## Friday, November 16, 2012

### Can Old Calendar Come Handy?

You have been cleaning your parents' apartment and found there a collection of old calendars for the last 10 years (2002-2011). All clean, with no scribble on them and all packed with retro images. You wish you could keep them around but you are afraid your parents may confuse the dates on the wrong calendar, unless ... you can use one of the old calendars in 2013. Can you?

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The 2002 calendar will have the correct day/date combinations for 2013.
I understand why but I'm not sure my explanation will make sense to anyone else; however here goes nothing...
There are 365 days in a year, and 7 days in a week, so a year is 52 weeks and 1 day. Each date is one weekday later per year, so you would need to go back 7 years to find a matching set... except that every leap year adds an extra day. 7 years prior to 2013 would be 2006, but that gap includes 2 leap years: 2008 and 2012. This means 2006 is actually 9 weekdays prior to 2013. To get the required 7 weekdays we would need to jump ahead 2 years, to 2008... but 2008 is a leap year, and 2013 is not, so after 28th February they would no longer match.
Since we cannot find a matching year which is 7 years prior to 2013, we must look 14 years prior, which would be 1999, outside the range of available calendars... however this 14-year gap includes 4 leap years: 2000, 2004, 2008, 2012. These add 4 extra days into the equation, so we are actually 18 days away from our desired dates. We need to go forward 4 weekdays: 1 leapyear and 2 standard years will give the desired result, so we jump forward 3 years from 1999 to 2002.
I hope that made sense to someone at least; apologies if it's not very clear!

Anonymous said...

I have actually done this before: re-used one year's print calendar in a future year. One calendar I had from an environmental organization actually listed on the back the next 5 future years with matching dates and days of the week to encourage such re-use.

The problem I have found with re-using calendars in this way is that even when the configuration of the days and days match for all the months, some information that is recorded on the regular (Gregorian style) calendars but that is based on other calendars/cycles does not match between the two years. This unmatching information includes religious holidays, for example, Passover, Rosh Hashanah, Easter, and so on. Because of the mismatch of the dates of these holidays between years and confusion that can then arise, I now recycle each year's calendar instead of reusing them.

In terms of which calendar year of 2001-2011 matches days of the week and dates for each month with the 2013 calendar, 2002 is a perfect match, and 2008 matches until Feb 28, 2013 (2008 was a leap yr, 2013 is not).

I probably cheated a bit on this question by at first not calculating this out myself. Back in the 1990s, I was given a pocket-size an event planning (for conventions, etc.) calendar that covered 20 years: 1998-2017. I have referred to it many times in the past 14 years and did to answer this question as well.

However, I have now also calculated it, working back through each year:
(Each 365 day year is 52 weeks + 1 day; each 366 day year is 52 weeks + 2 days), so
2013 starts on a Tuesday
2012 (leap year) started on a Sunday
2011 started on a Saturday
2010 started on a Friday
2009 started on a Thursday
2008 (leap year) started on a Tuesday
2007 started on a Monday
2006 started on a Sunday
2005 started on a Saturday
2004 (leap year) started on a Thursday
2003 started on a Wednesday
2002 started on a Tuesday
2001 started on a Monday

Only 2002, 2008, and 2013 all start on a Tuesday, but with 2008 being a leap year, only 2002 and 2013 match for all 12 months.

TracyZ

Wang said...

You can reuse your 2002 calendar for 2013 - that really is quite cool!

Jerome said...

Calendar Algorithms are very complex. I used a quick and dirty method of finding January1, from 2002 to 2013. The formula in excel is

=MOD(+(B1*365 + INT((B1-1) / 4) - INT((B1-1) / 100) + INT((B1-1) / 400)),7)
If this monster returns 0 it means Sunday and if it returns 6 if it is Saturday. Every other day increases by 1 from Sunday so Monday is 1 Tuesday is 2 and so on.

The next thing to do is to find the day of the week of March the first for all years between and including 2002 and 2013.

This is done by returning adding a mod 7 for 59 for non leap years and 60 mod 7 for leap years. That would be 3 for non leap years and 4 for leap years.

2012 March 1 returns (0 + 4) mod 7 = 4 which is a Thursday
2011 March 1 returns (6 + 3) mod 7 = 2 which is a Tuesday.

Now to cut to the chase. Only 2 years return a 5 Friday

Those 2 years are ….. Tada

2013 and 2002

The January 1 algorithm was found here.

http://stackoverflow.com/questions/478694/what-is-the-easiest-algorithm-to-find-the-day-of-week-of-day-zero-of-a-given-yea

So you could use 2002 and not buy a 2013 calendar <========Answer.

The question for me is “How did you do this Maria?” I can hardly wait for Monday morning!

There are fourteen unique calendars. A calendar can begin on any of the seven days of the week and each calendar can be for a regular or leap year.

A quick check shows that January 1st, 2002 and January 1st, 2013 both occur on a Tuesday and that neither is a leap year, so the 2002 calendar can be used in 2013.

Jerome said...

A couple of footnotes.

1. I was not the brightest nail in the jar. I should have just subtracted 1 from January 1st. That would have given me December 31 of the previous year. What you need is the 31st of every year from 2001 to 2013. Leave out any consideration of leap years. 2013 is not a leap year: neither is the one you have to choose from. It still comes out to 2002 for 2013.

2. You could work backwards using the fact that in 2002 for example if a day you are interested in was a Wedensday, the next year it would be a Thursday. A leap year would add 2 days. I just didn’t think of it.

3. The best news of all is that Excel can do this for you. If a1 in excel contains a date like “December 23, 2010”, then in B1 you could put =weekday(a1,1) and it will come back with a 5 which is Thursday. By the way, Excel automatically changes the date from December 23, 2010 to 23-Dec 10. See last week’s comment

Anonymous said...

2002 and 2013 are the same.

Gurubandhu

Annie said...

Yes, you can use 2002. Both 2002 and 2013 are not Leap Years. 2013 begins on a Tuesday. With the help of Google I found that 2002 also starts with a Tuesday so if the year is changed on the 2002 calendar to 2013, your parents should be in good shape! ( Granted this is not the most mathematical approach to the puzzles's solution!)

Ilya said...

I am submitting late, but hey it was my birthday on Sunday :-).

I think the answer is now. 2013 starts on a Tuesday. The only other year in the interval that started on a Tuesday is 2008, but alas, it's a leap year whereas 2013 is not.

Maria said...

Happy Birthday to Ilya but congratulations to everyone else - the calendar that can be reused is from the year 2002.

As many of you wrote the trick is to remember that a regular year shifts any date by 1 day forward and a leap year by 2 days. Therefore:

January 1st, 2013 is Tuesday
2012 was leap, to take 2 days off from Tuesday - getting Sunday
2011 regular year, taking 1 day off from Sunday - Saturday
2010 regular, take 1 day off - Friday
2009 regular, take 1 day off - Thursday
2008 leap, take 2 days off - Tuesday. Potential match, but the year is leap while 2013 is not, cant use. Continuing.
2007 is reg, take 1 day off - Monday.
2006 is reg, another day off - Sunday.
2005 is reg, another day off - Saturday.
2004 is leap, take 2 day off - Thursday.
2003 is reg, one day off - Wednesday.
2002 is reg, one day off - Tuesday. Potential match. Non-leap year. A perfect match!

Thanks to Jerome who posted how Excell can do this for us.

Tracy - I was very interested to read that some calendars are actually encouraging such reuse and list matching years. And you are right it is not very practical if you care about moon phases or observe any non-Gregorian holidays.

Puzzle point to everyone, but the birthday man. Sorry.

Tom said...

Sorry I missed this one, what fun. When I was just a lad there was a garage mechanic nearby who had a huge collection of those old R-rated Esquire calendars. He had dozens of them posted on the walls of his dirty old shop, always turned to the correct month, "Just so I never forget what day it is!"