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To calculate the day of the week for a given date, first of all we need to find out the number of odd days.

Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too.

Odd Days are number of days more than the complete number of weeks in given period.

Leap Year is the year which is divisible by 4.

A normal year has 365 days

A leap year has 366 days

One normal year = 365 days = 52weeks + 1day

One normal year has one odd day

One leap year = 366 days = 52weeks + 2days

One leap year has two odd days

100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days

100 years have 5 odd days

400 years have (20+1) 0 odd days

The number of odd days and the corresponding day of the week is given below

0-Sunday

1-Monday

2-Tuesday

3-Wednesday

4-Thursday

5-Friday

6-Saturday

So by finding out the number of odd days you can find out the day of the week. I hope this procedure Will be helpful in solving math problems in exams.

Thanks.

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,251

I think this should be in the "This is Cool" forum. By the way, nice trick!

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 545

There is 1 more trick extremely simple. For the trick you need to memorise the key of month and day. The key of month is different for different centuries. Since the 20th and the 21st centuries are mostly required so I am giving the key of these 2 centuries only.

20th century

Jan-1

Feb-4

Mar-4

Apr-0

May-2

Jun-5

Jul-0

Aug-3

Sep-6

Oct-1

Nov-4

Dec-6

21st century

Jan-7

Feb-3

Mar-3

Apr-6

May-1

Jun-4

Jul-6

Aug-2

Sep-5

Oct-7

Nov-3

Dec-5

Day key

Sun-1

Mon-2

Tue-3

Wed-4

Thu-5

Fri-6

Sat-0

Procedure: To find the day perform this calculation:

(L+L/4+M+D)MOD7

where, L=last 2 digits of yr.

M=month key

D=date

After the remainder is obtained match it with the day key to find the day on which that respective date falls!!!

Note:-During calculations, drop off the digits after the decimal point.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 545

Yeah and if the given yr is a leap year and the month is January or February then we go a day back from our actual answer to get our final answer.

And the key of the century works from 1 Jan 1901 to 31 December 2000 (for 20th century) and 1 Jan 2001 to 31 December 2100.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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