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Problem 3 (Friday-the-13th)

This month (November, 1998) the 13th falls on a Friday, making it the 3rd Friday-the-13th this year. When will the next Friday the 13ths fall over the next two years during 1999 and 2000 ? Keep in mind that the year 2000 is a leap year.

Note: The Gregorian calendar repeats itself every 400 years with leap years falling every 4th year (years divisible by 4), with the exception of century years which are not leap years unless the century year is divisible by 400. In other words, the century years 1700, 1800, 1900 were not leap years, but 2000 will be a leap year, 2100, 2200, 2300, will not be, 2400 will be, and so on. By using this strategy, the Gregorian calendar allows for 97 leap years every 400 year cycle, making on the average the number of days equal to 365 97/400, which is very close to the true astronomical number of days in a year.
A more challenging problem would be to determine the number of Friday-the-13ths that are possible in any one year. Is it possible for a year to have no Friday-the-13ths ? What is the most number of Friday-the-13ths that can occur in one year ? The interesting thing about mathematics is that one problem always leads to new problems. Someone once said a good mathematician is one who can not only solve problems, but to think of new problems.

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Last modified on Tuesday, January 12, 1999