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.

The maximum number of times that the number can be matched in a range of 87 years, is 13.

It just so happens that from 1776 to 1862 is the first range starting from 1776 that has this maximum number of values.

Also, the first range starting from 1776 that requires the minimum amount of years to achieve 1776 matched numbers starts at 1777, ending at 14202.

The minimum range size for n 'matched' years to occur is equal to the formula m=7(n-1)+1, where m is the minimum number of years required.

Posted by Justin on 2006-01-22 11:57:55