Reverse thinking is a technique very often used by Math teachers to help students verify their solutions. It is a way to prove that you have used the right technique to solve a mathematical problem.

This is a Math game

that is used to understand the processes involved in verification. It is also a great way to learn the effect that the four mathematical operations +, -, x, and / have on numbers. (You'll find other math games on the
Math game page.)

It demonstrates the predictable ways in which numbers behave and it is easy to get to the original number if you know the algorithm (the step-by-step process) and the final answer.

It can also be used to teach the process of finding the cost price if one knows, the selling price, the profit percentage / the discount percentage.

This is the technique that is used to play the game described on this page.

Let's play the game now.

1. Think of a number from 1-20 (you can use any range). This is just an example. Did you actually think of a number? You did not?! Well don't just read. Think of a number, only then will you comprehend the magic of this game.

2. Add 5 to it.

3. Multiply the sum by 11.

4. Subtract 20 from the product.

5. Divide the difference by 2

6. What did you end up with? Was it 78?

7. The number you thought of was 11.

Are you surprised? Don't be. The process is very simple.

Let's decipher how the reverse thinking game above worked.When your listener says the number that she finally ended up with apply your directions on that number in the reverse order. This is the technique of reverse thinking.

1. For instance if your friend ended up with the number 78, multiply 78 into two. (This is the reverse of direction 5)

2. You'll get 156. Now add 20 to 156. You'll get 176. (reverse of direction 4)

3. Divide 176 by 11 (reverse of direction 3). You'll get 16.

4. Subtract 5 from 16 (reverse of direction 2). You'll get 11, which is the number your friend started with.

In this way reverse thinking is used to identify the number that was thought of originally.

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