Chapter 10. Examples Explained : 5th February 2012 & 10th June 2012

I will explain two dates falling in a leap year, 2012. One is within 1st January - 29th February. While other date is outside of these two months.

Example 3. 5^th February 2012

Step 1. Note down the date: 5

Step 2. Note down the key number for month: 4 letters in January & February are common i.e. “uary”. Therefore, key number for February is 4… (See Key Numbers For Months:1st Group)

Step 3. Find and note down the key number for first two digits in year: First two digits from 2012 forms 20 and we have already found the key number for 20 as 0 in example 1.

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2012 forms 12.

• When we divide 12 by 4 we get quotient as 3.
• We subtract 1 from 12 and get 12-1=11.
• We add 3+11 and get 14.
• We divide 14 by 7 and get 0 as a remainder (14 is present in the multiplication table of 7) and this is the key number for 12.

Step 5. Add all the above noted numbers: 5 + 4 + 0 + 0 = 9.

Step 6. Divide above addition by 7 and find the remainder: If we divide 9 by 7 then we get 2 as a remainder.

Step 7. Check if the year is a leap year or not (only if the given date falls in between 1^st January to 29^th February, both the dates including): As given date i.e. 12^th January 2013 falls in between 1^st January to 29^th February we need to check if the year 2012 is a leap year or not. 

Last two digits from 2012 forms number other than 00 i.e. 12. So, we will check if 12 is completely divisible by 4 i.e. remainder is zero if 12 is divided by 4 (or we will check if 12 is present in the multiplication table of 4). 

4 x 3 = 12

So, we can conclude that 12 is completely divisible by 4. And hence the year 2012 is a leap year

Step 8. If the given date falls in between 1^st January to 29^th February and the year is a leap year then we need to go one day back from our calculated final day to get exact day.. So from Step 6 our final day would be Monday (2 points to Monday). But, for this scenario we need to go one day back from our calculated final day to get exact day.. So, our final day would be one day before Monday i.e. Sunday…!! Just check it..!! :)

Example 4. 10^th June 2012

Step 1. Note down the date: 10

Step 2. Note down the key number for month June: June comes after 5^th month (May). So, its key number will be 5... (See Key Numbers For Months: 2^nd Group)

Step 3. Find and note down the key number for first two digits in year: First two digits from 2012 forms 20 and we have already found the key number for 20 as 0 in Example 1.

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2012 forms 12. And we have already found the key number for 12 as 0 in previous example.

Step 5. Add all the above noted numbers: 10 + 5 + 0 + 0 = 15.

Step 6. Divide above addition by 7 and find the remainder: If we divide 15 by 7 then we get 1 as a remainder.

Step 7. Check if the year is a leap year or not (only if the given date falls in

between 1^st January to 29^th February, both end dates including): As given date i.e. 10^th June 2012 does not fall in between 1^st January to 29^th February we don’t need to check if the year 2012 is a leap year or not. So, 1 is our final result from Step 6. And as 1 points to Sunday, this is the day of week which falls on 10^th June 2012…!!!

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Chapter 9. Examples Explained : 12th January 2013 & 15th August 2013

Well… We have finally studied each and every single step in detail that we need to know while finding the day from any given date. And now it’s time to test our knowledge. It’s time to test ourselves!!

I will take total 8 examples those will cover all the date cases you may encounter with.

For that I would like to revise all the steps those we need to take into

account to find the day from date:

1. Note down the date.
2. Note down the key number for month.
3. Find and note down the key number for first two digits in year.
4. Find and note down the key number for last two digits in year.
5. Add all the above noted numbers.
6. Divide above addition by 7 and find the remainder.
7. Check if the year is a leap year or not (only if the given date falls in between 1^st January to 29^th February, both the dates including).
8. If the given date falls in between 1^st January to 29^th February and the year is not a leap year then the day corresponding to the remainder which we found from the step 6 will be our final day!! But, if the given date falls in between 1^st January to 29^th February and the year is a leap year then we need to go one day back from our calculated final day to get exact day!! 

So, let's see each example one by one in detail.

Example 1. 12^th January 2013

Step 1. Note down the date: 12

Step 2. Note down the key number for month: January is always the 1^st month of the year so it’s key number is 1… (See Key Numbers For Month: 1^st Group)

Step 3. Find and note down the key number for first two digits in year: First two digits from 2013 forms 20. Key number for 16 is 0, 17 is 5, 18 is 3 and 19 is 1. So, for 20 it will be 0 as above sequence will repeat… See Finding The Key Numbers For First Two Digits In A Year:Quick Steps

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2013 forms 13.

• When we divide 13 by 4 we get quotient as 3.
• We subtract 1 from 13 and get 13-1=12.
• We add 3+12 and get 15.
• We divide 15 by 7 and get 1 as a remainder and this is the key number for 13.

For detail steps see Finding The Key Numbers For Last Two Digits In A Year

Step 5. Add all the above noted numbers: 12 + 1 + 0 + 1 = 14.

Step 6. Divide above addition by 7 and find the remainder. If we divide 14 by 7 then we get 0 as a remainder (14 is present in multiplication table of 7).

Step 7. Check if the year is a leap year or not (only if the given date falls in between 1^st January to 29^th February, both the dates including): As given date i.e. 12^th January 2013 falls in between 1^st January to 29^th February we need to check if the year 2013 is a leap year or not.

Last two digits from 2013 forms number other than 00 i.e. 13. So, we will check if 13 is completely divisible by 4 i.e. remainder is zero if 13 is divided by 4 (or we will check if 13 is present in the multiplication table of 4).

4 x 3 = 12

4 x 4 = 16

So, we can conclude that 13 is not completely divisible by 4. And hence the year 2013 is not a leap year.

Step 8. If the given date falls in between 1^st January to 29^th February and year is not a leap year then the day corresponding to the remainder which we found from the Step 6 will be our final day!! From Step 6, we have got 0 as a remainder. Therefore from the table below the day on 12^th January 2013 is Saturday…!!!! Check your calendar…!!! :)

SUN	MON	TUE	WED	THU	FRI	SAT
1	2	3	4	5	6	0

Example 2. 15^th August 2013

Step 1. Note down the date: 15

Step 2. Note down the key number for month: If we subtract key number of May (i.e. 2) from key number of June (i.e. 5), we will get key number for August i.e. 3 (5-2=3)… (See Key Numbers For Month: 2^nd Group)

Step 3. Find and note down the key number for first two digits in year: First two digits from 2012 forms 20 and we have already found the key number for 20 as 0 in previous example.

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2013 forms 13. And we have found the key number for 13 as 1 in previous example.

Step 5. Add all the above noted numbers: 15 + 3 + 0 + 1 = 19.

Step 6. Divide above addition by 7 and find the remainder. If we divide 19 by 7 then we get 5 as a remainder.

Step 7. Check if the year is a leap year or not (only if the given date falls in between 1^st January to 29^th February, both the dates including): As given date i.e. 15^th August 2013 does not fall in between 1^st January to 29^th February we don’t need to check if the year 2013 is a leap year or not.

So, 5 is our final result. And therefore 5 points to Thursday i.e. the day of week on 15^th August 2013 …!!

These were the two examples for dates falling in a non-leap year i.e 2013.
First date (12^th January 2013) was within 1st January-28th February. While, second date (15^th August 2013) was outside 1st January-28th February.

In the next post I will take two examples for dates falling in a leap year i.e. 2012

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Chapter 8. Check If The Year Is A Leap Year Or Not

Ok, first of all why we need to check if a year is leap year or not?

Answer is simple! A leap year contains an extra day (i.e. 29^th February).

So, as per my conclusion if we select a date from a leap year and before 1^st March i.e. in between 1^st January & 29^th February (both dates including) then we need to go one day back from the day we calculated to get the exact day!

Didn't get the thing???? Don’t worry; you will be clear with it as I will explain it with an example in the next chapters.

First we will see how to find if a year is a leap year or not. And it is simple to find one. For that you will have to check if last two digits in a year (YYYY) are 00 or not. Based on that following are the two cases to know if a year is leap year or not:

Case 1. If last two digits in year are other than 00

If last two digits in year are other than 00 (as in 1996) then check if the number formed by these last two digits (96) is completely divisible by 4 i.e. remainder is zero (or we can say these last two digits form a number that is present in the multiplication table of 4).

If above condition is true then the given year is a leap year.

Example: 1996 is a leap year as 96 is completely divisible by 4 i.e. remainder is zero (96 is present in the multiplication table of 4).

If above condition is false then the given year is not a leap year.

Example: 1997 is not a leap year as 97 is not completely divisible by 4 i.e. remainder is not zero (97 is not present in the multiplication table of 4).

Case 2. If last two digits in year are 00

If last two digits in year are 00 (as in 2000) then check if the number formed by first two digits  (20) in the year is completely divisible by 4 i.e. remainder is zero (or we can say these last two digits form a number that is present in the multiplication table of 4).

If above condition is true then the given year is a leap year.

Example: 2000 is a leap year as 20 is completely divisible by 4 i.e. remainder is zero (20 is present in the multiplication table of 4).

If above condition is false then the given year is not a leap year.

Example: 2100 is not a leap year as 21 is not completely divisible by 4 i.e. remainder is not zero (21 is not present in the multiplication table of 4).

Now, we will summarize above two cases:

Case 1. If year is like YYYY (i.e. last YY are not 00) then–

Check if last YY (YYYY) is completely divisible by 4.

If yes then YYYY is a leap year.

If no then YYYY is not a leap year.

Case 2. If year is like YY00 (i.e. last YY are 00) then–

Check if first YY (YYYY) is completely divisible by 4.

If yes then YYYY is a leap year.

If no then YYYY is not a leap year.

That is to it!

Again one thing, you need to check if the given year is a leap year or not only if the date for which you are finding the day falls in either January or February!! For rest of the months’ date you should skip this step… :)

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Chapter 7. Finding The Key Number For The Last Two Digits In The Year

This is one of the most important steps. To explain this step, I will again take my example only i.e. year 1990… Now, last two digits in year 1990 form a number 90. To calculate key number for 90 (last two digits in year), follow the steps mentioned below:

STEP 1. Divide the number formed (90 in this case) by 4 and find the quotient.

(Note: Till now we were finding the reminder for division but this is the only step where we have to find quotient.)

Method to find the quotient is easy and similar to the method to find the remainder. First find the multiples of 4 till we get a number which is greater than or equal to 90.

4 x 23=92 (See multiplication table for 4) So, we will go one step back i.e. 4 x 22=88. And this 22 is nothing but our quotient…!

Note: If 90 were exact multiple of 4 then no need to go one step back. E.g. If our number would have been 92 instead of 90 then we would have got 4 x 23=92 i.e. 92 is exact multiple of 4. Therefore our quotient would have been 23.

To find quotient using calculator is even easier. Just divide 90 by 4, we get 22.5… And the number before decimal point is our quotient i.e. 22.

STEP 2. Subtract 1 from 90 (i.e. last two digits from year).

(Note: We always need to subtract 1 only.)

90-1=89.

STEP 3. Add quotient (from STEP 1) and subtraction result (from STEP 2).

22+89=111.

STEP 4. Divide the addition from STEP 3 (in this case 111) by 7 and find the remainder.

Find the multiples of 7 till we get the number greater than or equal to 111.

7 x 16=112 (See multiplication table for 7)

So, we will go one step back i.e. 7 x 15=105. Now we will subtract 105 from 111 and we get 6 (111-105=6). And this is our remainder!

To find remainder using calculator when 111 is divided by 7, we will first divide 111 by 7 and we get 15.8571…We will consider digits before decimal point i.e. 15. Now we will multiply 7 by 15 (digit before decimal point) and we get 105 (7 x 15=105). To find remainder when 111 is divided by 7 we subtract our multiplication (105) from 111 we get 6 (111-105=6)… And this is our remainder!

And this remainder (i.e. 6) is nothing but our key number for last two digits in year (i.e. 90 in this case).

So, this is the method to find the key number for the last two digits in the year. It needs a little practice and you can master this. :)

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