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    Number Theory?

    What is the most and the least number of Friday the 13ths you can get in one year? In a 12 month period? Proven mathematically...
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    Quote Originally Posted by bearej50 View Post
    What is the most and the least number of Friday the 13ths you can get in one year? In a 12 month period? Proven mathematically...
    For a standard year (repeat this for a leap year) list which day number corresponds to the 13th of each month these are d_1,\ ..,\ d_{12}.

    Now assume that the first friday in the year is on day d_F

    Now for d_F=1, .. \ 7 count how many of d_i-d_F,\ i=1,\ .. ,\ 12 is divisible by 7. The largest of these totals is the most Friday the 13th there can be in a standard year and the smallest is the fewest Friday the 13th there can be in a standard year.

    Repeat for a leap year.

    CB
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