Tips being coins and tricks being a magic trick to make a big coin.

How do I tell which months have 30 days and which have 31 without reference to a calendar?

Last updated: around 2003

Type:              Trick
Reliability:        - Very high
Ease of learning:   - Easy
Time saving:        - Moderate gain
Usefulness:         - Very useful
Difficulty:         - Easy
Overall:            - Great

1 Days in month trick

Either 30 or 31, it can be frustrating, especially in the long run. There is a trick to tell accurately which has which without memorization. The trick is as follows:

With both of your hands, make a fist and curl your fingers in toward your palms so they resemble the image below.
Put both hands together without criss-crossing them.
High spots represent more days as more is a higher quantity, thus a higher point.
Low spots represent less days, thus a lower point.
Ignore the gap between the two hands as you know July and August are the only two months consecutively within the same year that have 31 days.
February is the odd ball as you should know. It has either 28 or 29 days, depending on the year number.

2 Days in February

2.1 How to determine the numbers

A multiple of 4 is the obvious case for a leap year indication. There is yet another trick to tell whether February has 28 or 29 days.

If the year number was not a multiple of four [i.e. 2003], February has 28 days.
If the year number is a multiple of four [i.e. 2004], February has 29 days.
If the year number is a multiple of 100 but not 400 [i.e. 1900, not 2000], February has 28 days.
If the year number is a multiple of 400 [i.e. 2000], February has 29 days.

2.2 Some math behind years and this pattern

What's with the strange pattern with the 4 and 400? The true number of days in the year is 365.242199 days^*, not 365 1/4 [or 365.25 as a decimal to help you compare] as you may know of it better. Every year, about 1/4 of a day is "lost". Every 4 years is when a leap year occurs thus replacing those four lost days, however, upon doing so, and repeating it for 100 years, you'd have 0.7801 extra days. With a year not a multiple of 400 but 100, it'll take away an extra day giving a small loss. Repeat this 4 times, for 400, and then you've got an extra day added to the leap year and this resets it again. It'll be around the year A.D. 5500 before another special adjustment needs to take place. With the Earth slowing down on it's rate of spin, this factors in as well.

Footnotes:
* If you do a search in google for "days in year", you'll see this 365.242199 number. If you're wondering how many times a clock goes "tick tock" every full actual year if every "tick" was one second, it'll make 31,556,925.9936 ticks, or, which is super close to 31,556,926, or, as I commonly say, 31 5/9 million (which is 31,555,555 5/9 for comparison, hardly any difference).

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