| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
What percent of years have 2 Friday the 13ths? 0? 1? 3? 4?
John
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1140.1 | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Fri Oct 13 1989 23:10 | 6 | |
I think I read that all years have at least one, and
at most [I can't remember exactly] three or four. It
should be easy enough to check, there are only fourteen
"year types".
Dan
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| 1140.2 | 3/7 | DWOVAX::YOUNG | Really DWOVAX::YOUNG | Sat Oct 14 1989 21:52 | 40 |
Well, lets see, a year has one of 2 "shapes":
Normal: and Leap:
Jan 0 0
Feb +3 +3
Mar +3 +4
Apr +6 0
May +1 +2
Jun +4 +5
Jul +6 0
Aug +2 +3
Sep +5 +6
Oct 0 +1
Nov +3 +4
Dec +5 +6
Where the value after each month is the number of days in the week
offset from January 1st for the first day of that month. Thus if
January 1st fell on a monday, then August 1st would fall on a wenesday
on a normal year (+2) and on a thursday on a leap year (+3).
When a month has a Friday the 13th in some particular year, then any
other month will also have a Friday the 13th If and Only If it has the
same offest value. Thus we can form groups of months with Friday the
13th's as follows:
Normal:
(Jan,Oct) (Feb,Mar,Nov) (Apr,Jul) (May) (Jun) (Aug) (Sep,Dec)
Leap:
(Jan,Apr,Jul) (Feb,Aug) (Mar,Nov) (May) (Jun) (Sep,Dec) (Oct)
So exactly 2 Friday the 13ths will occur 3 out of 7 times in normal
years and also 3 out of 7 times in leap years.
Thus there is a 3/7 ths chance that there will be exactly 2 Friday the
13ths in any particular year.
-- Barry
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| 1140.3 | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Sat Oct 14 1989 22:39 | 7 | |
The current calendar cycles through the fourteen possible
years (two "shapes" times seven start dates per shape)
every four hundred years. So the different year types
don't all occur equally often. However, your 3/7 should
be close to the actual x/400 fraction.
Dan
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| 1140.4 | right | ESCROW::MUNZER | Mon Oct 16 1989 12:12 | 3 | |
Yes, not exactly 3/7. Like 511.*.
John
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