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.

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).

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.

Let us calculate the number of odd days between these two dates.

July month of 1984 has 29 days left. So odd days are 1.

Now August 1984 to June 1985 ===>> 3 + 2 + 3 + 2 + 3 + 2 + 0 + 3 + 2 + 3 + 2.

Now July 1985 till 2nd July contains 2 odd days.

Total 29 odd days. or 1 odd day.

So July 2, 1984, is 1 day before Wednesday. It is Tuesday.

As a year contains 365 days with factors of 7(1week) gives 1(day) as a reminder which adjusts one day extra to the next year.

Given year is divided by 4, and the quotient gives the number of leap years. But, as 100,200 and 300 are not leap years => 75 – 3= 72 leap years.

OR

A 300-year period can have either 72 or 73 leap years. Each 400-year cycle of the Gregorian calendar has 97 leap years, so the average number of leap years for a 300-year period is 72.75.

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
last day of a century cannot be Tuesday or Thursday or Saturday.
because 100 century consists 5 odd days, means Friday is the last day.
200 century consists 3 odd days, means Wednesday is the last day.
300 century consists 1 odd day, means Monday is the last day.
400 century doesn’t consist any odd day.
the cycle continues, hence proof.

Solution: First, we count the number of odd days for the leftover days in the given period.

Here,given period is 12.2.1986 to 1.1.1987

Feb Mar Apr May June July  Aug Sept Oct Nov Dec Jan

16   31    30  31   30    31   31   30   31  30   31   1 (left days)

2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days) = 1 odd day

So,given day Wednesday + 1 = Thursday is the required result.

Repetition of leap year ===> Add +28 to the Given Year.

Repetition of non leap year

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2:  Add +6 to the Given Year.

Solution :

Given Year is 2024, Which is a leap year.

So, Add +28 to the given year (i.e 2024 + 28) = 2052

Therfore, The calendar of the year 2024 can be used again in the year 2052.

Repetition of leap year ===> Add +28 to the Given Year.

Repetition of non leap year

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2:  Add +6 to the Given Year.

Solution :

Given Year is 1993, Which is a non leap year.

Step 1 : Add +11 to the given year (i.e 1993 + 11) = 2004, Which is a leap year.

Step 2 : Add +6 to the given year (i.e 1993 + 6) = 1999

Therfore, The calendar for the year 1993 will be same for the year 1999

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
last day of a century cannot be Tuesday or Thursday or Saturday.
because 100 century consists 5 odd days, means Friday is the last day.
200 century consists 3 odd days, means Wednesday is the last day.
300 century consists 1 odd day, means Monday is the last day.
400 century doesn’t consist any odd day.
the cycle continues, hence proof.

First,we count the number of odd days for the left over days in the given period.Here,given period is 18.3.1994 to 25.2.1995

Therefore, No. of Odd Days = 6 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 3 + 4 = 36 = 1 odd day

So, given day Friday + 1 = Saturday is the required result.

As day after tomorrow is Monday, today will be Saturday and yesterday will be Friday…