# 3. Math Magic Trick ### Math Magic trick

Request the person who has thought about the number to perform the following tasks and understand this math magic trick.

Step 1. Multiply it by any number, eg, say (a ).

Step 2. Divide the product by any number, eg, say b.

Step 3. Multiply in quotient by c.

Step 4. Divide this result by d.

Step 5. Divide the  result by the number selected at first time.

Step 6. Add to the result of operation in step 5 the number thought of at first.

Step 7. Ask to be told the result of the last step : then , if ac/bd is subtracted from the this result , the remainder will be the number chosen originally.

let For , if n was the number selected , the result of the first four operations is to form n(ac/bd) ; operation in step 5 gives ac/bd; and step 6  gives n + (ac/bd) .

Explanation

Suppose the selected number is n . Then applies these successive operation

Step 1 . na .

Step 2.  n(a/b)

Step 3.  n(ac/b)

Step 4.  n(ac/bd)

Step 5.  n(ac/bd)/n = ( ac/bd)

Step 6. ( ac/bd) + n

Step 7. Ask for the sum .

For you subtracted (ac/bd) from sum

Let  k = sum – ( ac/bd)

the k will be the number chosen originally.

Example :

In this puzzle at least two parties are involved like

A and B.

A” is a performer of this puzzle.

B” is a listener of this puzzle.

A asked to B :  You can Choose any number in your mind.

B : OK done ! (  I thought 7  in mind)

A : Multiply by the number a ( =5  depends on you)

B : OK done ! (  calculation in mind 7 x 5 = 35 )

A : Divide by the number b ( =6  depends on you )

B : OK done ! (  calculation in mind 7 x 5 / 6 = 35/6 )

A : Multiply by the number c ( =8  depends on you)

B : OK done ! (  calculation in mind  35 x 8 / 6 )

A : Divide by the number d ( = 4  depends on you )

B : OK done ! (  calculation in mind  35 x 8 / 6×4 = 70/6 )

A : Divide by the number selected at first time.

B : OK done ! (  calculation in mind  70/6×7 = 10/6)

A : Now  add the number selected at first time.

B : OK done ! (  calculation in mind  7 + 10/6)

A : Ask for the sum at this step.

B :  52/6.

For you subtracted (5×8/6×4 = 10/6) from sum

Let  k = 52/6 – 10/6

=  42/6 = 7

the 7 will be the number chosen originally.

This is recreational mathematics magic trick , because number of successive operation hide original thought . So , it’s feel look like a magic trick. By the way enjoy this math trick with your friends or with family members.

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