A Sunday is called a Succinct Sunday if the pth Sunday in a given year falls on the pth day of a month. For example, the 1st Sunday of 2012 fell in January 1 - so that January 1, 2012 is a Succinct Sunday.

(i) Determine the total number of Succinct Sundays from January 1, 2001 to December 31, 2100 inclusively.

(ii) Determine the year(s) having the maximum number of Succinct Sundays in period covered under (i).

(iii) Determine the first and the last Succinct Sundays in the period covered under (i).

Ii) There are 122 Succinct Sundays between January 1, 2001 and December 31, 2100. (There are no Succinct Sundays in August or later in a year as the 31st Sunday in a year does not occur later than August 5th.)

(ii) The maximum number of Succinct Sundays in a year is 3.
The years with 3 Succinct Sundays are:
2005, 2006, 2011, 2017, 2022, 2023, 2028, 2033, 2034,
2039, 2045, 2050, 2051, 2056, 2061, 2062, 2067, 2073,
2078, 2079, 2084, 2089, 2090, and 2095.

(iii) For the given period, the first Succinct Sunday is April 15, 2001, and the last Succinct Sunday is March 10, 2097.

 

Posted by Dej Mar on 2012-07-24 09:33:36