Math is not Magic

So, there are these guessing game websites where the computer guesses what number you have in your head. And, surprise, they always get it right.

It's because they cheat.

No, the internets don't have a direct line into your brain. Nor are they looking over your shoulder (that's the government's job, ha ha ha, just kidding, pay no attention to man behind the curtain).

Okay, here's one example: Re-gifting Robin.

Robin asks you to think of any two digit number (that's a fancy way of saying, "Pick any number between 10-99"). Then, from the number you're thinking of subtract the first digit (the tens) and then the second digit (the ones). Then they show you a grid of potential presents to regift (this is the trick, you've substituted answers here, this is important). Then once you get the gift in your head you click to have Robin "guess" your gift. And, low and behold, she gets it right. Every time.

Because she cheated. First is the basic mathmatics. Here is how the equation works: for values of X and Y from 1 to 9.
((10Y + X) - Y) - X = Z
(10Y + X) is your guessed two digit number, Z is your product from the subtraction.

Their example is guess = 25 so then you do the equation 25-2-5=18.

Then you find your gift on chart. This is where they stack the deck. Pay attention.

Notice a few things. One; the numbers go from 1-99, and the columns are 11 deep. This does two things. It confuses you (you're expecting columns of 10's) and gives you the impression there are more options than there really are.

See, no matter what two digit number you select, you can only obtain one of nine numbers: 9, 18, 27, 36, 45, 54, 63, 72, or 81. Why? Okay, let's look at the equation again.
((10Y + X) - Y) - X = Z

This can also be written:
(10Y - Y) + (X - X) = Z or Z = 9Y

That's the mathematics part: a selection between 10 and 99 will only result in 9 possible answers. Let's look at that chart again.


Guess what Robin's guess is going to be.

Now. They mix up the guesses every time, but all those numbers will be the same guess every time. They mix up the chart with all the other blocks being random to break up your pattern recognition skills. They use the 11 deep chart to break up the fix. (Why they did 90 I'll never know, my guess is they messed up the pattern because they knew the fix - you can't get an answer of 90 with this test)

Hope that helps you out. Now, if you'll excuse me, I've won this European email lottery and they want to know my bank routing numbers and I've got to get it to them soon so I can get my money.