zSnout

Make People Think of Numbers

Force people to think of certain numbers with math tricks.

Did you know that using math we can force people to think of certain numbers? We can use 9, 1089, or any other number you can think of using the simple tricks described below.

The First Trick

The first trick you’ll learn can work for any set of two numbers, making it more versatile than using 9 or 1089. It’s also really simple to pull off.

Preparation

  1. Let aa be an integer ranging from 2 to 6. In examples, we’ll use 3.
  2. Let bb be an integer ranging from 3 to 5. In examples, we’ll use 4.
  3. Let cc be a×ba \times b. In examples, we’ll use 12.

The Trick

  1. Ask each person in the audience to select a number between 1 and 100. Make sure they don’t tell it to you. In examples, we’ll use 7.
  2. Ask the audience to multiply their numbers by aa. We chose 7, so we now have 7×3=217 \times 3 = 21.
  3. Ask them to add cc to their number. We used c=12c = 12, so we now have 21+12=3321 + 12 = 33.
  4. Ask them to divide their number by aa. For us, a=3a = 3, so we now have 33÷3=1133 \div 3 = 11.
  5. Ask each person to subtract their original number. We had 77, so we now have 117=411-7 = 4.
  6. Announce that you already knew their number! Say it was bb, which all the numbers will now be.

The Explanation

We’ll track a number nn as it progresses through the process, them simplify the final answer.

  1. Let nn be an integer.
  2. We multiply n×an \times a.
  3. We add n×a+cn \times a + c.
  4. We divide n×a+ca\frac{n \times a + c}{a}.
  5. We subtract n×a+can\frac{n \times a + c}{a} - n.

To simplify, we can remember that c=a×bc = a \times b. Let’s substitute it to get n×a+b×aan\frac{n \times a + b \times a}{a} - n.

We can factor out aa to get a(n+b)an\frac{a(n + b)}{a} - n.

Because a/a=1a/a = 1, we can simplify to n+bnn + b - n.

Now we can finally simplify to bb, our final result!

Forcing 9

This method forces the number 9 on the audience.

  1. Ask each person to think of a six-digit number. For our example, we’ll use 173924.
  2. Ask each person to shuffle the digits in their number randomly, and to remember the result. (329471)
  3. Ask each person to take the difference between their larger number and their smaller one. (329471 - 173924 = 155547)
  4. Ask each person to add the digits in their number together, and to keep doing that until they have a one-digit number. (1+5+5+5+4+7 = 27, 2+7 = 9)
  5. Each member of the audience now has 9.

Forcing 1089

This method forces the number 1089 on the audience.

  1. Ask each person to think of a non-symmetrical three-digit number where the digits are decreasing. We’ll use 932932 as an example.
  2. Ask each person to reverse the digits in their number. We got 239239.
  3. Ask each person to subtract their smaller number from the larger. We’ve got 693693.
  4. Ask each person to reverse the new number. In our example, we have 396396.
  5. Ask each person to add the two numbers together. We have 693+396=1089693 + 396 = 1089.
  6. Every person should now have 1089, which we do!