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.

These two ranges would each have 87 years that were 'matched'.

Of course, thanks to Harry, I remembered the Gettysburg Address, "Four score and seven years ago our ...." That got me thinking, and I first tested starting at 1960, and then thought about it some more. Seeing as how I was born in 19(87), I figured I would try that number, and go until there were 87 matched years. This or course occurs from 1987 to 2599.

Now, off to find the range of 87 years, that has the most matched years. Any other takers?

Posted by Justin on 2006-01-22 11:34:09