Brain Teaser: Can you figure out why this method works for finding the day of the week for a calendar date?
This is a method devised by the matematician John Conway. There are two parts, one for even numbered months and one for odd numbered months. The part for odd numbered months is not nearly as good as the even month one, so we will just work with the even numbered months.
The idea is to find a way of determining the day of the week for one day in each month and then use that date to figure out any other day in the month. All that you have to know is that the following dates all fall on the same day of the week: last day of February, April 4 (4/4), 6/6, 8/8, 10/10 and 12/12. The associated day for this year is Saturday.
That the last day of February and 4/4 fall on the same day is a happy coincidence, but the matchup for the rest of the days depends on a regularity in the way months are numbered that has only one exception. If not for the exception, there would be no need to remember “30 days have September, April, June and November.” Take a look at a calendar and check the pattern for which months have 30 days and see if you can do some simple arithmetic to show why the indicated dates all fall on the same day of the week.
As a bonus, when I give the answer I will tell a legend which does a great job of explaining the exception in the month numbering, whose only fault is that it is completely untrue, but it does make for a great story.
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Does not look as if I am going to get any takers. This will be the first time. Well I thought it is a good technique for finding the day of the week for a given date, useful for those times when you do not have a computer or calendar handy.
The pattern for months with 30 days and months with 31 days is that they alternate, except for July and August, which both have 31 days. Even with this exception, it is still the case that for each even numbered month and the following month, one will have 30 days and the other will have 31 days. As an example, the number of days from 4/4 to 5/4 is 30, because April has 30 days. The number of days from 5/4 to 6/4 is 31, because May has 31 days. So the number of days from 4/4/ to 6/6 is 30 + 31 + 2 = 63, which is divisible by 7, and so fall on the same day of the week.
The story for the allocation of days for each month, which is apocryphal, is that even numbered months originally all had 30 days and odd numbered months 31 days, except for February, which only had 30 days in a leap year. Think of how easy this would make things. Even months would have 30 days, easy to remember because 30 is even and odd numbered months would all have 31 days.
July was named for Julius Caesar and August for Augustus Caesar (this is the only part of the story that is true). July had 31 days, but August only had 30. Augustus felt slighted and grabbed a day from February and added it to August and then rearranged the months after August so that they agian alternated between 30 and 31 days.
As to why the months are given the number of days they have, I would guess that it is no coincidence that February is the coldest month of the year and August the warmest. Someone decided that it was best to have more days in a summer month and fewer in a winter month.
thanks for making my brain hurt.
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