Should months be of even lengths?

Dear Calendar People

One can have a calendar where all months begin on the same day of week within the same year, without interrupting the 7-day week, although that day of week would vary from year to year.

Then below would become

·         All years

   All Months correspond to each other

This can be achieved with a 13 month calendar, if all months but the 13^th month have 28 days. The 13^th month would have 29 days in a common year and 30 days in a leap year. If the leap day were to coincide with February 29^th months would begin on the following dates:

Month 1: Mar 1 – Mar 28

Month 2: Mar 29 – Apr 25

Month 3: Apr 26 – May 23

Month 4: May 24 – Jun 20

Month 5: Jun 21 – Jul 18

Month 6: Jul 19 – Aug 15

Month 7: Aug 16 – Sep 12

Month 8: Sep 13 – Oct 10

Month 9: Oct 11 – Nov 7

Month 10: Nov 8 – Dec 5

Month 11:  Dec 6 – Jan 2

Month 12: Jan 3 – Jan 30

Month 13: Jan 31 – Feb 28/29

Unlike Sonny’s suggestion, it is not possible to make a month coincide with February, because this would cause some years to have some months beginning on different days of the week.

It can also be done with 12 months with near equal quarters, by having months of 28 or 35 days, except the last month, which is the same as in the 13-month calendar.

For example:

Month 1: Mar 1 – Mar 28 

Month 2: Mar 29 – May 2 

Month 3 May 3 – May 30

Month 4: May 31 – Jun 27

Month 5: Jun28 – Aug 1

Month 6: Aug 2 – Aug 29

Month 7: Aug 30 – Sep 26

Month 8: Sep 27 – Oct 31

Month 9: Nov 1 – Nov 28

Month 10: Nov 29 – Dec 26

Month 11: Dec 27 – Jan 30

Month 12: Jan 31 – Feb 28/29

Also every month from Month 1 to Month 10 would end on Doomsday in either the 13-month or 12-month example.

Karl

12(07(27

This is an interesting question from the recent MATH magazine 

                                                                                                                  The answers for the 13 quads calendar are:

·         Common year

o    0, I, II, III, IV, V, VI, VII, VIII, IX, X, XI

o    No other quads correspond to Quad XII (29 days)

·         Leap year

o    I, II, III, IV, V, VI, VII, VIII, IX, X, XI

o    0 and XII (29 days)

·         All years

o    Same as leap year

Dear Irv and Calendar People

See http://en.wikipedia.org/wiki/Doomsday_rule and it has been mentioned in CALNDR_L .

Karl

Dear Calendar People

For years beginning March 1^st, the correspondences would be as follows:

·         All Years

March and November

April and July

May and January

June and February

September and December

No month corresponds to August or October

The pairs of corresponding months occur at an intervals of 3 or 8 months.

There are no triplets. Hence the maximum number of Friday 13^ths in a year beginning with March is two (rather than three for 2012).

Karl

12(07(27

This is an interesting question from the recent MATH magazine 

                                                                                                                  The answers for the 13 quads calendar are:

·         Common year

o    0, I, II, III, IV, V, VI, VII, VIII, IX, X, XI

o    No other quads correspond to Quad XII (29 days)

·         Leap year

o    I, II, III, IV, V, VI, VII, VIII, IX, X, XI

o    0 and XII (29 days)

·         All years

o    Same as leap year