first day of 1999 is sunday.what day is the last day?
This is pretty simple, there's 365 days in a year. Divide 364 (We already know Sunday) by 7, take the remainder and count from Sunday and you'll have your answer:
$\displaystyle \frac{364}{7} = 52 \ remainder \ 0$
The end of the year is also a Sunday. If it is a leap year, it will be the day after that.
It's not monday... If you look at any calendar that has many years recorded on it... All years start and end on the same day of the week, unless it is a leap year, then it ends on the day after.
You cannot include a day once it has been considered already. If you see it started on Sunday and count a week after that, you get Sunday:
Sunday...
Monday... 1
Tuesday.. 2
Wednesday... 3
Thursday. 4
Friday..... 5
Saturday. 6
Sunday... 7
If you continue this till the end of the year, you get 364 days.
That means, all years start and end on the same day except on Leap Year.
If the number if days in a year was a multiple of 7, then a given day would land on the same weekday every year because the week and year cycles would be aligned. If the year was 7 days long, what would the 8th day be? If they were 14 days long, what would the 15th day land on? The same as the first day, right?
However,
365/7 = 52 and 1/7th (i.e. one day longer than 52 weeks)
366/7 = 52 and 2/7ths (i.e. two days longer than 52 weeks)
So if, say, in a normal 365 day year, the first day was Tuesday...
The first 52 weeks would be
[Tue,Wed,Thu,Fri,Sat,Sun,Mon]
Then the spare day at the end of the year would be a Tuesday.
Making the first day of the next year a Wednesday
If it were a leap year, then you would have 2 spare days after the 52 - Tuesday and Wednesday, making the first day of the next year a Thursday.