# How to find the day of a January 1st ?

This has to be an absolute classic of a shortcut that I came across  in the book “Secrets of Mental Maths”.

Using this shortcut, you can find the day of January 1st of any year after 2000. Mind you this technique is only applicable for years after 2000. For years prior to 2000, you have to calculate using the normal method.

Let’s say, we want to find the day of the week of Jan 1st 2009.

Let’s say, we want to find the day of the week of Jan 1st 2009.

Step 1 : Take up the last 2-digits, 09 in this case. Divide this number by 4 and add to it

9+ 9/4 = 9 + 2 = 11

Step 2 : Now take 11 mod 7. We get 4 as the reminder.

From the table, 4 refer to Thursday. So, January 1st 2009 is a Thursday

Consider another example, let’s say want to find the day of the week of Jan 1st 2013.

13 + 13/4 = 16/7 = 2 reminder.

So, Jan 1st 2013 = Tuesday.

Very easy 🙂 ?

## Wait a Minute

Like any Calendar based problem, there is an exception when the year is a leap year.

Let’s say, we want to find the day of the week of Jan 1st 2012.

Step 1 : Take up the last 2-digits, 12 in this case. Divide this number by 4 and add to it

12+ 12/4 = 12 + 3 = 15

So far the steps remain the same. However we need to subtract 1 when the year is a leap year.

Step 2 : Take (15 – 1)  mod 7. We get 0 as the reminder

From the table, 0 refers to Sunday. So, January 1st 2012 is a Sunday.

Consider another example, let’s say want to find the day of the week of Jan 1st 2020.

20 + 20/4 = 25 =>  24/7 = 3 reminder

From the table, 3 refers to Sunday. So, January 1st 2020 is a Wednesday.

I will posting a new shortcut in few days on finding the day of way of any year.  I picked up this shortcut from a genius Mathematician Suhas Halkude in Maharashtra. Watch this space :).

### Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

1. Hilal

The answer: my guess would be 60s. That’s the LCM, isn’t it? The hcf (I’m amuissng that means Highest Common Factor, because in my country, we call it GCF which means Greatest Common Factor) is 3, isn’t it? Well, the 15s train can never catch up to the 12s train so the only possible time they are side by side is when the 12s train and the 15s train meet at their starting point. It will take the 12s train 5 revolutions around the circuit and it will take the 15s train 4 revolutions until they are side by side again at their starting point.

• Kiran Chandrashekhar

You have a very good understanding about it. Thanks 🙂 What do you study?
Thanks
Kiran

2. k p mandal

how to calculate the day of a January 1st 2000

• Kiran Chandrashekhar

There are number of ways. But, if you have to use the shortcut, find Jan 1st of 2001 and go 2 days before. You have the Jan 1st 2000
Hope it helps

3. biswajit

the method is not working for the years like 2001, 2002, 2003!

• Kiran Chandrashekhar

Sorry, I thought it worked. I need to check, I will get back to you.
Thanks
Kiran