## Number Tricks

You can try out some of these mind reading examples on your friends. And, if you can do a little simple algebra you can usually figure out why they work and then make up some of your own. Have fun!

1. Choose a number, any number.

Add three.

Multiply by two.

divide by two.

Subtract your original number.

Your result is? (Hint: It is the same no matter what number was chosen in the beginning.)

2. Use a similar procedure.

Choose a number.

Double it.

Add nine.

Add your original number.

Divide by three.

Add four.

Subtract your original number

Your result is? 7 maybe?

Let's figure out why the last problem works using some algebra.

Choose a number, let's call it N.

Double it, 2N.

Add nine, 2N + 9.

Add you original number, N + 2N + 9 = 3N + 9.

Divide by three, (3N + 9)/3 = N + 3.

Add four, N + 7.

Subtract your original number, N + 7 -N = 7 is your answer.

Try to extend your thinking. Will this idea work for fractions? How about decimals?

3. Now, make up a similar problem on your own. It should be pretty easy when you use a little algebra.

4. Lastly, choose a number.

Triple it.

Add the number 1 larger than your original number.

Add eleven.

Divide by four.

Subtract three.

The result is? Your original number. Why?

5. We can't quit yet. Pick a number and four more successive numbers to add to your original. For example 5, 6, 7, 8, and 9. Ask for that sum. You can recover the first number in the list by simply dividing the sum by 5. In the example list above, 5 + 6 + 7 + 8 + 9 = 35. Divide by 5 and you get 7, the number we chose. Why? Use some simple algebra to see what happens when you sum these numbers and divide by 5.

Isn't this fun?

6. How much money is in your pocket? Start with your change.

Multiply by 2.

Add three.

Multiply by 5.

Subtract 6.

Ask for the result.

What do you get? To read your friends' mind to figure out the amount of money in his/her pocket, all you have to do is drop the digit in the one's place. For example, if the answer is 359, then the amount of money to start with was 35 something -- maybe cents, maybe won, maybe baht, yen, or whatever you please.

Add three.

Multiply by two.

divide by two.

Subtract your original number.

Your result is? (Hint: It is the same no matter what number was chosen in the beginning.)

2. Use a similar procedure.

Choose a number.

Double it.

Add nine.

Add your original number.

Divide by three.

Add four.

Subtract your original number

Your result is? 7 maybe?

Let's figure out why the last problem works using some algebra.

Choose a number, let's call it N.

Double it, 2N.

Add nine, 2N + 9.

Add you original number, N + 2N + 9 = 3N + 9.

Divide by three, (3N + 9)/3 = N + 3.

Add four, N + 7.

Subtract your original number, N + 7 -N = 7 is your answer.

Try to extend your thinking. Will this idea work for fractions? How about decimals?

3. Now, make up a similar problem on your own. It should be pretty easy when you use a little algebra.

4. Lastly, choose a number.

Triple it.

Add the number 1 larger than your original number.

Add eleven.

Divide by four.

Subtract three.

The result is? Your original number. Why?

5. We can't quit yet. Pick a number and four more successive numbers to add to your original. For example 5, 6, 7, 8, and 9. Ask for that sum. You can recover the first number in the list by simply dividing the sum by 5. In the example list above, 5 + 6 + 7 + 8 + 9 = 35. Divide by 5 and you get 7, the number we chose. Why? Use some simple algebra to see what happens when you sum these numbers and divide by 5.

Isn't this fun?

6. How much money is in your pocket? Start with your change.

Multiply by 2.

Add three.

Multiply by 5.

Subtract 6.

Ask for the result.

What do you get? To read your friends' mind to figure out the amount of money in his/her pocket, all you have to do is drop the digit in the one's place. For example, if the answer is 359, then the amount of money to start with was 35 something -- maybe cents, maybe won, maybe baht, yen, or whatever you please.

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It's probably appropriate here to give you a little background on the invention and inventor of Algebra. The material below comes from a xeroxed copy of a booklet called The Mathematical Way of Thinking. Unfortunately, the author of the set of paragraphs below is unknown.

The Origins of Algebra

"The term 'algebra' derives from the Arabic al-jebr,which the mathematician Al-Khowarizmi adopted to explain his ideas for solving what we call equations. Later, the term acquired a wider meaning, and today it includes a broad range of mathematics.

Mohammed ibn Musa Al-Khowarizmi, an Arabian astronomer and mathematician (died about A.D. 850), was active in the "House of Wisdom' in Baghdad ... His arithmetic used the Indian system of notation. Although his original Arabic book on the system is lost, a Latin translation survives as Algorithmi: De numero indorum (about Indian numbers). The author explains the system so clearly that when the system spread through Europe it was assumed the Arabs were the inventors. ... Al-Khowarizmi's most important book, Al-jebr wa'l-muqabalah, literally the science of reducing and comparing, gave us the word "algebra'. ... Al-Khowarizmi's mathematical works contain all [most?]of the the solving procedures we learn in school." Our word 'algorithm' also dates to his work.

We now see again that the study of mathematics has been a global enterprise for a long time, with different people in different places and cultures borrowing from each other's knowledge and understanding in order to build even more impressive work. Isn't this great? In the short paragraph above we started in Iraq, via India, traveled to Europe 1250+ years ago, and now see the continuing study of Algebra all across the planet.

It's probably appropriate here to give you a little background on the invention and inventor of Algebra. The material below comes from a xeroxed copy of a booklet called The Mathematical Way of Thinking. Unfortunately, the author of the set of paragraphs below is unknown.

The Origins of Algebra

"The term 'algebra' derives from the Arabic al-jebr,which the mathematician Al-Khowarizmi adopted to explain his ideas for solving what we call equations. Later, the term acquired a wider meaning, and today it includes a broad range of mathematics.

Mohammed ibn Musa Al-Khowarizmi, an Arabian astronomer and mathematician (died about A.D. 850), was active in the "House of Wisdom' in Baghdad ... His arithmetic used the Indian system of notation. Although his original Arabic book on the system is lost, a Latin translation survives as Algorithmi: De numero indorum (about Indian numbers). The author explains the system so clearly that when the system spread through Europe it was assumed the Arabs were the inventors. ... Al-Khowarizmi's most important book, Al-jebr wa'l-muqabalah, literally the science of reducing and comparing, gave us the word "algebra'. ... Al-Khowarizmi's mathematical works contain all [most?]of the the solving procedures we learn in school." Our word 'algorithm' also dates to his work.

We now see again that the study of mathematics has been a global enterprise for a long time, with different people in different places and cultures borrowing from each other's knowledge and understanding in order to build even more impressive work. Isn't this great? In the short paragraph above we started in Iraq, via India, traveled to Europe 1250+ years ago, and now see the continuing study of Algebra all across the planet.