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rmac22
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Posted on Fri, Feb 01, 2013 08:25

Puzzle

 

Considering the calendar system we now use, neglecting the corrections that have to be done every century, or even less often, but including leap years, how many unique calendars are there not considering the year? 

 

That is, remove the year from a calendar, and in the course of time there will be another year with exactly the same arrangement of days.  You could put the different year on it and it would be exactly right.

 

You can solve how many unique calendars there are with pure reasoning, by working through it year by year, or some combination of both.    

 

Related to that, what is the minimum worst case number of years it takes to use them all?  That too you can solve with pure reasoning, etc.

 

This may be entirely too easy for a bunch as intelligent as you all, but we shall see. 

 

RMac



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Livnlov
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Posted on Fri, Feb 08, 2013 10:50

Quoting rmac22:

Hi Liv,

 

I think you are making this much too tough.  The puzzle only has to do with the common calendars we have currently been using.     What you bring up re the biblical stuff is fascinating and what the relationship to current calendars and time I do not know.

 

To explain leap years why and how, look up “The Gregorian calendar – timeanddate”  Both Bing and Google searches popped up the best article.  Wikipedia not as good.    

 

Thanks,

 

RMac 


RMac - I have a knack for complicating the uncomplicated and demystifying the complex! C'est tres triste, non?

 

Liv.



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rmac22
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Posted on Fri, Feb 08, 2013 09:50

Quoting Curious2078:

I haven't read through every post here, Mac, but I have read your initiating blog.  And I can't quite figure out what you question is--or if you even have one.  But if you're looking for a perpetual calendar, or asking us to come up with one, I do have one.  But it goes on for well over a hundred years.  I hope you don't want me to post the entire thing here.

 

ROFLMAO



No thst was not the question.  Read Dakota's solution, and my somewhat more detailed one.

Thanks,

RMac

 



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Curious2078
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Posted on Thu, Feb 07, 2013 18:15

Quoting rmac22:

Puzzle

 

Considering the calendar system we now use, neglecting the corrections that have to be done every century, or even less often, but including leap years, how many unique calendars are there not considering the year? 

 

That is, remove the year from a calendar, and in the course of time there will be another year with exactly the same arrangement of days.  You could put the different year on it and it would be exactly right.

 

You can solve how many unique calendars there are with pure reasoning, by working through it year by year, or some combination of both.    

 

Related to that, what is the minimum worst case number of years it takes to use them all?  That too you can solve with pure reasoning, etc.

 

This may be entirely too easy for a bunch as intelligent as you all, but we shall see. 

 

RMac



I haven't read through every post here, Mac, but I have read your initiating blog.  And I can't quite figure out what you question is--or if you even have one.  But if you're looking for a perpetual calendar, or asking us to come up with one, I do have one.  But it goes on for well over a hundred years.  I hope you don't want me to post the entire thing here.

 

ROFLMAO



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rmac22
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Posted on Wed, Feb 06, 2013 07:36

Quoting Livnlov:


“Can we start again please, because I flunked this exam! “

 

Hi Liv,

 

Would you like another puzzle?  I have a bunch more.  Next one I did not make up.  Found it.  It might be easier -- hard to tell though.  As I said earlier – “Everything is easy, once you ‘see.’”

 

RMac



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rmac22
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Posted on Tue, Feb 05, 2013 17:07

Solution: 

First off you need to realize that if non-leap year January 1st is on a Sunday, then any other non-leap year where January 1st is on a Sunday will have an identical calendar save the year and the pictures.  The same is true for Monday, Tuesday, Wednesday, etc.  So we have 7 unique calendars so far.  

 

Using the same reasoning for leap years we have another7  unique calendars for a total of 14.

 

The least worst case number of years would have to be 28, which is 7 times 4, but did we truly cover all the unique calendars.  For that we would need to construct a table and march through the progression of calendars to make sure. 

 

For Dakota’s example starting this year, the first year after a leap year and January first was on a Tuesday or the 3rd day of the week.   So, we have 3, 4, 5, 6, and the next leap year will have January First on the 6th day of the week or a Friday.   Now since leaps years add a day our next number sequence does not start with Saturday, but Sunday, that is 1, 2, 3, 4, and the next leaps years January First is on a Wednesday. 

 

So, when we get all done, we have a little table like this and our seven leap years January Firsts happened on the days of the week in the last column. 

 

3              4              5              6

1              2              3              4

6              7              1              2

4              5              6              7

2              3              4              5

7              1              2              3

5              6              7              1

 

Thus although in an interesting order, Friday, Wednesday, Monday, Saturday, Thursday, Tuesday, and Sunday.   They are all there.   The same for the third column, the third year of the four year sequences, they are all there.   Ditto the second year -- second column, and the first year—first column. 

 

Now, if we stated with a leap year and ended with a leap year we could shave off 3 years.  That is why I asked for the least worst case. 

 

RMac

 



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Dakota35
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Posted on Mon, Feb 04, 2013 21:59

Quoting rmac22:

That is -- 14 unique calendars and 28 minimum worst case years to get through them all.

 

Both are correct. I’ll leave the explanation for the time being. Someone else may want to explain why.

 

RMac

 


Just have to remember leap years.  I had to write all the dates down making note of each leap year...going through seven.  Start on 2013 go through seven leap years then count the years.



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rmac22
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Posted on Mon, Feb 04, 2013 19:51

Quoting Livnlov:

RMac,

 

You are way too intelligent for my liking, LOL! NOT!! You are a smart man! You've got my brain cells so cooked they feel like mash potatoes!

 

Can we start again please, because I flunked this exam!

 

OK, OK, I will come clean - I know what you are talking about. You know, just 2 days ago, I was wondering about what impact Joshua's extra hours of the day (the sun stood still in the old testament during a battle between Israel and one of its neighbours) must have on current calendar and what relationship, if any, it may have with leap years etc???!!! Does anyone know? Oh dear, I risk being labelled a religious zealot, but I did read that there was some scientific evidence of the sun really standing still sometime way back in the history of this precious planet.

 

So repititions of the days in a format that exhibit exactitude is quite clearly possible and of course this could lead to perfectly symmetrical date sequence upon super-imposition of one corresponding set over the other. But frankly, I have never sequenced these out nor tried to extrapolate if there is a further sequence/definitive pattern to the frequency of such a re-occurrence - NEVER.

 

But a great thought RMAC!

 

Thanks for sharing.

 

Liv.



Hi Liv,

 

I think you are making this much too tough.  The puzzle only has to do with the common calendars we have currently been using.     What you bring up re the biblical stuff is fascinating and what the relationship to current calendars and time I do not know.

 

To explain leap years why and how, look up “The Gregorian calendar – timeanddate”  Both Bing and Google searches popped up the best article.  Wikipedia not as good.    

 

Thanks,

 

RMac 



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rmac22
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Posted on Mon, Feb 04, 2013 19:04

Quoting Dakota35:

14 and 28y.? Not sure about the 28??? I really suck at word problems so...take it my answers with a laugh.



That is -- 14 unique calendars and 28 minimum worst case years to get through them all.

 

Both are correct. I’ll leave the explanation for the time being. Someone else may want to explain why.

 

RMac

 



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Livnlov
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Posted on Sun, Feb 03, 2013 18:49

RMac,

 

You are way too intelligent for my liking, LOL! NOT!! You are a smart man! You've got my brain cells so cooked they feel like mash potatoes!

 

Can we start again please, because I flunked this exam!

 

OK, OK, I will come clean - I know what you are talking about. You know, just 2 days ago, I was wondering about what impact Joshua's extra hours of the day (the sun stood still in the old testament during a battle between Israel and one of its neighbours) must have on current calendar and what relationship, if any, it may have with leap years etc???!!! Does anyone know? Oh dear, I risk being labelled a religious zealot, but I did read that there was some scientific evidence of the sun really standing still sometime way back in the history of this precious planet.

 

So repititions of the days in a format that exhibit exactitude is quite clearly possible and of course this could lead to perfectly symmetrical date sequence upon super-imposition of one corresponding set over the other. But frankly, I have never sequenced these out nor tried to extrapolate if there is a further sequence/definitive pattern to the frequency of such a re-occurrence - NEVER.

 

But a great thought RMAC!

 

Thanks for sharing.

 

Liv.



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Dakota35
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Posted on Sun, Feb 03, 2013 09:21

14 and 28y.? Not sure about the 28??? I really suck at word problems so...take it my answers with a laugh.



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rmac22
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Posted on Sat, Feb 02, 2013 10:47

Hi Hope -- My phone is not too smart. I keep having to add money.

I would give you a hint, but it is pretty easy anyway.

I know, everything is easy once you "see."

My weekend mid way through Saturday is going pretty good. \

So far I only have missed up on paying my land line phone bill. Over paid it. By a lot. Long story.

Correction, I over cooked some burgers messing with this.

Maybe I need to work on that emotional intelligence. Organizational intelligence. One of those intelligences.

You have a great weekend too.

RMac



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Hoping4Love2000
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Posted on Sat, Feb 02, 2013 07:28

RMAC? RMAC?? Are you in there??? 

 

HELLO? HELLOOOOO??? 

 

RMAC..... RMAC!! I'm afraid I can hear your voice..

 

but I'll be darned if I'v e a clue of what you're saying!! 

 

WAAAAHHHHHH!!!!!!

 

When I need to know what day or year it is........ I just look at my "smart" phone!! 

 

It's a good thing the Princess has high "Emotional Intelligence"...... cuz you people sure lose me when you start throwing around numbers!  ;)

 

HAVE A GREAT WEEKEND!! 



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