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Friday the 13th

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... a Friday, January 13th must be on a Tuesday (6 mod 7 is on a ... have consecutive months with Friday the 13th (in February and March, i.e. when January ... – PowerPoint PPT presentation

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Title: Friday the 13th


1
Friday the 13th
To see in which months Friday the 13th can occur
in the same calendar year, its helpful to number
the dates 1 365. In the table below, the 13th
of every month is numbered as it falls in the
year and each 13th has its equivalent mod 7 day
number
From this table, we can see that there must be a
Friday the 13th every year, because the 13th of
the months fall on some value 0 6 at some point
in the calendar year this means that the 13th
will fall on every day of the week at some point
in the calendar, and this must include
Friday. The most Friday the 13ths that can occur
in one year would occur in February, March and
November in a non-leap year. In a leap year,
three Friday the 13ths could occur in the months
January, April and July.
From the table, its evident that in a non-leap
year, February and March 13th are both equivalent
to 2 mod 7, so a Friday the 13th in February will
be followed by a Friday the 13th in March. These
are the only months that have consecutive
equivalent values for the 13th in mod 7. In
order for the 13th of February and March to occur
on a Friday, January 13th must be on a Tuesday (6
mod 7 is on a Tuesday, 0 mod 7 is on Wednesday, 1
mod 7 is on a Thursday and 2 mod 7 is on a
Friday). This would indicate that January 1st
would need to fall on a Thursday.
2
To forecast the years where January 1st will fall
on a Thursday, we can look at recent years and
find a pattern
3
By using the sum of days in each year mod 7, we
can predict the years that will have consecutive
months with Friday the 13th (in February and
March, i.e. when January 1st is on Thursday)
2009, 2015, 2026, 2032, 2037, 2043, 2054, 2060,
2065, 2071, 2082, 2088, 2093, 2099.
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