Thursday 16 May 2013

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 1st January to 29th February, both the dates including).
  8. If the given date falls in between 1st January to 29th 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 1st January to 29th 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. 12th January 2013

Step 1. Note down the date: 12

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

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 1st January to 29th February, both the dates including): As given date i.e. 12th January 2013 falls in between 1st January to 29th 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 1st January to 29th 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 12th January 2013 is Saturday…!!!! Check your calendar…!!! :)

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

Example 2. 15th 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: 2nd 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 1st January to 29th February, both the dates including): As given date i.e. 15th August 2013 does not fall in between 1st January to 29th 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 15th August 2013 …!!

These were the two examples for dates falling in a non-leap year i.e 2013.
First date (12th January 2013) was within 1st January-28th February. While, second date (15th 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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2 comments :

  1. how to calculate jan 1 2008 find day of the week?

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  2. Hi Dinesh, thanks for your comment. For 1st Jan 2008, below is the calculation-
    1 (Date) + 1 (key number for Jan) + 0 (key number for 20) + 2 (key number for 08) = 4. Now 4 indicates Wednesday. But, since 2008 is a leap year and the given date falls in Jan we need to go one day back. So, the day of week on 1st Jan 2008 was Tuesday! I have explained similar example in detail in next chapter for 5th Feb 2012. Check it out.

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