Aptitude - Calendar - Discussion

What's that thing that once a year twice a week for four months and a day is 6 times?

Lets see that 2000 was a leap year so 1, 2, 3, 5 is non leap year and 2004 is leap year. So counting from 2001, to 5 there will be 6 odd day 1 for each non leap and 2 for 1 leap year next see in 2006 January has 31 day means 3 odd day (31/7), February has 0 (28/7), March has 3, April has 2, and for 28 in May 0 odd days.

So means total 8 days in 2006 means 1 week 1 day hence we total left of 1 odd day. From 2001 to 5 we have 6 odd and 1 in 2006 total 7. So 1 week again so starting day Sunday is answer.

By, doomsday method:

= Tuesday+(06/12)+rem(06/12)+rem(06/12)/4.

= Tuesday+0+0+0 means on 4th April Tuesday.

From 4th April to 28th may = 55 days = remain 6 odd days.

= Tuesday+6 = Sunday.

Use doomsday method to get faster result.

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

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.

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.

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

Can we apply dooms algorithm for all such problems?

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.