**Even Odd Magic Trick**

Step 1. Ask to someone to choose a **number** and then **triple** that number.

Step 2. Product may be **even** or **odd** .

- if product is
**odd**:

- if product is

Request him to add **unity** to it & take **half** of it.

b) if product is **even** :

Request him to take **half** of it.

Step 3. Tell him to **multiply** the result of the second step by **3**.

Step 4. Ask how many integral times **9** divides into the latter product third step : suppose the answer to be** n**.

Step 5. Then the number thought of was **2n** or **2n + 1** , depends on the **first step** was **even** or **odd**.

**Explanation** :

It is obvious , because **even** number is of the form **2n** . And applies these successive operation step-by-step—

Step 1. 2n x 3 = 6n ( even)

Step 2. 6n / 2 = 3n

Step 3. 3n x 3 = 9n

Step 4. 9n / 9 = n

Step 5. 2n

Every **odd** number is of the form **2n + 1** . And applies these successive operation step-by-step—

Step 1. (2n + 1 ) x 3 = 6n + 3 ( odd)

Step 2.(6n+3+1) / 2 = 3n + 2

Step 3. (3n + 2) x 3 = 9n + 6

Step 4. (9n + 6) / 9 = n + a ( remainder )

Step 5. 2n + 1.

These results are formulated from above method.

**Example** :

In this **puzzle or math magic** at least two parties are involved like **A** and **B**.

“A” is a** performer** in this **puzzle**.

“B” is a **listener** in this **puzzle**.

**A asked to B : **

choose any **number** and **triple** it.

B : OK done ! ( calculation in mind , let choose a number **5** , then 5 x3 = 15 )

A : This product may be **even** or** odd** .

a) if product is **odd** :

Request him to **add unity** to it & take **half** of it.

b) if product is **even** :

Request him to take **half** of it.

B : it is** odd** ( calculation in mind ; 15+1= 16 and 16/2 = 8).

A : Now **multiply** by **3** .

B : OK done ! ( calculation in mind 8×3 = 24 )

A : Now **divide** by **9**.

B: OK done ! ( calculation in mind 24 / 9 = 2(**quotient**) + 6(remainder)

A : Tell me **quotient**.

B :** 2**

A : **5** will be the number originally thought.( **2n + 1 )**

B : **surprised.**

**Readers** can also surprised your friends , using this **math magic trick** & try it.