The days of the week (d.o.w) which are Sunday, Monday, Tuesday,Wednesday,Thursday,Friday and Saturday (in that order) are respectively denoted by the numbers 0,1,2,3,4,5 and 6 . Any given year commencing with a particular d.o.w is assigned that value corresponding to that d.o.w. For example, the value ‘0’ would be assigned to a year commencing with a Sunday.

# A year is defined as ‘Matched’ if the remainder obtained, when the year is divided by 7, corresponds precisely with the value assigned to that particular year. For example, 2003 A.D. is NOT A Matched year since 2003 leaves a remainder of 1 upon division by 7 but January 1,2003 occurred on a Wednesday which is denoted by 3.

Determine the total number of ‘Matched’ years between 1960 A.D. and 2560 A.D.(both years inclusive) in accordance with the Western (Gregorian) Calendar System.

(In reply to re: Analytical solution by Richard)

Well, maybe if there were something remotely important attached to the answer of this puzzle, I'd try harder and/or use a computer program.  I think you'll agree there is nothing important about the number of arbitrarily defined "matched" years within an arbitrarily chosen time period.  Why do I even bother then?  'Cause I'm crazy like that.

Posted by Tristan on 2006-01-23 15:08:53