## HOW TO SOLVE HARD AND IMPOSSIBLE PUZZLES PART 2

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Hello Friends ! Welcome Today we are going to discuss some of the puzzles, challenges or brain teaser which are viral in social media such as Face book ,whats app, twitter and Google+ etc. which are based on Mathematics directly or indirectly . You have seen such types of puzzles mentioned 99.9% Fail , Solve if you are genius like this........

Let us try to discuss and solve them.

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PUZZLE # 1

Which number should replace the ?

Hello Friends ! Welcome Today we are going to discuss some of the puzzles, challenges or brain teaser which are viral in social media such as Face book ,whats app, twitter and Google+ etc. which are based on Mathematics directly or indirectly . You have seen such types of puzzles mentioned 99.9% Fail , Solve if you are genius like this........

## PUZZLE # 1

Which number should replace the ?
4 , 9 , 19 , 39 , 79 ?

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when we subtract 4 from 9 we get 5 i.e 9 - 4 = 5
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when we subtract 9 from 19 we get 10 i.e 19 - 9 = 10

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when we subtract 19 from 39 we get 20 i.e. 39 - 19 = 20

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when we subtract 39 from 79 we get 40 i.e. 79 - 39 = 40

Now analyse the trends of answers ,we are getting double of the previous number as a result every time . Similarly if we follow the same trend from 79 to next term ,then we shall get 80 as answer. So to get 80 as answer "Add 80 to 79 to get 159 ". when we subtract 79 from 159 ,we get the double of the previous result .

So final answer is 159 - 79 = 80.

4 , 9 , 19 , 39 , 79 , 159

Therefore " ? " will replace 159 as Answer.

Now analyse the trends of answers ,we are getting double of the previous number as a result every time . Similarly if we follow the same trend from 79 to next term ,then we shall get 80 as answer. So to get 80 as answer "Add 80 to 79 to get 159 ". when we subtract 79 from 159 ,we get the double of the previous result .

4 , 9 , 19 , 39 , 79 , 159

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PUZZLE # 2

But before we proceed to discuss the Puzzle-1, let us discuss some of the necessary keywords/definitions which have been used in it.

But before we proceed to discuss the Puzzle-1, let us discuss some of the necessary keywords/definitions which have been used in it.

## Even Number

When any Number is divisible by 2 then that number is called An Even number . If we take 2,16,84,22,20,100 etc then they are Even Numbers as they can be divided by 2.

Let us learn Multiplication , division , arithmatic and simplification short cut ,tips and tricks after buying this Book of Magical Mathematics .

Let us learn Multiplication , division , arithmatic and simplification short cut ,tips and tricks after buying this Book of Magical Mathematics .

## Odd Number

When any number is

**NOT**divisible by 2 then that number is called An ODD number .If we take 21,15,49,21,57,101 etc then they are Odd Numbers as they can NOT be divided by 2.## A Multiple of 3

An number which is divisible by 3 or which comes in the table of 3 is called multiple of 3. if we take 57,102,69,9,6,21,39 etc numbers , as these numbers comes in the table of 3 or these are divisible by 3 , so they are Multiple of 3.

## Prime Number

Any number which has only two Factors 1 and the numbers itself is called Prime number. 1 is not the the prime number,

**2 ( It is the 1st prime number )**, 3,5,7,11,13,17,19,23 etc are examples of Prime numbers as these numbers have only two factors 1 and the number itself.## Square Number

Any number whose square root is a Natural number is called square Number . such as 1,4,9,16,25,36,49,64,81,100,121,144 etc.

## Factors of 360

All those numbers which can divide 360 are called factors of 360 .Here We can take such numbers as 1,2,3,4,5,6,8,9,10,12,18,36 etc

## How to Solve

## Have you still not visited "HOW TO SOLVE HARD AND IMPOSSIBLE PUZZLES PART 1"

## PUZZLE # 3

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When we multiply 2 with 4, we get 8

When we multiply 3 with 6, we get 18

When we multiply 4 with 8, we get 32

When we multiply 5 with 10, we get 50

When we multiply 6 with 12, we get 72

When we multiply 7 with 14, we get 98

When we multiply 8 with 16, we get 128

When we multiply 9 with 18, we get 162

When we multiply 10 with 20, we get 200

When we multiply 3 with 6, we get 18

When we multiply 4 with 8, we get 32

When we multiply 5 with 10, we get 50

When we multiply 6 with 12, we get 72

When we multiply 7 with 14, we get 98

When we multiply 8 with 16, we get 128

When we multiply 9 with 18, we get 162

When we multiply 10 with 20, we get 200

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Analyse the Answers above , we get 4,6,8,10,12,14,16,18 and 20 . Is there any relation between them. Of course , Because every answer is 2 more than the previous Answer. So Last number should be 200. so in order to get answer 200 we have to multiply 20 with 10.

So If 2 = 8
3 = 18
4 = 32
5 = 50

6 = 72

7 = 84

8 = 128

9 = 172

10 = 200

Then 10 = 200

In order to get any number any of any term based upon this trends we can use the formula 2n^2 , where "n " is the number appearing on left side of the Puzzle.

So If 2 = 8

6 = 72

7 = 84

8 = 128

9 = 172

10 = 200

## So Final Answer will be 200

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There are two numbers 'a' and 'b' in 1st and 2nd columns then 3rd column has been occupied by their combination as follows

a*b = (

*+**a*^{2}*- 1,**b*^{2})
1*3 = (

*+**1*^{2}*- 1 = ( 1 + 9) -1 = 10 - 1 = 9**3*^{2})
3*4 = (

*+**3*^{2}*- 1 = ( 9 + 16) -1 = 25 - 1 = 24**4*^{2})
2*5 = (

*+**2*^{2}*- 1 = ( 4 + 25) -1 = 29 - 1 = 28**5*^{2})
4*5 = (

*+ 5**4*^{2}*- 1 = (16 + 25) -1 = 41 - 1 = 40*^{2})

**So 40 will replace ? in this puzzle**

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