Puzzles Questions

All the above will stay where they are when they goes off. Basically anything that can swithch on or off will come under this.

- Send the box with the lock to Alex. 

- Alex can't open it, but can put another lock on the box. 

- Alex sends this box with the 2 locks back to you, you unlock your lock and send it back to Alex again.

- So there is just Alex's lock on the box and Alex can now open it.

In each row, 

Sum of 1st two digit number + last two digit number = Middle two digit number

i.e., 1st row 15 + 40 = 55

2nd row 46 + 47 = 93

Similarly, 7x + 16 = 87 => x = 1.

As you were asleep, none of the things could have happened without doing "open your eyes" first.

Our solution:

Toss the coin twice.
Let TH, HT and TT correspond to the three choices.
And if you get HH, just repeat (so it takes 8/3 tosses on average).


BIASED COIN

If the coin was biased, TH and HT would occur with equal probability.
So you could assign THHT, HTTH and THTH to the three choices, with other 4-toss outcomes rejected.
Or you could assign HTT, THT and TTH to the three choices, with other 3-toss outcomes rejected.

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.

From the given data,

1 + 9 + 8 = 1

ONE + NINE + EIGHT

Consider the first letters and join them viz O N E = 1

So, now consider 2 + 8 + 9 in similar way

TWO+EIGHT+NINE

First letters are T E N = 10

2 + 8 + 9 = 1⃣0⃣