Friday the 13th -- excess detail

Normal Calendar Cycle

The year has 365 or 366 days. This yields 52 weeks and 1 or 2 days.
So, the weekday of a specific date falls one or two days later each year.

For the calendar, this gives a cycle of:
Year 1 Jan Leap year
1904 Friday Yes
1905 Sunday
1906 Monday
1907 Tuesday
1908 Wednesday Yes
1909 Friday
1910 Saturday
1911 Sunday
1912 Monday Yes
1913 Wednesday
1914 Thursday
1915 Friday
1916 Saturday Yes
1917 Monday
1918 Tuesday
1919 Wednesday
1920 Thursday Yes
1921 Saturday
1922 Sunday
1923 Monday
1924 Tuesday Yes
1925 Thursday
1926 Friday
1927 Saturday
1928 Sunday Yes
1929 Tuesday
1930 Wednesday
1931 Thursday
1932 Friday Yes

Note that 1932 ended up just the same as 1904 -- a leap year starting on Friday.

Friday the 13th distribution

The number of Friday the 13ths within each of those calendars is:
1 Jan Leap year Num 13s
Sunday Yes 3
Monday Yes 2
Tuesday Yes 1
Wednesday Yes 2
Thursday Yes 2
Friday Yes 1
Saturday Yes 1
- - - - - -
Sunday No 2
Monday No 2
Tuesday No 2
Wednesday No 1
Thursday No 3
Friday No 1
Saturday No 1

Full Gregorian Calendar Cycle

The fill calendar cycle is 400 years long, and no, I am not going to spell it out in complete detail.

The justification I will give is that 400 years will take you from one century leap year to another with an even set of weeks (no excess days). That is supported by:

Calendar Count Excess Days
Each Total
normal non-leap year 300 1 300
century non-leap year 3 1 3
normal leap years 96 2 192
century leap years 1 2 2
Total 497

A quick check shows that 497 is 71 * 7, so the 400 year time span does indeed complete (20871 weeks total) with no stray days left over.

Back to the shiny objects

Copyright 1997, Drew Lawson.
[Last updated: 18 April 1997]
URL: http://www.furrfu.com/magpies/calendar_notes.html
Email drew@furrfu.com