Friday the 13ths

DDEckerslyke · Joined: 05 Aug 2007 Posts: 21

Occasionally we have to endure staff meetings in which senior management
read out whatever it is they are projecting on to the screen in front of us
and then use buzzwords they came across on their last away day. (My
favourite was 'emphatic'. We had a meeting that was 'emphatic' this and
'emphatic' that until, of course, inevitably, we had 'emphatic emphasis'. At
which point there was an embarrassed mumbling of something about 'one too
many emphasises'. Priceless.)

One of the ways I get through these meetings is to sit at the back and
pretend I am taking notes. This gives you an ideal excuse for writing. I
used to try and recall the proof that sqrt2 is not a fraction and then
generalise it to sqrt 3. I am now quite good at this so I was looking for
something else to do when I came across the following problem (I know it's
not difficult but it took just the right amount of time to organise and
check and I thought others here might have a few minutes to kill on a bus or
a train journey):

What is the most and least number of Friday the 13ths there can be in one
year?

cheers

dd

Archived from group: rec>puzzles

John Smith · Joined: 05 Aug 2007 Posts: 30

"DDEckerslyke" wrote in message@mk-nntp-1.news.uk.worldonline.com...
> Occasionally we have to endure staff meetings in which senior management
> read out whatever it is they are projecting on to the screen in front of
us
> and then use buzzwords they came across on their last away day. (My
> favourite was 'emphatic'. We had a meeting that was 'emphatic' this and
> 'emphatic' that until, of course, inevitably, we had 'emphatic emphasis'.
At
> which point there was an embarrassed mumbling of something about 'one too
> many emphasises'. Priceless.)
>
> One of the ways I get through these meetings is to sit at the back and
> pretend I am taking notes. This gives you an ideal excuse for writing. I
> used to try and recall the proof that sqrt2 is not a fraction and then
> generalise it to sqrt 3. I am now quite good at this so I was looking for
> something else to do when I came across the following problem (I know it's
> not difficult but it took just the right amount of time to organise and
> check and I thought others here might have a few minutes to kill on a bus
or
> a train journey):
>
> What is the most and least number of Friday the 13ths there can be in one
> year?
>
> cheers
>
> dd
>
In such meetings I like to differentiate functions from first principles

Cliff Ray · Joined: 05 Aug 2007 Posts: 4

>
> What is the most and least number of Friday the 13ths there can be in one
> year?
>
> cheers
>
> dd
>
>

1 to 3 on a normal year

0 to 4 on a leap year.

Ed Murphy · Joined: 05 Aug 2007 Posts: 4

On Tue, 23 Mar 2004 23:10:24 +0000, Cliff Ray wrote:

>> What is the most and least number of Friday the 13ths there can be in one
>> year?

> 1 to 3 on a normal year
>
> 0 to 4 on a leap year.

No, it's 1 to 3 on leap years as well; I worked this out a few days
ago, in response to that rambling numerologist from New Zealand.

If January 13 is a ... then the other months' 13ths are
3 1 3 2 3 2 3 3 2 3 2 3
Sunday W R U T F U W A M R A T -> 1
Monday R F M W A M R U T F U W -> 2
Tuesday F A T R U T F M W A M R -> 2
Wednesday A U W F M W A T R U T F -> 2
Thursday U M R A T R U W F M W A -> 1
Friday M T F U W F M R A T R U -> 3
Saturday T W A M R A T F U W F M -> 1

(sUn Mon Tue Wed thuR Fri sAt)

Patrick Hamlyn · Joined: 05 Aug 2007 Posts: 1

Ed Murphy wrote:

>On Tue, 23 Mar 2004 23:10:24 +0000, Cliff Ray wrote:
>
>>> What is the most and least number of Friday the 13ths there can be in one
>>> year?
>
>> 1 to 3 on a normal year
>>
>> 0 to 4 on a leap year.
>
>No, it's 1 to 3 on leap years as well; I worked this out a few days
>ago, in response to that rambling numerologist from New Zealand.
>
>If January 13 is a ... then the other months' 13ths are
> 3 1 3 2 3 2 3 3 2 3 2 3
> Sunday W R U T F U W A M R A T -> 1
> Monday R F M W A M R U T F U W -> 2
> Tuesday F A T R U T F M W A M R -> 2
> Wednesday A U W F M W A T R U T F -> 2
> Thursday U M R A T R U W F M W A -> 1
> Friday M T F U W F M R A T R U -> 3
> Saturday T W A M R A T F U W F M -> 1

Something a little odd with your counts in the last few lines
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms-subscribe@egroups.com)

Paul · Joined: 05 Aug 2007 Posts: 1

you're all a bunch of nerds.

Cliff Ray wrote in message ...
>
>>
>> What is the most and least number of Friday the 13ths there can be in one
>> year?
>>
>> cheers
>>
>> dd
>>
>>
>
>1 to 3 on a normal year
>
>0 to 4 on a leap year.
>

Steve Grant · Joined: 05 Aug 2007 Posts: 1

"Paul" wrote in message$fa$1@mws-stat-syd.cdn.telstra.com.au...
> you're all a bunch of nerds.

Thank you! I was hoping someone would notice.

Ed Murphy · Joined: 05 Aug 2007 Posts: 4

On Wed, 24 Mar 2004 00:43:03 +0000, Patrick Hamlyn wrote:

>>If January 13 is a ... then the other months' 13ths are
>> 3 1 3 2 3 2 3 3 2 3 2 3
>> Sunday W R U T F U W A M R A T -> 1
>> Monday R F M W A M R U T F U W -> 2
>> Tuesday F A T R U T F M W A M R -> 2
>> Wednesday A U W F M W A T R U T F -> 2
>> Thursday U M R A T R U W F M W A -> 1
>> Friday M T F U W F M R A T R U -> 3
>> Saturday T W A M R A T F U W F M -> 1
>
> Something a little odd with your counts in the last few lines

You're right, the last line should have 2 rather than 1. The
next-to-last-line is correct, though; January 13 is itself a
Friday-the-13th, and so are April 13 and July 13.

Kevin Green · Joined: 05 Aug 2007 Posts: 1

"Ed Murphy" wrote in message@socal.rr.com...
> On Wed, 24 Mar 2004 00:43:03 +0000, Patrick Hamlyn wrote:
>
> >>If January 13 is a ... then the other months' 13ths are
> >> 3 1 3 2 3 2 3 3 2 3 2 3
> >> Sunday W R U T F U W A M R A T -> 1
> >> Monday R F M W A M R U T F U W -> 2
> >> Tuesday F A T R U T F M W A M R -> 2
> >> Wednesday A U W F M W A T R U T F -> 2
> >> Thursday U M R A T R U W F M W A -> 1
> >> Friday M T F U W F M R A T R U -> 3
> >> Saturday T W A M R A T F U W F M -> 1
> >
> > Something a little odd with your counts in the last few lines
>
> You're right, the last line should have 2 rather than 1. The
> next-to-last-line is correct, though; January 13 is itself a
> Friday-the-13th, and so are April 13 and July 13.

Um, you have one too many in your Wednesday line. That
last Friday is in January of the next year.

Kev

moriman · Joined: 05 Aug 2007 Posts: 1

"Paul" wrote in message$fa$1@mws-stat-syd.cdn.telstra.com.au...
> you're all a bunch of nerds.
>

and you are here because....¿

>
> Cliff Ray wrote in message ...
> >
> >>
> >> What is the most and least number of Friday the 13ths there can be in
one
> >> year?
> >>
> >> cheers
> >>
> >> dd
> >>
> >>
> >
> >1 to 3 on a normal year
> >
> >0 to 4 on a leap year.
> >
>
>

Ed Murphy · Joined: 05 Aug 2007 Posts: 4

On Wed, 24 Mar 2004 07:23:48 +0000, Ed Murphy wrote:

> On Wed, 24 Mar 2004 00:43:03 +0000, Patrick Hamlyn wrote:
>
>>>If January 13 is a ... then the other months' 13ths are
>>> 3 1 3 2 3 2 3 3 2 3 2 3
>>> Sunday W R U T F U W A M R A T -> 1
>>> Monday R F M W A M R U T F U W -> 2
>>> Tuesday F A T R U T F M W A M R -> 2
>>> Wednesday A U W F M W A T R U T F -> 2
>>> Thursday U M R A T R U W F M W A -> 1
>>> Friday M T F U W F M R A T R U -> 3
>>> Saturday T W A M R A T F U W F M -> 1
>>
>> Something a little odd with your counts in the last few lines
>
> You're right, the last line should have 2 rather than 1. The
> next-to-last-line is correct, though; January 13 is itself a
> Friday-the-13th, and so are April 13 and July 13.

Also correct. Still, the point is that a leap year can't have
more than 3 or less than 1 Friday-the-13ths.

For non-leap-years, move January and February back a day, while
leaving the rest the same:

A T R U T F U W A M R A -> 1
U W F M W A M R U T F U -> 2
M R A T R U T F M W A M -> 1
T F U W F M W A T R U T -> 2
W A M R A T R U W F M W -> 1
R U T F U W F M R A T R -> 2
F M W A M R A T F U W F -> 3

ObFollowup: What proposed calendar would give us 13 Friday-the-13ths
every year?

Cliff Ray · Joined: 05 Aug 2007 Posts: 4

> Also correct. Still, the point is that a leap year can't have
> more than 3 or less than 1 Friday-the-13ths.

Yep, just checked and one of my Friday 13this was in fact a Thursday Smile

>
> ObFollowup: What proposed calendar would give us 13 Friday-the-13ths
> every year?
>

13, 28 day long months would do that. You could make up the missing bit
with a 48 hour long news year's eve, but that would give a terrible
hangover the next day.

Michael Jørgensen · Joined: 05 Aug 2007 Posts: 1

"Cliff Ray" wrote in message@nildram.net...

> 13, 28 day long months would do that. You could make up the missing bit
> with a 48 hour long news year's eve, but that would give a terrible
> hangover the next day.

Oh, how that does appeal to me Smile

-Michael.

Ken Starks · Joined: 05 Aug 2007 Posts: 14

In article , Cliff Ray
writes
>
>13, 28 day long months would do that. You could make up the missing bit with a
>48 hour long news year's eve, but that would give a terrible hangover the next
>day.

Rather a nice symmetrical Calendar (not much to do with
Friday being the thirteenth) is:

One civil year = 4 'quarters' of 91 days + one or two extras
Each quarter starts on a Sunday, consists of 13 weeks, and ends
on a Saturday.
You always get an extra day just after the fourth quarter, named
'New Years Eve' and not named any of 'Sunday' to 'Saturday'. (It
falls between Sat December 31st and Sun January 1st.)
On Leap Years you get an extra day named 'Leap Day' at the end of the
second quarter (Between Sat June 30th and Sun July 1st ).

So-called 'Leap seconds' are added or subtracted between the other
quarters. (e.g. to add two seconds, civil time would go:
....
11:59:59 Saturday
11:59:60 Saturday
11:59:61 Saturday
00:00:00 Midnight (Sat/Sun)
00:00:01 Sunday
....

Each quarter is 3 months of length 30, 31, and 30 days.

With this system, New Years Day would always be a Sunday,
and can be spent recovering from your double
party (Sat + New Years Eve).
By the way, the 13th falls on Friday, Sunday, or Wednesday
depending on which month of a quarter you are in. So you
always get four a year.

- -
Ken, __O
-\<,_
(_)/ (_)
Virtuale Saluton.

Prai Jei · Joined: 05 Aug 2007 Posts: 3

Ed Murphy (or somebody else of the same name) wrote in message
thusly:

> On Wed, 24 Mar 2004 07:23:48 +0000, Ed Murphy wrote:
>
>> On Wed, 24 Mar 2004 00:43:03 +0000, Patrick Hamlyn wrote:
>>
>>>>If January 13 is a ... then the other months' 13ths are
>>>> 3 1 3 2 3 2 3 3 2 3 2 3
>>>> Sunday W R U T F U W A M R A T -> 1
>>>> Monday R F M W A M R U T F U W -> 2
>>>> Tuesday F A T R U T F M W A M R -> 2
>>>> Wednesday A U W F M W A T R U T F -> 2
>>>> Thursday U M R A T R U W F M W A -> 1
>>>> Friday M T F U W F M R A T R U -> 3
>>>> Saturday T W A M R A T F U W F M -> 1
>>>
>>> Something a little odd with your counts in the last few lines
>>
>> You're right, the last line should have 2 rather than 1. The
>> next-to-last-line is correct, though; January 13 is itself a
>> Friday-the-13th, and so are April 13 and July 13.
>
> Also correct. Still, the point is that a leap year can't have
> more than 3 or less than 1 Friday-the-13ths.
>
> For non-leap-years, move January and February back a day, while
> leaving the rest the same:
>
> A T R U T F U W A M R A -> 1
> U W F M W A M R U T F U -> 2
> M R A T R U T F M W A M -> 1
> T F U W F M W A T R U T -> 2
> W A M R A T R U W F M W -> 1
> R U T F U W F M R A T R -> 2
> F M W A M R A T F U W F -> 3
>
> ObFollowup: What proposed calendar would give us 13 Friday-the-13ths
> every year?

Spoiler

Spoiler

Spoiler

The Fortean calendar?.

The Shire Calendar (LotR appendix D) has two Friday 13th's every year.
--
Paul Townsend
I put it down there, and when I went back to it, there it was GONE!

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