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Math Puzzle: Day of the Week

Date: 02/04/98 at 10:18:24
From: Griffin, William
Subject: Why does the following math problem work

Dr. Math,

My question is, why does the following math problem work, irrespective 
of what number you use 0 - 7 for the day of the week?

Here is the question;

1. First of all, pick the number of days a week that you would like to 
   go out.

2. Multiply this number by 2.

3. Add 5.

4. Multiply it by 50.

5. If  you  have  already had your birthday this year, add 1748. 
   If you haven't, add 1747.

6. Last step: Subtract the four-digit year that you were born.


You  should  now  have a three-digit number:

The first digit of this was your original number (i.e. how many times
you want to go out each week).

The second two digits are your age! It really works.

This is the only year that this problem will work.

Again thanking you in advance.


Date: 02/04/98 at 16:24:12
From: Doctor Sam
Subject: Re: Why does the following math problem work

This is a number trick that seems magical when you do it with numbers
but is not too hard to understand if you use a little algebra.   

1. Start by calling the number you pick N.

2. Your first step is to multiply by 2. This gives 2N

3. Now add 5. In algebra notation this gives 2N + 5

4. Multiply by 50. This gives 50(2N+5) which can be simplified to

   100N + 250     

5. Now add either 1748 or 1747.   This gives:

   100N + 250 + 1748  or  100N + 250 + 1747   which simplify to

   100N + 1998  (had birthday)  or  100N + 1997  (no birthday yet)

6. Subtract your birth year. If you have had your birthday, then if
   you subtract your birthyear from 1998 (this year) you will get
   your present age (try it!)

   If you haven't had your birthday yet, then 1997 was the last year
   you had a birthday.  Subtract your birthyear from 1997 and you
   will again get your age. 

   In both cases, the algebra shows that you are left with 
   100N + your age.

So, for example, if you had started with 7 and you are 23 then you
now have 723.

Since you are multiplying N (your chosen number) by 100, this shifts
the number to the left and adds two zeros to the number. These two
zeros "make room for" your age, which will fit nicely iinto the last 
two spaces of your number.

By the way, the algebra shows that you do not have to restrict 
yourself to the numbers 1 through 7. ANY whole number should work
because 100N will still end up looking like a number ending in "00". 
Of course, it will only be a three digit number if you choose 
N = 1, 2, 3, 4, 5, 6, 7, 8, or 9.

I hope that helps.

Date: 02/04/98 at 16:40:16
From: Griffin, William
Subject: RE: Why does the following math problem work

Stupendous, Dr. Math.  You are right, when you look at the problem
algebraically it does make sense.  Thank you so much.

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