Additional Math Pages & Resources

Wednesday, November 11, 2009

Happy Birthday, I guess

Happy Birthday!

Did you ever wonder about birthdays? I think about things like this:
  • Are people born on all days of the year? 
  • Or is there a day when it never happens?  
  • Are equal numbers of people born every day of the year?
How could we find out?

One way is to ask. That should be reliable, but there is some chance that a few people do not know their exact birthday, and that others might lie. But who could ask enough people, and expect to get an honest answer?
  1. Certain agencies of the government could ask (military, census, DMV, IRS, passport, etc.)
  2. Some companies, such as life insurance, could ask.
This guy who works for an insurance company analyzed over 400,000 birthday records.

Days of the Year

He found that people ARE born every day, there is NO day when women stop having babies, and NOT all days have an even number of births.

Days in the Week
There are two days of the week with fewer births - that's right, Saturday and Sunday. This is probably due to doctors taking those days off and not scheduling Cesarean-section births on those days. C-Sections are about 15% of the total births nowadays.

Months of the Year

In the United States, some months (July, August, September) have more births, and some have fewer (February, April) than expected. This is usually explained by the fact that people have more time on their hands during the winter months and are more likely to be conceiving children than during the summer months.


There are some famous birthday questions, such as how many people have to come into a room before two of them have the same birthday. If that sort of thing is interesting, here are some equations that attempt to simulate the problem. Let me know if you come to a conclusion!

I think this is beyond even my math skills. But the answer is around 23.

Here are some more of my birthday questions:
  • Why should we even care about our birthdays and have parties for ourselves? 
  • Why have parties for young children who don't know they are one year old?
  • Do you have to invite the whole class if you invite anyone from your class?

Happy Birthday from Scrooge 
 I'm perfectly happy with a bar or bat mitzvah, or a QuinceaƱera, or other rites of passage. It's this annual business that bugs me.

Here's a Happy Birthday present for you:

It says 22 people might be enough to have 2 with the same birthday, but 23 definitely works.

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