A friend of mine sent me to a website that purports to be able to “read your mind” by guessing a product that you have in mind. It turns out that you can use algebra to debunk the premise of the site by finding out how the trick works.

First, check out the site here.

Now that you see how it works, here’s the algebra behind this “mind-reading” site.

Take any two-digit number.

Call the tens digit x; call the ones digit y.

Then the value of the two-digit number is 10x + y

As an example, take the number 73.

This is 10 x 7 + 3 = 70 + 3 = 73

See what I mean?

Then, if you subtract the individual digits from the

two digit number, that would be the same as writing down:

– x – y.

Putting the two expressions together, you get:

(10x + y) – x – y

Simplify that, as follows:

(10x + y) – x – y

= 10x + y – x – y

= 10x – x + y – y

= 9x

Now since x was a whole number to start with, the value of 9x must be a multiple of 9, such as 18, 27, 36, etc.

Now check it out. Do this process with a variety of two-digit #s

and you’ll see that the answer is always a multiple

of 9.

Now here’s the “kicker”: Look at the grid, and you’ll see that every time you see the grid, all products labeled with a multiple of 9 display the same product.

So that’s how this program “knows” your product.

They know it’s a multiple of 9, and they set up all

of those to have the same product.

Sneaky, and it works to trick lots of people. But not you, any more, since you have the power of algebra on your side.

Here’s a less ambitious implementation that is also followed by an explanation: http://www.cut-the-knot.org/Curriculum/Magic/MindReaderNine.shtml.