## Thursday, 6 June 2013

### Chapter 11. Examples Explained : 28th February 2100 & 11th November 2100

Year 2100 is a century year. Also it is a non leap year. I will explain two dates in the year 2100 which are 8th February 2100 and 11th November 2100.

Example 5. 28th February 2100

Step 1. Note down the date: 28

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 2100 forms 21. Key number for 16 is 0, 17 is 5, 18 is 3, 19 is 1. The above sequence will repeat again. So, for 20 it will be 0 and for 21 it will be 5…

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2100 forms 00.
• When we divide 00 by 4 we get quotient as 0.
• We subtract 1 from 00 and get 00-1=-1.
• We add 0+ (-1) and get -1.
• We divide -1 by 7 and get -1 as a remainder and this is the key number for 00.
(Note: - If we get a year in the format YY00 i.e. if last two digits form 00 then key number for 00 will always be -1.)

Step 5. Add all the above noted numbers: 28 + 4 + 5 + (-1) = 36.

Step 6. Divide above addition by 7 and find the remainder. If we divide 36 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 1st January to 29th February, both the dates including): As given date i.e. 28th February 2100 falls in between 1st January to 29th February we need to check if the year 2100 is a leap year or not.

Last two digits from 2100 forms number 00. So, we will check if first two digits in year 2100 i.e. 21 is completely divisible by 4 i.e. remainder is zero if 21 is divided by 4 (or we will check if 21 is present in the multiplication table of 4).
4 x 5 = 20
4 x 6 = 24
So, we can conclude that 21 is not completely divisible by 4. And hence the year 2100 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 1 as a remainder. The day on 28th February 2100 is Sunday…!!

Example 6. 11th November 2100

Step 1. Note down the date: 11

Step 2. Note down the key number for month: November is the first member of our 4th group. So its key number will be 4... (

Step 3. Find and note down the key number for first two digits in year: First two digits from 2100 forms 21 and we have already found the key number for 21 as 5 in previous example.

Step 4. Find and note down the key number for last two digits in year: Last two digits from 2100 forms 00. And we have found the key number for 00 as -1 in previous example.

Step 5. Add all the above noted numbers: 11 + 4 + 5 + (-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. 11th November 2100 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 11th November 2100 …!!

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