Solution:

According to the clock, sunset is impossible at this hour.

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:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.

Solution:

Jeff Killed Mike

1. Jack is not the murderer, because he is the brother of the murderer.
2. Dan can't be the murderer since he ran a marathon, and the murderer recently had his leg amputated, and wouldn't be running a marathon of any magnitude that quickly.
3. Ben is not the murderer if he just met Jack, since Jack and the murderer grew up together.
4. This leaves Jeff and Mike.

Since Jeff is still alive (he wants to install a new computer next week, present tense) he must be the murderer. Mike also didn't grow up with Jack. It has been determined that Jack, Dan and Jeff are all alive. Ben must also be alive since Jeff plans to install Ben's computer next week. This means that Jeff killed Mike.

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

Everyone will done one day or other.

Abraham Lincoln era is too old and we expect most of them(if not all) to be dead by now.

Solution:

7, 4, 6, 5, 8

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

At 01:05

Solution:

Kid1, he was left with one rock.

Solution:

The young lady was presented with a bill which belonged to the elderly woman. She had asked the waiter to collect the bill from her daughter.