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: computer solution achieved (not posted here) by HarryHotspur)

Ok, the only reason I didn't post it right away, was because I was reading the forums, and saw how people didn't really like it when one person raced to post the solution. Therefore, I wanted to wait until someone else posted it, or at least had a little more time to work on it. And yes, I too got the answer of 84 'Matched years'.

Posted by Justin on 2006-01-22 11:25:40