Question

If 1st Jan is Tuesday in a year then number of Sunday between 4th March to 20 September of the same year are

Answer 1

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.