The pain transfers the pain to the baby’s father. The wife cheated on her husband with the mailman and it was his baby. It never mentions that the husband is the baby’s father.

“Is she older than her?” (He would ask one of the daughters if one of the other daughters is older than the last daughter). He always should pick the younger daughter based on what he knows. If he asks the older daughter and she says yes, then the youngest daughter will be known. If he asks the older daughter and she says no, then the youngest daughter is the other one. If he asks the youngest daughter and she says yes, she is lying and he will still pick the oldest. If he asks the youngest and she says no, he will just pick the other like in the first case. If he asks the middle daughter it doesn’t matter because both will be acceptable choices.

When he gets on the subway it is 6 stops away from the end of the line (end of the track). So when it reaches this point it begins to work backwards. So when it goes back one stop he has traveled 7 stops but is only 5 away from where he began.

43.

After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6’s and 9’s). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn’t fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).

You could drop it at floor 1 first (because you start at floor 1). Then you would go to the floors: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100. Whatever floor your first coconut breaks at, go to the floor above the last floor the coconut survived and drop the second coconut from this floor. Then go up by one floor until the second coconut breaks and that is the lowest floor it will break at.

833 apples.

Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go.
Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville.

This is the famous Josephus Problem. The solution requires getting the nearest smaller number that is the power of 2,in this case 64 and subtract it with the given number.100-64=36.Now we apply the formula 2n+1. 2*36+1=72+1=73.

Let’s say you ask from A that Do you know B?
If A knows B => A can not be a celebrity.
If A does not know B then B can not be a celebrity.

So you strike out one name from your list, so on each question you can reject one name.

When there are only two people left in the list, then you will ask first person, “Do you know the second person ?”. If he says yes then second person is the celebrity and if he says no then the first person is the celebrity.

Thus you need to ask a maximum of n questions to correctly figure out celebrity name.

You can measure 1 hour by burning any rope from one end, now if we burn the rope from both the ends, it will take half of the time, i.e. 30 minutes, thus we can measure 30 minutes by burning the rope from two ends.

But we need to measure 15 minutes, we can measure 15 minutes if we burn a rope from two ends, which generally take 30 minutes in burning from one end. In order to achieve that we can use second rope given to us.

Steps to measure 15 minutes

Light Rope #1 from both ends.
At the same time light Rope #2 from one end.
When Rope #1 burns fully, it will be 30 minutes and Rope #2 will take 30 more minutes to burn, light the other end of Rope #2 at this time, thus it will take 15 minutes to burn.
Start cooking your egg at the same point.
Stop cooking when Rope #2 burns fully.

Lets take some simple cases first
c = 1: in this case person who has hat on his head can see that no one else has hat on their head, so he will understand that he is the one with hat.

c = 2: in this case person with hat will see one other person with hat, rest all will see two hats. Now had there been only 1 hat, this case would have been solved on very first day, but in this case no one will go on first night, so the guy who see one hat will understand that there must be one hat on his head, so both of them will go underwater on second night.

c = 3: in this case person with hat will see two hats and rest all will see two hats, now had there been 1 or 2 hats some guys would have gone on first or second night, thus on third day guys who see 2 hats will understand that they have hats on their head and they will all go underwater on third night.

Similarly we can see that it will take c days to remove all hats.