If 1st Jan is Tuesday in a year then number of Sunday between 4th March to 20 September of the same year are
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The year isn't a leap year?
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1st Jan = Tuesday => 6th Jan is a Sunday. it is the 6th day of the year.
=> 7 n + 6 th day of the year is a Sunday, where n is a non-negative integer
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Case 1: If the year is not a leap year:
4th March = 31 + 28 + 4 = 63rd day of the year.
=> 63th day = 7 * 9 + 0 So it is a Monday.
20th Sep : 31+28 + 31+30+31+30+31+31+20 = 263th day of the year
263 = 7 * 37 + 4 , Hence, it is a Friday.
number of days between 63rd and 263rd days: 201 (including both dates)
In 201 days, there are 28 weeks + 5 days.
Hence there are 28 Sundays. In the remaining 5 days from Monday 4th March, there is no Sunday.
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case 2 : the year is a leap year:
4th March : 31+29+4 = 64th day : 7 * 9 + 1 : Tuesday
20th Sep : 264th day : 7 * 37 + 5 : So it is a Saturday.
Hence, there are 201 days between the two days. In that period, there are 28 Sundays (28 weeks) and in the remaining 5 days, there is no Sunday.
=> 7 n + 6 th day of the year is a Sunday, where n is a non-negative integer
=======
Case 1: If the year is not a leap year:
4th March = 31 + 28 + 4 = 63rd day of the year.
=> 63th day = 7 * 9 + 0 So it is a Monday.
20th Sep : 31+28 + 31+30+31+30+31+31+20 = 263th day of the year
263 = 7 * 37 + 4 , Hence, it is a Friday.
number of days between 63rd and 263rd days: 201 (including both dates)
In 201 days, there are 28 weeks + 5 days.
Hence there are 28 Sundays. In the remaining 5 days from Monday 4th March, there is no Sunday.
==========================================
case 2 : the year is a leap year:
4th March : 31+29+4 = 64th day : 7 * 9 + 1 : Tuesday
20th Sep : 264th day : 7 * 37 + 5 : So it is a Saturday.
Hence, there are 201 days between the two days. In that period, there are 28 Sundays (28 weeks) and in the remaining 5 days, there is no Sunday.
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