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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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by kpkarthik

The year isn't a leap year?

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by kpkarthik

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.

=>

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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.

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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,