Think of a number, any positive integer (but keep it small so you can do computations in your head).
1. Square it.
2. Add the result to your original number.
3. Divide by your original number.
4. Add, oh, how about 17.
5. Subtract your original number.
6. Divide by 6.
The number you are thinking of now is 3!
How did I do this?
Presentation Suggestions:
Ham it up with magician’s patter. Step 4 could be anything you want—someone’s age, or their favorite number— just ask the crowd for suggestions. (This will change the final outcome of Step 6, but see below for how.)
The Math Behind the Fact:
Clearly no matter what you start with, the answer should come out the same (zero wasn’t allowed because of Step 3). We can see why this trick works by using a little bit of high school algebra! If you follow the instructions starting with the variable X instead of an actual number, you will see that X is eliminated by Step 5.
Using this idea, you can make up your own mental math trick right on the spot! (Just don’t do anything too obvious, like tell people to add 5, subtract their original number, and say “the number you are thinking of is 5”.)
You can see other Fun Facts on mathematical magic or check out the reference.
How to Cite this Page:
Su, Francis E., et al. “Mind-Reading Number Trick.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.
References:
A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.
Fun Fact suggested by:
Francis Su