Solution:

Let us simplify the question and then it will lead us to the answer easily. There are three possibilities. Thus the probability of choosing any door is 1/3rd. 1/3 of the time the door to heaven will be chosen by Amanda and thus 1/3 of the time it will take her zero days. 1/3 of the time, the day which leads to hell for one day will be chosen and of those the right door will be chosen the next day. So 1/9 trips take one day. In the similar manner, 1/9 will take to the door which takes to 2 days hell.

When that happens, the cases will be split again and again. Thus on average, it will take three days for Amanda to reach Heaven by choosing the right gate.

Solution:

There are many ways in which you can think a solution for the problem. Your approach should be to minimize the efforts. What if you took out one candy from the box labeled Peach and Grape?

What you have to consider is the fact that every box is labelled incorrectly. Thus if you pick a candy from the box labelled with Peach and Grape, it is evident that the box will not have a mixture of both (as it is labelled wrong). Thus you will get to know which candies are present in that box.

Suppose the candy you take out turns out to be peach flavored, then the box labeled as Grapes is the one which contains a mixture of both peach and grapes. This is because it is labelled incorrectly and since we have already figured out the box with Peach candies, we can be confident of the fact. And then the jar labelled as peach will be the one containing grape flavored candies.

If the candy you take out from the mixed labeled box is Grape flavored, you can use the same logic to find out the rest.

Consider picking a candy from the other two boxes instead of what is told in the solution and you will find out that you will have to take out a candy from each of the boxes before being sure.

Solution:

We know you must be having numerous thought about it. But trust us that when you know the solution to the problem you will regret for not thinking in that direction.

You just have to ask the person, "Which way is your city?" Just follow the path he directs you to and you will reach Truthcity. How?

Well if the person belongs to Liarcity, he will speak lie and will tell you the direction of the Truthcity and if the person belongs to Truthcity, he will tell the truth and will lead you to the Truthcity.

Isn't it simpler than you thought?

Solution:

This is quite a famous interview puzzle and is usually asked as a warm up question. While you can figure out endless possibilities, the answer is quite simple. Detective Hoffman will just have to wait till the night. When there is no sun, he can simply walk out of the door that leads to the chamber built with magnifying glass.

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:

Did you consider the fact that we could be talking months here?
January - 31 days
February - 28 days
March - 31 days
April - 30 days
May - 31 days

Thus the next number in the sequence will be 31.

Solution:

In this question, let us think through the mind of Lincoln. At the first information of the product of the ages being 72, he must have calculated the number of ways in which the three ages can be multiplied in order to obtain 72. Of course there are many ways and therefore he asked for more info. Then Michael tells him how to find the sum of the ages of his children. Of course, we don't know what he saw. But he said that the information was still not enough.

Now why did he say so? It is because there must be two permutations with the same sum or he would have identified the ages easily. Now what are those two permutations?

The two possible permutations are 8 3 3 and 6 6 2. Both of them adds up to 14 (which would be the bar's address).

The last hint by Michael was that his youngest child loves to eat strawberry ice cream. The term youngest means that there is only one youngest child. If you see the permutation 8 3 3, it will mean that there are two youngest children. Thus it does not stand valid with the third hint. So, we are only left with one possibility i.e. 6 6 2.

Thus the ages of his children are 6, 6 and 2.

Solution:

Let us assume that the z axis denotes the time and x and y axis denote the 2D planet. The four trajectories in that case are straight lines. Since no collisions involved more than two air planes, the four lines must be lying in the same plane. Now you must be thinking that the other two planes will collide as well.

But consider the fact that they might have collided in the negative time. Thus you can't be sure with the provided facts if the two remaining planes will collide or not.

There can be both possibilities. The first assumption depicts that the four air planes fly in a manner that there is no collision between the ships. However in the second diagram, the four airplanes fly in a manner that there is collision between them.

Solution:

Even though the question might sound quite difficult, there is quite a simple solution for it if you light up your logics. All you have to do is turn two switches on and keep one off. Keep them in the same position for some 10 minutes and then shut one of them off. Hurry up into the room now.

There can be two possibilities - either the light are on or they are off. If they are on, you know which switch controls the lights as you have left only one switch on. If the lights are off, it can be either of the two remaining switches. All you have to do is touch the lights with your bare hand. If the lights are hot, it is the switch which you just turned off before entering the room and if the lights are cold, it is the switch which was left untouched and was off since the beginning.

Solution:

Let us denote the cats with A, B, C and D in a fashion that A is chasing B, B is chasing C, C is chasing D and D is chasing A. The cats are moving in symmetry and thus the only logical answer is that they will meet at the center of the square.

At any point of time, the Cat A is perpendicular to cat B and Cat B is perpendicular to Cat C and so on. Cat A runs for Cat B but Cat B does not run towards or away from Cat A for it is moving in a perpendicular direction to Cat A. Thus the distance that need to be covered by Cat A to grab Cat B will be exactly same as the original distance between them which in this case is one unit (as it is a unit square).

Thus the speed of each cat towards the cat it is chasing will be [1 + cos (x)] where x denotes the angle on each corner.

Thus speed of the cat = 1 + cos (90) = 1 + 0 = 1

The time needed = Distance / Speed = 1/1 = 1 unit