Solution:

South

Explanation:
If you turn the picture upside down, you will see South.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)

Solution:

The girl was born on 29 February. Thus her birthday came once in four years only while her sister was born on a normal day and celebrated her birthday every year. Thus the girl had a chance of depositing money only 10 times in 4 years through which she collected $2500 while her sister took $50 from the piggy bank every year making the total amount to be $2000. Thus when the piggy bank was opened, it had just $500.

Solution:

10,15,9,20,12

Explanation:
The score obtained on the first throw is 10.
The score obtained on the second throw is 15.
The score obtained on the third throw is 9.
The score obtained on the fourth throw is 20.
The score obtained on the fifth throw is 12.

Solution:

You can ask this question to any one person, "if I ask the man who is next you: which is the correct way and the road to the village, what would the person next to you answer?"
If you happened to ask this question to the liar, he will show you the wrong way.
And if you happened to ask this question to the one who says truth, he will also show you the wrong way.
Once you are done with this, take the other way. This will lead you to the village

Solution:

So that the following plan can be followed, let us number the coins from 1 to 12. For the first weighing let us put on the left pan coins 1,2,3,4 and on the right pan coins 5,6,7,8.

There are two possibilities. Either they balance, or they don't. If they balance, then the different coin is in the group 9,10,11,12. So for our second one possibility is to weigh 9,10,11 against 1,2,3

(1) They balance, in which case you know 12 is the different coin, and you just weigh it against any other to determine whether it is heavy or light.
(2) 9,10,11 is heavy. In this case, you know that the different coin is 9, 10, or 11, and that that coin is heavy. Simply weigh 9 against 10; if they balance, 11 is the heavy coin. If not, the heavier one is the heavy coin.
(3) 9,10,11 is light. Proceed as in the step above, but the coin you're looking for is the light one.

That was the easy part.

What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these coins could be the different coin. Now, in order to proceed, we must keep track of which side is heavy for each of the following weighings.

Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against 2,7,8. If they balance, then the different coin is either 3 or 4. Weigh 4 against 9, a known good coin. If they balance then the different coin is 3, otherwise it is 4. The direction of the tilts can tell us whwther the offending coin is heavier or lighter.

Now, if 1,5,6 vs 2,7,8 does not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy coin, or 1 is a different, light coin.

For the third weighing, weigh 7 against 8. Whichever side is heavy is the different coin. If they balance, then 1 is the different coin. Should the weighing of 1,5, 6 vs 2,7,8 show 1,5,6 to be the heavy side, then either 5 or 6 is a different heavy coin or 2 is a light different coin. Weigh 5 against 6. The heavier one is the different coin. If they balance, then 2 is a different light coin.

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200

Solution:

It will take the man 58 minutes to reach the top.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

Solution:

At every floor, the detective had to open the window himself. If the man had committed suicide, then at least one of the windows must have been open. A person who is committing suicide won’t close the window behind him. Thus he knows that someone pushed him off the edge and closed the window afterwards.

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

NONE, holes are empty.