1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday.
∴ The year 700 is not a leap year.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
∴ On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days ≡ 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.
For two years having same calendar must have two common conditions: both having same length in terms of number of days and first day of the week.
The year 1991 has 365 days,,that is 1 odd day , year 1992 has 366 days , i.e. 2 odd days , year 1993 has 365 days i.e. 1 odd day. the years 1994,1995,1996 have 1 odd day each.
the sum of odd days so calculated from year 1990 to 1996 .
(1+2+1+1+1+1)=7 odd days. 5
hence, the year 1997 will have same calendar as that of year 1990.
Each day of the week is repeated after 7 days
? After 63 days, it would be Friday
So, After 62 days, it would be Thursday
The year 1984 being a leap year, it has 2 odd days. So, the day on 2nd July, 1985 is two days beyond the day on 2nd July, 1984. But, 2nd July 1985 was Wednesday.
? 2nd July, 1984 was Monday
No of days = Jan. + Feb. + March
30 + 28 + 15 = 73 days
Starting with 1988, we go on counting thye number of odd days till the sum is divisible by 7
Year 1988 odd days = 2
Year 1989 odd days = 1
Year 1990 odd days = 1
Year 1991 odd days = 1
Year 1992 odd days = 2
So total odd days = 7;
? Calendar for 1993 is the same as that of 1988.
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