The year 2004 is a leap year. It has 2 odd days.

 The day on 8^th Feb, 2004 is 2 days before the day on 8^th Feb, 2005.

Hence, this day is Sunday.

The number of days more than the complete weeks are called odd days in a given period.

1 ordinary year = 365 days = (52 weeks + 1 day)
Hence the number of odd days in 1 ordinary year= 1.
1 leap year = 366 days = (52 weeks + 2 days)
Hence the number of odd days in 1 leap year= 2.

100 years = (76 ordinary years + 24 leap years )
= (76 x 1 + 24 x 2) odd days = 124 odd days.
=> (17 weeks + 5 days)
≡ 5 odd days.
Hence the number of odd days in 100 years = 5.

Number of odd days—->Day of the week
==>0—->Sunday
==>1—->Monday
==>2—->Tuesday
==>3—->Wednesday
==>4—->Thursday
==>5—->Friday
==>6—->Saturday
The last day of a century cannot be Tuesday or Thursday or Saturday.
because 100 century consists of 5 odd days, which means Friday is the last day.
200 century consists of 3 odd days, which means Wednesday is the last day.
300 century consists of 1 odd day, which means Monday is the last day.
400 century doesn’t consist of any odd day.
the cycle continues, hence proof.

1995 is an ordinary year, it has 1 odd day. So, the first day of 1996 will be one day beyond Sunday, i.e. it will be Monday.

29th Feb, 2016 = Monday => 28th Feb, 2012 = Sunday
28th Feb 2017 = Tuesday (because 2016 is a leap year, there will be 2 odd days)
Therefore» Feb 28th, 2018 (Wednesday), Feb 28th, 2019 (Thursday), Feb 28th, 2020 (Friday), Feb 29th, 2020 (Saturday)
Or, Feb 29th to Feb 29th after 4 years, we have 5 odd days.
So, every subsequent birthday would come after 5 odd days.
2020 birthday – 5 odd days
2024 birthday – 10 odd days = 3 odd days
2028 birthday – 8 odd days = 1 odd day
2032 birthday – 6 odd days
2036 birthday – 11 odd days = 4 odd days
2040 birthday – 9 odd days = 2 odd days
2044 birthday – 7 odd days = 0 odd days. So, after 28 years, his birthday would fall on Monday.
The next birthday on Monday would be in the year 2072 (further 28 years later), the one after that would be in the year 2100. But we are told that she lives up to the year 2099.
So, there are 2 occurrences of his birthday falling on Monday – 2044 & 2072.

Note: In an ordinary year, there are 365 days, which means 52 x 7 + 1, or 52 weeks and one day. This additional day is called an odd day.

• 1 ordinary year = 365 days = (52 weeks + 1 day.) 1 ordinary year has 1 odd day.
• 1 leap year = 366 days = (52 weeks + 2 days) 1 leap year has 2 odd days.
• 100 years = 76 ordinary years + 24 leap years. = (76 x 1 + 24 x 2) odd days = 124 odd days. = (17 weeks + days) 5 odd days.

Let us find the day on 1st July 2004.

2000 years have 0 odd days. 3 ordinary years have 3 odd days.

Jan. Feb. March April May June July

31 + 29 + 31 + 30 + 31 + 30 + 1

= 183 days = (26 weeks + 1 day) = 1 t .

Total number of odd days = (0 + 3 + 1) odd days = 4 odd days. ‘

:. 1st July 2004 was ‘Thursday’,-,-

Thus, 1st Monday in July 2004 _as on 5th July.

Hence, during July 2004, Monday fell on 5th, 12th, 19th, and 26th…

18th February 1997 was Tuesday.
So, 18th February 1998 was Wednesday.
Therefore, 18th February 1999 will be Thursday.

The mentioned month begins on a Saturday and has 30 days
Sundays = 2nd, 9th, 16th, 23rd, 30th
=> Total Sundays = 5
Every second Saturday is a holiday.
1 second Saturday in every month
Total days in the month = 30
Total working days = 30 – (5 + 1) = 24

The two conditions that decide that a year is a leap year or not is:
• For a year to be a leap year, it should be divisible by 4.
• No century is a leap year unless it is divisible by 400.
Hence, the year 2100 is not a leap year as it is not divisible by 400.

On 31st December,2005 it was Saturday.

Number of odd days frame the year 2006 to the year 2009=(1+1+2+1)=5 days.

 ∴ On 31st December 2009 , it was Thursday. In this way, on first jan, 2010 it is Friday

The century divisible by 400 is a leap year.
∴ The year 700 is not a leap year.

350 days, 350/7 = 50, no odd days, so it will be a Monday.

(or)

After 350 days, again there will be Monday.

Because 350 is exactly divisible by 7 and after every 7 days, Monday comes.

(or)

Since 350 is a multiple of 7, we know that in 350 days it will be Monday.

Going backward, 349 days from today will be Sunday,

348 it will be Saturday and, finally,

347 days from now it will be Friday.

59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = Thursday + 3 odd days = Sunday.

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.

The day of 5th March 2005 will be 1 day beyond the day of 5th March 2004.

Given that, 5th March 2005 is Monday.

5th March 2004 is Sunday (1 day before to 5th March 2005).