The twelve months January, February, March, .........., November and December (in that order) of a year are respectively assigned the values 0,1,2,.....,10 and 11.

A given month corresponding to a specific year is defined as succinct 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, 1990 when divided by 12 yields a remainder of 10; but November, 1990 did not contain five Sundays. Consequently November, 1990 was not a succinct month.

Considering all the succinct months occurring between 1945 A.D. and 2176 A.D. inclusively in accordance with the Gregorian calendar system, when does the 50^th succinct month occur? Determine the maximum number of years between two consecutive succinct months in the stated period.

If I did my analysis correctly, the 50^th succinct month from 1945 occurs in 2091.
The maximum number of years between consecutive succinct months between 1945 and 2176 is 7 (and 8 months), occuring twice during the given period. The first gap occurs between August 1999 and April 2007; and the second gap occurs between August 2083 and the 50^th succinct month, April 2091.

Posted by Dej Mar on 2008-12-06 16:13:43