Expert: Paul Klarreich - 3/16/2006

Question
Hi Paul,
I'm sorry if i bother you. I've been away and didn't check the solution you sent to me for three days and that means i can no longer check it. Could you please help resend it.
Thank you for your time.

Answer
Hi, Pharell,

I received a similar question from 'Neil' yesterday. Here is a copy of his question and my reply:

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Neil wrote:
Calculating day of birth from date of birth
Question: Hello Paul,

I have always been interested in mathamatics and tend to take a mathamatical view on many things in life. Recently I have been presented with a challenge that I hope yo can help me with.

A friend of mine has an excellent memory for dates and events that occured on that date, but his party piece is the ability to tell you the day of the week that fell of any given date. This talent is all the more extraordinary because the answer comes back in less than 2 seconds (often under 1 second).

Now his memory and knowledge are without question, but I challanged him that because of its diversity this party piece could not be based upon memory, but on mathamatics. I believe that with the correct mathamatical approach and the use of a common algorithm, anyone with a basic mathamatical mind can do this in their head.

There lies my challenge (and now yours too!). Clearly, the 1st January falls on the same day every 7 years so the principle must be based on an extention of this concept.

Can you help ?

Best regards,

Neil.
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Answer: Hi, Neil,
I have heard of this trick, but unfortunately I know little about it.

Also, it is a little more complex than you think, because the first of January does not fall on the same day every 7 years. It would, if all years had the same number of days, which they do not. There is this nasty thing called leap year.

So if Jan 1 of year N falls on Sunday, the next time Jan 1 will be a Sunday won't be year N + 7, it will be year N + 5 or N + 6, depending on the number of Feb 29ths that intervene. For example,

If Jan 1, 1960 was a Sunday (I don't know that it was.) then there will be two 2/29 dates before Jan 1, 1965, which is another Sunday.

So try stumping him with these additional issues:

A. years ending in 00, like 1900, are NOT leap years, but years that are multiples of 400, like 2000, are. This is intended to correct for the inexact number of days in a revolution of the earth. This scheme will probably lead to some inaccuracy in the calendar about 20000 years from now. (So if worrying is part of your religion, you can start now.)

B. my grandfather was born in Russia in the late 1800s. But Russia was using a different calendar from the rest of Europe then, and changed later.