Solution:

Now this problem is a bit tricky. Before you start panicking about the solution let us give you a hint. You need to think in terms of binary numbers.

There are 1000 bottles which should be labeled from 1 to 1000 first. Now write those numbers in binary format.

Bottle Number 1 = 0000000001
Bottle number 2 = 0000000010
Bottle number 500 = 0111110100
Bottle number 1000 = 1111101000

Now the king will summon ten prisoners and label them from 1 to 10. The prisoner labeled as 1 will take a sip from those bottles that have a 1 in its least significant bit and the prisoner labeled as 10 will take a sip from every bottle that have a 1 in its most significant bit etcetera.

Let us frame an example. The wine from the bottle number 924 will be sipped by 10, 9, 8, 5, 4 and 3. Thus if that bottle will be poisoned, only those 6 prisoners will die.
After a month's time, all the king need to do is line up the prisoners in order and call each living prisoner as 0 and each dead prisoner as 1. N such a manner the number that the king will get will be of that bottle which is poisoned.

Now also note that if there would have been 1024 or more bottles, there would have been more prisoners required for the very same task.

Solution:

It can be down as shown below.

Solution:

45 minutes

Explanation :
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.

Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.

Solution:

Playing chess

Game needs two players so Brother-8 is playing chess with Brother-2

Solution:

This is more of a philosophical question than being a riddle or a puzzle. The action of Brian directly led to the result which is the death of Chris. Thus he murdered Chris. In a sense, Chris died due to the lack of water. It is the circumstances that ultimately led to his death.

Solution:

If we have to measure precisely, it is impossible. Because we are asked to measure odd number of liters whereas all the jars we have can contain only even liters of water.

* Tricky question asked in ias/infosys/infoedge/ibibo interview

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49

Solution:

17 mins

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let’s brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let’s put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

36 meters.

100/v1 = 80/v2
100/v2 = 80/v3

20+(20/v2)*v3=20+16 = 36