The best “number tricks” are probably deserving of a better name: “Mental Magic” or “Mathematical Deception.” Then again, number tricks does justice to the underlying simplicity of the best and most fun mathematical illusions.
Below are several number ruses, ranging from borderline practical to “psychic” mind reading. All these tricks require is the ability to perform simple addition, subtraction, multiplication, and division (if you need a calculator, it’s not exactly a trick, is it?). With just seconds of practice, you can start impressing anyone willing to listen.
Use this class on the secrets of mental math for a deeper understanding of how spontaneous math works.
3’s A Charm
This is commonly referred to as the “Any Number Trick” or the “3 Trick” because you can start with any number, follow a short series of instructions, and the result will always be 3. Of course, presumably you will be asking a friend to do all of this. Let’s look at the instructions first:
- Choose any number.
- Double it.
- Add 9.
- Subtract 3.
- Divide by 2.
- Subtract your original number.
That’s it, and the answer will always be 3. Here’s a quick example if we start with the number 7:
7 * 2 = 14
14 + 9 = 23
23 – 3 = 20
20 / 2 = 10
10 – 7 = 3
It’s usually a good idea to make sure that whoever is choosing the number doesn’t pick a decimal or ridiculously huge number.
Mind Reading #1
This is an awesome mind reading trick that can be easily adjusted so that you don’t get the same answer every time, which makes it far more convincing and difficult to figure out. You can trick kids all day with this one. For best effects, you’ll want to put on a good acting show of reading little Timmy’s mind.
- Pick a number, any number . . . (although if you are playing with kids, it might be easier for them if you limit the number range to 1-10).
- Multiply by 2.
- Add 10.
- Divide the number by 2.
- Subtract the original number from (not by) the current number.
And the answer is? Well, in this case the answer will be 5. But it won’t always be, and you can easily control the outcome. First, let’s look at how this plays out, assuming we start with the number 9:
9 * 2 = 18
18 + 10 = 28
28 / 2 = 14
14 – 9 = 5
As promised, the answer is 5. If you follow the above instructions to a “T”, you will always get 5; if you don’t, then someone is doing the math wrong. You can encourage adults to pick higher numbers. For example, the number 52:
52 * 2 = 104 ; 104 +10 = 114 ; 114 / 2 = 57 ; 57 – 52 = 5
Ok, so you’re probably wondering how we’re going to alter the equation for different results. The key is in the third step where we currently “Add 10.” If you haven’t spotted the trick yet, I’ll spell it out: half of 10 is 5. It’s that easy. You can replace 10 with any number, and the answer will always be half of that number, even if it’s an odd number and returns a decimal. Just to prove my point, let’s replace 10 with 43. The number we’ll start out with will be 15:
15 * 2 = 30 ; 30 + 43 = 73 ; 73 / 2 = 36.5 ; 36.5 – 15 = 21.5
And of course, 21.5 * 2 = 43, which is the number that replaced 10. It’s easy to see why this trick is a personal favorite. If you want to increase your speed and precision with these tricks, this foundations of algebra course is guaranteed to help (and help you get better grades in school, too).
Mind Reading #2
This trick is even simpler than Mind Reading #1, but the answer is invariable. Still, because the trick relies on a personal detail (the year someone was born), it tends to perk interests. Here are the two easy steps:
- Begin with the last two digits of the year you were born.
- Add this number to the age you will be at the end of the year.
The answer should be 114. The exception would be the increasing number of people born after the year 2000. This trick is really only good for those who were born in the 20th century. If you give it some thought, you can figure out how the trick works. In it’s most basic explanation, the older someone is, the smaller the number will be that is made by taking the last two digits of the year he or she is born (for example, someone born 1950 has a lower number than someone born in 1960). But this difference is offset by their age difference. The person born in 1950 is ten years older, so they break exactly even with the person born in 1960.
Please note that will every changing year, the answer changes. In 2015, the answer will be 115, and so on.
This is my last mind reading trick, but if you like this style of illusion, read this article on mind reading tricks that will amaze and delight. It even tells you how to sell your tricks.
Powers Of 5
Multiplying by powers of 5 has always been considered relatively easy, but the larger the numbers get, the less comfortable we feel handling them. What’s 72 * 5? Exactly. It gets tough. If you’re using this post to help you prepare for an interview, do yourself a favor and get the real deal with this fast-math case interview preparation course.
The trick is to realize that you can go forward and backward on the powers of 5 scale to make the equation simpler. Let’s take our example: 72 * 5. Obviously, “5” is our power of 5. The next closest power of 5 is 10 (so 5 = 10 / 2).
Instead of trying to piece together 72 fives, let’s just multiple 72 by 10. That’s easy: 720. Now just divide by 2 for the answer: 360.
72 * 5 = 360
That’s helpful if you’re multiplying by 5, but what if your power of five is, say, 25? In other words, how do we find out what 25 * 64 is equal to? The general idea, with any multiple of 5, is to recognize that by simple multiplication or division you can arrive at a wieldy multiple of ten. In this case, we will go all the way up to 100 (but 50 would be a good number, as well, if your mental math skills are strong).
We know that 25 = 100 / 4. So if we multiply 64 by 100 we get 6400. Now we can get to the bottom of this quickly by dividing by 4:
6400 / 4 = 1600
The Practical Side
You could argue that some of these tricks are at least marginally practical, but for the most part they exist for show. If you want to learn some tricks you can use in every-day life, such as calculating tips and dealing with decimals, check out this post on mental math tricks and learn how to put those, and others, to use with this course on the applications of finite math.