Birthdate Puzzle

Date: 01/11/98 at 23:49:01
From: Anonymous
Subject: Birthdate problem

Hi, and thank you for your help.

I have the following to do:

  1. write the number of the month in which you were born
  2. multiply by 4
  3. add 13
  4. multiply by 25
  5. subtract 200
  6. add the day of the month you were born
  7. multiply by 2
  8. subtract 40
  9. multiply by 50
 10. add the last two digits of the year you were born
 11. subtract 10,500

It works, but the teacher wants to know why.

My parents and I have worked on this for 2 hours now and we have come 
up with the following partial stuff:

  multipliers - 2x25x2x50 - 10,000 - that's part of the subtraction 
     of 10,500

  4 x 25 - throws previous steps into the 100 spot

  2 x 50 - moves it over again to the thousand spot

The other things we have looked at don't seem to make any math sense: 
all the additions, +13 -200 -40 etc., don't mean much because there 
are the multipliers, etc. We have taken the 3 {the 4 times minus the 
one for the month} from step 1 and continued from there but we came up 
with 20,500, which didn't hit a nerve either.

Can you help? (written by mother)

Sheri

Date: 01/14/98 at 11:50:11
From: Doctor Bill
Subject: Re: Birthdate problem

Sheri,

If you take each step of your problem and write it mathematically you 
get the following, where each number is a 2-digit number (the leading 
digit might be zero):

   50(2{[25(4mm + 13) - 200] + dd} - 40) + yy - 10,500

Notice that the month (mm) gets multiplied by 4*25*2*50 = 10,000.  
This moves the month number over 4 places, Thus it will be the month 
number followed by 4 zeros, i.e. mm0000.  

The day (dd) gets multipled by 2*50 = 100. This moves the day number 
over 2 places and it will then be the day number followed by 2 zeros, 
i.e. dd00. 

The year (yy) isn't multiplied by anything. 

Now when you add these three numbers together you get something 
that looks like this:

    mm0000
    + dd00
    +   yy
   --------
    mmddyy

The other numbers that are added and subtracted are just thrown in to 
confuse you. Notice that after they have been multiplied, all of the 
adding and subracting numbers add up to 10,500, which is then 
subtracted at the end. The numbers in steps 3, 5, and 8 can be any 
numbers, and then the last number in step 11 will be a number that you 
will add or subtract from that total to give zero.

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