Submitted by frlarry on Wed, 01/29/2014 - 14:39

One version of the Mother Goose rhyme...

Thirty days have September,
April, June, and November;
February has 28 alone,
All the rest have 31;
Except leap year, that's the time,
When February's days are 29.

You can also remember which months have 31 by counting on and between your knuckles. Beginning with January, you run out of knuckles on one hand (at July) and start over (with August). December and January are also two months in a row requiring 31 days.

As a mathematician, I like simplicity, not that the above is two awful complicated. From an information-theory perspective, comparing the content of the information to the formula used to define it, it's complicated.

So, given that our years have 365 days (except for leap years, which have 366 days, unless the leap year happens to fall on a century mark, etc....), can this be simplified?

My first instinct is to take one day from each of, say, July and January, and add those days to February. That makes February a 30-day month, except when it has 31 days (as in leap year, a non-century leap year, mind you). Then we have the following pattern:

January 30
February 30
March 31
April 30
May 31

June 30
July 30
August 31
September 30
October 31
November 30
December 31

That pattern gets upset, of course, in leap year, when we might add an extra day, say, to June, yielding a distinctly different pattern. Alternatively, if we're prepared for a radical change, we might try the following:

January 30
February 30
March 31
April 30
May 31
June 30
July 31
August 30
September 31
October 30
November 31
December 30

Then, in leap year, we add 1 day to January.

Or, again, as another radical alternative, we could do the following:

January 30
February 31
March 30
April 31
May 30
June 31
July 30
August 31
September 30
October 31
November 30
December 30

and, in leap year, add the extra day at the end of the year to December. Either way, counting the days of the year is simplified...

7x30 + 5x31 = 210 + 155 = 365
6x30 + 6x31 = 180 + 186 = 366 in leap year