### 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(a**c**/b)

Step 4. n(ac/b**d**)

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**.