A Very Old Math Trick !!

Here is a math trick you might enjoy. It comes from a math book that was published in 1760!

Follow the steps and see if you are amazed. Then try to figure out how it was done.

If you have a theory, explain it to me. You might be right! If you are correct, I will award a "valuable prize" to you.
 

Note: To perform this trick you must know the difference between even and odd numbers.

Step 1

Write an odd number on a slip of paper. Set the slip of paper on the left or right side of your desk.

Next step
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Step 2

Write an even number on a second slip of paper. Set the slip of paper on the other (left or right) side of your desk.

Remember which side of your desk each number is on. I will guess their locations!

Next step
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Step 3

Multiply the number on the left side of your desk by 2. Multiply the other number by 3.

Now add the two products.

Next step
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Step 4

Now look at the sum of the two products. Tell me if the sum is even or odd.

                       Click for even.         Click for odd.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Step 5

It is even.

That means the slip of paper on which you wrote the even number was originally set on the right side of the desk.

Are you amazed?

Do you have an idea about why this trick works?
 
 

Step 5

It is odd.

That means the slip of paper on which you wrote the odd number was originally set on the right side of the desk.

Are you amazed?

Do you have an idea about why this trick works?