Panther's Math Magic

This is a neat neat trick you can try, which uses some highschool math. It's not the easiest trick in the world, but it's very impressive. It's called finding the weekday by sevenths.

The Illusion

Have a friend pick a date, any day in the 20th century. For example, let's say they choose August 25, 1967. You are able to tell your friend almost immediately that it was a FRIDAY. How the hell did you know that? They will think you're a genius (or autistic, like in the movie Rainman).

How It's Done

First, you need to understand what a mod (modulo) is. It's basically the remainder when you divide. For example, 23 mod 7 is 2. (23 / 7 = 3 remainder 2). Also, 21 mod 7 is zero, because 7 divides into 21 with no remainder.

Take the year's last two digits (i.e. 67) and add this to the same number divided by 4 (always round down). Then, add the day. Now, you add a number for the month as follows:

Jan = 0, Feb = 3, Mar = 0, Apr = -1, May = 1, Jun = 4, Jul = -1, Aug = 2, Sep = -2, Oct = 0, Nov = 3, Dec =-2

So if you have been following along (using Aug 25, 1967), you should have this:

                           year + year/4 + day + monthcode

                            67  +   16   +  25 +    2      = 110

Here's where the modulo comes in. Now you take that final number, and do a MOD 7. For our example, 110 MOD 7 gets a final number of 5. Now you choose the day of the week from this list (this should be easy to remember):

Sun = 0, Mon = 1, Tue = 2, Wed = 3, Thr = 4, Fri = 5, Sat = 6

That is how we know August 25th, 1967 was a FRIDAY.

Special Consideration: If, when you divided by four, the number came out without a remainder (i.e. the year was 1924, 1980, etc) then it's a leap-year. If your friend picked January or February as the month, you need to remember to subtract 1 (or back up one day - if it's Wed, it becomes Tue).

This will work for any date from Jan 1, 1901 to December 31, 1999!

Tips

To do the trick fast, you will need to memorize the following list of numbers: 0 3 0 -1 1 4 -1 2 -2 0 3 -2. Or if your memory is really bad, write it down secretly, and peek when the other person is not looking.

To do the trick SUPER fast, you need to keep a total as the person is telling you the date. For example, if a person starts saying "November..." then right away I'm thinking "3+". Then if she says "17th..." I think "17+3=20". Then if she says "1921" I think "20+21+5=46 mod 7=4 = THURSDAY!!!" In other words Nov 17, 1921 was a Thursday.

If you are slow at doing modulo 7 on big numbers, just subtract 98 first! For example, I can tell you 102 MOD 7 = 4 really fast, because I just do 102 - 98 = 4 in my head!

Similarly, dividing by 4 is easy. I can tell you that 63 / 4 is 15, because I know 60 / 4 is 15.

Panther - [email protected]
Last Update: September 16, 1999