A Neat Trick For Quickly Computing The Day Of The Week For Your Birthday

Number Theory Level 3

Aditya celebrated his 16th birthday on Saturday, March 2, 2013. What day of the week was Aditya born?

Details and assumptions

The recent leap years are 2012, 2008, 2004, 2000, 1996, $\ldots$ .

Saturday Monday Friday Sunday

13 solutions

Avian Schiffer
Jan 11, 2014

16 years + 4 leap years = 20 day before Saturday => Sunday

i think answer may be monday

Syed Shamsuddin - 7 years, 3 months ago

I agree with you

Nazeem Shaik - 7 years, 3 months ago

I think it is Monday...For 21 we have to take day before saturday.For ex: if 1st day is sunday then 8th day is sunday and 7th day is day before sunday i.e., saturday. Similarly for 20 we have to take second day before saturday i.e., Monday. Lets check it once

Nazeem Shaik - 7 years, 4 months ago

juz use the calender in your computer

Ephraim Raj - 7 years, 3 months ago

nice approach

vinothini thangamani - 7 years, 4 months ago

What is the answer??

DHIWAKAR S - 7 years, 3 months ago

the easiest way is check on the calendar in computer...easy and fast, haha

syahidah rozi - 7 years, 1 month ago

Use da dam calender

Clerence Pereira - 7 years ago

smart approach!

Waqar Mastan - 7 years, 4 months ago

Francis Ganapin - 7 years, 2 months ago

i thought it was monday

Pei Qi - 7 years, 2 months ago

4*2=8

Debjyoti Chattopadhyay - 7 years, 4 months ago

What the heck is this explanation you are giving? @Debjyoti Chattopadhyay

Anuj Shikarkhane - 6 years, 6 months ago

Prithwish Bose
Jan 8, 2014

We have to back calculate it. We know, each year the day at the same date increases by 1, for eg- if 9/1/2013 is thursday then 9/1/2014 will be friday. For leapyear, the day increase by 2. So, start counting:
2/3/2013-saturday
2/3/2012-friday
2/3/2011-wednesday (2012 was leap year)
2/3/2010-tuesday
2/3/2009-monday
.......... similarly if you do it upto 1997 (because aditya is 16 years old), you will get 2/3/1997-sunday.

nice

manish raut - 7 years, 4 months ago

hmmmmmmmmmm

Nisha Ahmad - 7 years, 4 months ago

ok thanx

Rahul Malhotra - 7 years, 4 months ago

think very carefully

Ajoy Dey - 7 years, 4 months ago

i think its correct

mansi kela - 7 years, 3 months ago

Monday. Just google it. Or view it in the calendar.

Kent Adoniram Paguinto - 7 years, 2 months ago

its monday

Bhanu Prakash A - 7 years, 2 months ago

Yes now i got it....

zarree khan - 7 years, 2 months ago

i did in the same way, but i had 1 mistake.==

Dương Tươi - 7 years, 2 months ago

Leello Tadesse
Jan 13, 2014

Aditya turned sixteen. This means she is $16 \times 365.25 = 5844$ days old. $5844 \equiv 6 \mod 7$ So her birthday shifted six days meaning she was born on SUNDAY.

aditya is a name for a boy.

Eka Kurniawan - 7 years, 3 months ago

well done

Karthi Keyan - 7 years, 4 months ago

Nice :)

Saikat Dey - 7 years, 4 months ago

Nice

SreeHarsha Kalluru - 7 years, 4 months ago

Mayankk Bhagat
Jan 6, 2014

if today is 16 January, then this very date of the very next year shall correspond with a day of the week ,which's one day ahead of the day of this year which happened to be 16th January, that is, suppose 16th jan,2013 was Friday then 16th jan,2015 would be a Saturday unless nd until it is a leap year...... if it is a leap then the day of the week happens to be 2 days ahead....like if 16th jan 2015 happens to be a Saturday then,16th jan 2016(being a leap) would be a Monday instead of a sunday. simply follow this method and count in the reverse manner ..from 2013 to 1997

The question is wrong 16 th birthday should refer to the day when he is becoming 15 years of age so he was born in the year 1998 not 1997 ...if he was born in 1997 then his actual birthday would be considered his 0th birthday not his first birthday which is wrong

Santanu Banerjee - 7 years, 5 months ago

So you are saying your first birthday is when you turn 0? It's always the case the 21st birthday means the person turned 21

Parth Tawde - 7 years, 5 months ago

I don't know when shud be mah first b'day..but I just computed the day of the date sixteen years back

Mayankk Bhagat - 7 years, 4 months ago

The first birthday means the day I was born ..... don't you consider that day as your first birthday ????

This is ridiculous The day I was born got to be my first birthday

It should also be understood that on my N th I must turn N-1 as it would be the completion of my N-1 th birth anniversary.

Priyanka Banerjee - 7 years, 5 months ago

@Priyanka Banerjee – That is the Korean method of counting birthdays. The Western method of counting birthdays counts your first birthday as a celebration of one year alive.

Sadie Robinson - 7 years, 5 months ago

@Sadie Robinson – Agree. It's unfortunate that some people got this one wrong because of cultural differences. I guess the question should have made it clearer.

Anh Tuong Nguyen - 7 years, 5 months ago

Sudeshna Pontula
Jan 26, 2014

Assuming that all years are not leap years, we would go back $16$ days through the week from Saturday. But from $2013 - 1997$ , there are $4$ leap years, which cause us to go back another extra day, per leap year.

Now we have to back $20$ days through the week, which is also $6\mod 7$ days, from $\mbox{Saturday}$ , which brings us to $\mbox{Sunday}$ .

Nitish Dubey
Jan 20, 2014

For every non leap year subtract 1 day.
For every leap year subtract 2 day.
In these 16 years (1997-2013) we have , 4 leap years & 12 non leap years.
Therefore, Net years to be Subtracted is = ( $2*4$ + 12) = 20.
Removing greatest multiple of 7 (<20) i.e,14 {20-14=6} [As subtraction of 7 will give the same day(Saturday)]. after removing 6 Days we get Sunday

Rengachari Rukmani
Jan 10, 2014

The day shd be 16 days back in the week ie. on Thursday But there are 4 leap years and hence it shd be again 4 days back . That makes it Sunday. Each year birthday will advance by one day of the week and during leap years gy 2 days.