Puzzles Questions

Let the required number be 'X'

Condition 1 :  

$$\begin{gathered} XX = 2X \\ => 2X2 = X \\ => X = 12 \end{gathered}$$

Condition 2 :

$$\begin{gathered} X × X = X2 \\ => X = 12 \end{gathered}$$

Therefore, 12 is the number which becomes double when it is divided by itself and becomes half when it is multiplied by itself.

Given

6 = 3 => Number of letters in SIX = 3

12 = 6 => Number of letters in TWELVE = 6

14 = 8 => Number of letters in FOURTEEN = 8

Similarly,

22 = 9 => Number of letters in TWENTY TWO = 9

Therefore, 22 = 9.

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

Starting from letter 'S' add 5 in the clock wise direction to get the next letter in English alphabets.

Here S + 5 => 19 + 5 = 24 => X

X + 5 = 24 + 5 = 3 => C

Similarly, 

B + 5 = G

A Sandal.

It has sticking strips to make them fit for our feet. If you bind them only you can start walking or other wise it comes out.

Looking at the diagram in  rows, the central circle equals half the sum of the numbers in the other circles to the left and right of the centre.

That 8 letter word is Whatsapp (a messenger app)

First four letters:   WHAT a question
 
Letters 2,3,4:     HAT protects our head

Letters 5,6,7:   SAP an IT company

Letters 7,8:    PP same.

In the given puzzle, the logic is

2 + 3 = 10 => (2 + 3) * 2 = 10

6 + 3 = 54 => (6 + 3) * 6 = 54

8 + 3 = 88 =>  (8 + 3) * 8 = 88

Similarly,

9 + 7  => (9 + 7) * 9 = 16 x 9 = 144.