 odd day (2005)+1 odd day (2006) = 7.

Week day is 7.

Then 7/7=0.

So this answer is sunday.

Hi Guys,

We can solve this by simple formula method and it is called dooms algorithm.

Dooms day = Anchor day+(year/12)+Reminder(year/12)/12+(Reminder(year/12)/12)/4.

For 1900 to 1999 - Anchor will be Wednesday.

2000 to 2099 - Anchor will be Tuesday.

Out come of this doom day will be last day of February, 4th April (4/4), 6 June (6/6), 8th Aug (8/8), 10th Oct (12/12) and 12th Dec (12/12).

By seeing this this formula would be bit confusing but once you have applied this method it will be very handy.

Now the question is 28th May, 2006.

Dooms day = Tuesday+06/12+Remainder(06/12)+Remainder(06/12)/4.

= Tuesday+6+12+3 = Tuesday+21 = Tuesday (There is no ODD days because Rem 21/7 is Zero).

Now from the above method pick a date closest to date which you have to find our problem states May month, so I picked 4th April (4/4).

Now we knew that 4th April is Tuesday (from dooms day algorithm).

We have to find 28th May which is Tuesday+26.

(Remaining days of April)+28(May) = Tuesday+54 = Tuesday+5(ODD days) = Sunday.

Can we apply dooms algorithm for all such problems?

Why do we take 1600 and 400? What is the relation of these two years particularly with the May?

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.

Day = Given date+Month no.+(x-1900)+(x-1900)/4.

X = The year we have to calculate.

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Important notice for all who follow this formula.

First you should check whether the given year is a leap year or not.

If it is not a leap year our formula is perfect holds for every thing.

But if it is a leap year you should subtract 1 from the obtained answer otherwise you don't get correct answer.

Here is the reason for why 1600 and 400 are 0.

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.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. Has 0 odd days.

Why the no. of odd days of 400 and 1600 are zero? Why not 2 they are leap years right?