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        riddles >> medium >> A Coincidental Month Puzzle
        
(Message started by: K Sengupta on Feb 23^rd, 2006, 10:55pm)

Title: A Coincidental Month Puzzle
Post by K Sengupta on Feb 23^rd, 2006, 10:55pm

The twelve months Janauary, February, March, ....................., November and December (in that order) of a year are respectively assigned the values 0,1,2,............,10, 11 .
A given month corresponding to a specific year is defined as "Coincidental" when the remainder obtained by dividing a given year by 12 precisely corresponds to the value assigned to a month containing five SUNDAYS. For example, 2006 when divided by 12 yields a remainder of 2 but March,2006 does not contain five Sundays. Consequently MARCH,2006 is NOT A "COINCIDENTAL" MONTH.
Determine the total number of "Coincidental" Months occurring between 1980 A.D. and 2140 A.D.( both years inclusive) in accordance with Western (Gregorian) Calendar System.

Title: Re: A Coincidental Month Puzzle
Post by markr on Feb 24^th, 2006, 10:51pm

After a little bit of spreadsheet manipulation, I got 55 with the largest gap being 1999-2007 (exclusive).