A Seasonal Puzzle

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A Seasonal Puzzle

Palmen, KEV (Karl)
Dear Calendar People

What is
21, 22, 22, 21, 21,  22, 22, 21, 21, 21,  ...
in the UK
21, 22, 22, 21, 21,  22, 22, 21, 21, 22,  ...
in much of Europe and
21, 21, 22, 21, 21,  21, 22, 21, 21, 21,  ...
in the Eastern United States?

Karl

07(15(21
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Re: A Seasonal Puzzle

Amos Shapir
The day in December in which the winter (er... Southern) solstice occurs?
If this is the solution it's too easy...


>From: "Palmen, KEV (Karl)" <[hidden email]>
>Date: Wed, 21 Dec 2005 12:39:16 -0000
>
>Dear Calendar People
>
>What is
>21, 22, 22, 21, 21,  22, 22, 21, 21, 21,  ...
>in the UK
>21, 22, 22, 21, 21,  22, 22, 21, 21, 22,  ...
>in much of Europe and
>21, 21, 22, 21, 21,  21, 22, 21, 21, 21,  ...
>in the Eastern United States?
>
>Karl
>
>07(15(21

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A Seasonal Puzzle (a century clue)

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Calendar People

A 100 years earlier it would be
22, 22, 23, 22, 22,  22, 22, 22, 22, 22
in the UK.

Karl

>  -----Original Message-----
> From: Palmen, KEV (Karl)  
> Sent: 21 December 2005 12:39
> To: East Carolina University Calendar discussion List (E-mail)
> Subject: A Seasonal Puzzle
>
> Dear Calendar People
>
> What is
> 21, 22, 22, 21, 21,  22, 22, 21, 21, 21,  ...
> in the UK
> 21, 22, 22, 21, 21,  22, 22, 21, 21, 22,  ...
> in much of Europe and
> 21, 21, 22, 21, 21,  21, 22, 21, 21, 21,  ...
> in the Eastern United States?
>
> Karl
>
> 07(15(21
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Re: A Seasonal Puzzle

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Amos and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Amos Shapir
Sent: 21 December 2005 16:18
To: [hidden email]
Subject: Re: A Seasonal Puzzle


The day in December in which the winter (er... Southern) solstice occurs?
If this is the solution it's too easy...

KARL SAYS: Amos has part of the answer.
We also need to know from when the years are counted from.

Karl

07(15(21


>From: "Palmen, KEV (Karl)" <[hidden email]>
>Date: Wed, 21 Dec 2005 12:39:16 -0000
>
>Dear Calendar People
>
>What is
>21, 22, 22, 21, 21,  22, 22, 21, 21, 21,  ...
>in the UK
>21, 22, 22, 21, 21,  22, 22, 21, 21, 22,  ...
>in much of Europe and
>21, 21, 22, 21, 21,  21, 22, 21, 21, 21,  ...
>in the Eastern United States?
>
>Karl
>
>07(15(21

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A Seasonal Puzzle (answer)

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Amos, Victor and Calendar People

-----Original Message-----
From: Palmen, KEV (Karl)
Sent: 21 December 2005 16:20
To: 'East Carolina University Calendar discussion List'
Subject: RE: A Seasonal Puzzle


Dear Amos and Calendar People

I give the answer and explanation at the end of this note.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Amos Shapir
Sent: 21 December 2005 16:18
To: [hidden email]
Subject: Re: A Seasonal Puzzle


The day in December in which the winter (er... Southern) solstice occurs?
If this is the solution it's too easy...

KARL SAYS: Amos has part of the answer.
We also need to know from when the years are counted from.

Karl

07(15(21


>From: "Palmen, KEV (Karl)" <[hidden email]>
>Date: Wed, 21 Dec 2005 12:39:16 -0000
>
>Dear Calendar People
>
>What is
>21, 22, 22, 21, 21,  22, 22, 21, 21, 21,  ...
>in the UK
>21, 22, 22, 21, 21,  22, 22, 21, 21, 22,  ...
>in much of Europe and
>21, 21, 22, 21, 21,  21, 22, 21, 21, 21,  ...
>in the Eastern United States?
>
>Karl
>
>07(15(21


The answer is indeed the day of December that the solstice occurs.

We still need to determine when the years are counted from and we can assume that these years are not far from this year 2005.

A decrease in the number can only occur in a leap year. Hence the 4th and 8th years are leap years.

I show the puzzle again with a wide space before each leap year:
---------------------------------------------
What is
21, 22, 22,  21, 21, 22, 22,  21, 21, 21,  ...
>in the UK
21, 22, 22,  21, 21, 22, 22,  21, 21, 22,  ...
in much of Europe and
21, 21, 22,  21, 21, 21, 22,  21, 21, 21,  ...
in the Eastern United States?
----------------------------------------------

The 10th year is the only year what has a different date in Europe compared to the UK. Therefore its solstice must be between 23:00 and 23:59 UT on 21 Dec.
Conversely, only such years can have a solstice between 23:00 and 23:59 UT on 21 Dec.

Looking at
http://aa.usno.navy.mil/data/docs/EarthSeasons.html
or
http://www.stellafane.com/moon_phase/equinox.htm
We see that 2010 is such a year and also it is 2 years after a leap year. This also applies to 2014, but unlike 2014, it has no year with UK/Europe difference in the preceding 9 years. There can be no other year that fits this description between 1900 and 2099. Hence the 10 years shown begin with 2001 and end with 2010.

Karl

07(15(22