## HOW TO SOLVE HARD AND IMPOSSIBLE PUZZLES PART 3

Welcome once again . Let us discuss some of the puzzles, 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 also have seen such types of problems mentioned 99.9% Fail , Solve if you are genius like this...

## TODAY'S PUZZLE FOR YOU

Let us try to discuss and solve some of the Puzzles given below one by one.

##

PUZZLE #1

##

Look at 1st Row, there is no direct connection between 9, S and 10. Also it seems no connection between 4,5,M,,1,3 in 2nd row ,Similarly 3,1,1,L,2,?,1 have no direct connection between them.

But if we recall English Alphabet A,B,C,D,E,F,.. ..Y,Z and check that which letter is at 9th and 10th position, we shall find that this is not "S" .But let us check what is the position of Letter "S" in English alphabet. We find that it is in 19th position, as 9+10= 19 , It means that "S" is equal to 19.
So now check the position of letter "M" , which is 13th , and the sum of all the digits in 2nd Row is 4+5+1+3 = 13, Similarly we can check that 1+2+4+5=12, 12th is the position of letter "L" and 3+2=5 ,5th is the position of letter E.

##

##
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So by this trend we can add all the digits in 3rd row and put its total equal to 8, as position of the letter "I" is 9th in English Alphabet. The difference between the position of the letter "I" and total of all the digits in same time must be equal to each other.

##

So let us try new pattern right from the 1st line. If we square the 1st number and then subtract the 2nd number from it, Let us check it from 1st line .

So following the same pattern we can calculate answer

for the line containing 6 - 1 like this

###

So we have to multiply with 2 on left side of our question to get left

digit and multiply 5 with 2 to get 10 on right side of the answer.

Hence Our answer will for 45= (2×4)(2×5) = 810

The Formula for this Puzzle is ab = (2a)(2b)

If we multiply the 1st number with 2 and add both the

**Therefore 1(one) is the digit to be occupied by ?**##
**
****PUZZLE 2**

**PUZZLE 2**

In this Puzzle we have five circles in all ,and some of them are overlapping each others , Look at 1st line 15,12,24 ,It seems no relation between these numbers.But if we add all the numbers lying in any circles , then from 1st circle of 1st line we shall have 15 + 10 = 25 and from 3rd circle of 1st line we shall have 24 + 1 = 25 .

Similarly from 2nd circle of 2nd line we shall have 4 + 1 + 20 = 25.

It means total of all the numbers lying in any circle must be 25 . So

from 2nd circle of 1st line we shall have 12+? + 4= 25 implies that ? must be 9 and when we consider 1st circle of 2nd line we shall have 10 + 6 + ? = 25 this also implies that ? must take the value 9.

**So our Answer will be 9**

## PUZZLE # 3

Look at 1st line if we subtract 1 from 1 ,we get 0 , we get our 1st line's answer . Same pattern should be followed in the next and remaining lines. But when we subtract 1 from 2 in 2nd line we get 1,which is not our answer.

So let us try new pattern right from the 1st line. If we square the 1st number and then subtract the 2nd number from it, Let us check it from 1st line .

*1*^{2}- 1 = 1 , It is working for 1st line*2*^{2}- 1 = 3,*It is working for 2nd line**3*^{2 }- 1 = 8,*It is working for 3rd line**4*^{2}- 1 = 15,*It is working for 1st line**5*^{2}- 1 = 24,So following the same pattern we can calculate answer

for the line containing 6 - 1 like this

*- 1 = 35**6*^{2}###
*So our answer is 35.*

*So our answer is 35.*

The formula for this puzzle is x-1 =The formula for this puzzle is x-1 =

*x*^{2}**- 1 ,**

where x is the 1st numberwhere x is the 1st number

**PUZZLE # 4**

From the 1st line it can be seen that 21 × 2 = 42, But 39 × 3 ≠ 618 .

so if we multiply 1st digit of left side with 2 then we shall have 4,6,2 as our digit/digits in left side of answers and when we multiply 2nd digit with 2 , we shall have 2,18,14 as right side of answer .

So we have to multiply with 2 on left side of our question to get left

digit and multiply 5 with 2 to get 10 on right side of the answer.

Hence Our answer will for 45= (2×4)(2×5) = 810

The Formula for this Puzzle is ab = (2a)(2b)

## PUZZLE # 5

If we add all the digits , we can not get the answer .we have to try something new . But if we square the 1st number and add both remaining numbers to it ,the we can get result of 1st line like this 2 + 3 + 4 =

Let us check the same pattern for 2nd line 3 + 4 + 5 =

Now we have to try one more formula for this puzzle . *2*^{2}+3 + 4 = 11.Let us check the same pattern for 2nd line 3 + 4 + 5 =

*+ 4 + 5 = 18, but 18 is not the answer . It means this will not work here.**3*^{2}If we multiply the 1st number with 2 and add both the

remaining numbers to it.

###
*Let us check all the line respectively.*

*1st line is 2×2 + 3 + 4 = 11, which *
*is **right answer.*

*2nd line is 2×3 + 4 + 5 = 15, which *
*is** right answer.*

*3rd line is 2×4 + 5 + 6 = 19, which *
*is **right answer.*

*So let us follow this pattern to find *
*the **answer of the **given puzzle** **as*
*follows*

*4th line is (2×7) + 8 + 9 = 31, which is*
* right answer.*
*
*

*Let us check all the line respectively.*

*1st line is 2×2 + 3 + 4 = 11, which*

*is*

*right answer.*

*2nd line is 2×3 + 4 + 5 = 15, which*

*is*

*right answer.*

*3rd line is 2×4 + 5 + 6 = 19, which*

*is*

*right answer.*

*So let us follow this pattern to find*

*the*

*answer of the*

*given puzzle*

*as*

*follows*

*4th line is (2×7) + 8 + 9 = 31, which is*

*right answer.*

###
**So formula we can use for this puzzle a+b+c = 2a+b+c**

## PUZZLE # 6

To solve this puzzle , multiply 1st two digits with each other to get 1st two digits of the answer, After that multiply 1st and last digits to get 3rd and 4th digits of the answer, Now add the numbers formed from 1st two steps and subtract 2nd number from it, we shall have 5th and 6th digits of the answer.

1st line can be written as (5×3)(5×2)(15+10-3) = 151222,

2nd line can be written as (9×2)(9×4)(18+36-2) = 183652

3rd line can be written as (8×6)(8×3)(48+24-6) = 482466

4th line can be written as (5×4)(5×5)(20+25-4) = 202541

Similarly we can write last and final line

Final line can be written as (7×2)(7×5)(14+35-2)=143547

Formula for this Puzzle is abc=(ab)(ac)(ab+ac-b)

##
PUZZLE 7

This problem is based on solution of linear equation of two variables. so it can be solved as follows .

## If we put A,B,C and D then

we shall have following equations

A + B = 8--------------------(1)

C - D = 6--------------------(2)

A + C = 13-------------------(3)

B + D = 8--------------------(4)

Now we have to solve these equations for A,B,C and D.

From eq (1) we have A = 8 - B ,put this value of A in (3),

we get 8 - B + C = 13, Rewrite it

B - C = -5 --------------------(5)

Now adding (2) and (5) ,we get

C - D + B - C = 6 - 5

B - D = 1 ---------------------(6)

Adding (4) and (6),we get 2B = 9 ⇒

**B = 9/2 = 4.5**
Putting the value of B in Eq (1), we get

4.5 + A = 8 ⇒

**A = 3.5 ,**
Put "A" in (3) ,we get

**C = 9.5**
Put the value of "B" in (4)

4.5+D = 8 ⇒

**D = 3.5**So Final Answers are

**A = 3.5,**

**B = 4.5,**

**C = 9.5,**

**D = 3.5**

## Conclusion

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