Calendar Trick

Date: 12/04/96 at 20:45:40
From: Jerry Simms
Subject: Addition tricks and calendar trick

I've searched the net to no avail!  I have always been mathematically
oriented, but now I'm stuck on something that no one yet has been able 
to explain to me:

What formula would allow you to determine the day of the week on which 
someone was born?  For instance, if I asked "what day of the week was 
July 8, 1954,"  what formula would you use to answer the question 
(possibly in your head) without looking at a calendar?   A man on TV 
was able to tell the day of the week for a date/year that someone else 
picked.  The year was 1822 and he still answered correctly within 
about 4 seconds!

Your help is much appreciated.  I'm going crazy considering 
possibilities.  The concept is quite amazing when you see someone put 
it into use.

Thanks!

Jerry

Date: 12/11/96 at 21:16:20
From: Doctor Rob
Subject: Re: Addition tricks and calendar trick

From the FAQ (Frequently Asked Questions) file for the Usenet 
newsgroup sci.math:

Here is a standard method suitable for mental computation:

(1) Take the last two digits of the year.
(2) Divide by 4, discarding any fraction.
(3) Add the day of the month.
(4) Add the month's key value: JFM AMJ JAS OND: 144 025 036 146
(5) Subtract 1 for January or February of a leap year.
(6) For a Gregorian date, add 0 for 1900's, 6 for 2000's, 
    4 for 1700's, 2 for 1800's; for other years, add or subtract 
    multiples of 400.
(7) For a Julian date, add 1 for 1700's, and 1 for every additional 
    century you go back.
(8) Add the last two digits of the year.
(9) Divide by 7 and take the remainder.

Now 1 is Sunday, the first day of the week, 2 is Monday, and so on.

Comments by me:

(a) You would have to memorize the key values of Step 4.
(b) You would have to memorize the century values of Step 6 or 7.
(c) A remainder of 0 would give you Saturday at the end.
(d) You could cast out 7's as you go along if you wish, to keep the
    number small, and then step 9 is redundant.
(e) You can do steps (1 and 2), 3, 4, 5, and 6 in any order.      
    As soon as someone starts to tell you the date "July ..." 
    you can do step 4, and probably reject doing step 5; 
    then when he says "... 8th..." you can do step 3. When he says 
    "... 19 ..." you can do step 6.  This makes it seem as though you 
    have done all the calculation after hearing the date, whereas you 
    have done some of it *while* hearing it.

The example of July 8, 1954, would go like this:

   (1) 54
   (2) 54/4 = 13
   (3) 13 + 8 = 21
   (4) 21 + 0 = 21
   (5) 21 - 0 = 21
   (6) 21 + 0 = 21
   (8) 21 + 54 = 75
   (9) 75 - 7*10 = 5 <--> Thursday.

Casting out 7's would give:

   (1) 54
   (2) 6
   (3) 0
   (4) 0
   (5) 0
   (6) 0
   (7) 5 <--> Thursday

The reasons why this works are fun to figure out.  You might like to
try it.  If we can be of further assistance, let us know.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/