There are ten people in a house. Everybody wants to make a hand shake with only people shorter than themselves. Assume everybody is different in height. How many hand shakes are made?

0, because a taller person wants to shake hands with a shorter person. But the shorter person doesn't want to shake hands with him.

Brad starred through the dirty soot-smeared window on the 22nd floor of the office tower. Overcome with depression he slid the window open and jumped through it. It was a sheer drop outside the building to the ground. Miraculously after he landed he was completely unhurt. Since there was nothing to cushion his fall or slow his descent, how could he have survived the fall?

Brad was so sick and tired of window washing, he opened the window and jumped inside.

You have two lengths of rope. Each rope has the property that if you light it on fire at one end, it will take exactly 60 minutes to burn to the other end. Note that the ropes will not burn at a consistent speed the entire time (for example, it's possible that the first 90% of a rope will burn in 1 minute, and the last 10% will take the additional 59 minutes to burn).
Given these two ropes and a matchbook, can you find a way to measure out exactly 45 minutes?

The key observation here is that if you light a rope from both ends at the same time, it will burn in 1/2 the time it would have burned in if you had lit it on just one end.
Using this insight, you would light both ends of one rope, and one end of the other rope, all at the same time. The rope you lit at both ends will finish burning in 30 minutes. Once this happens, light the second end of the second rope. It will burn for another 15 minutes (since it would have burned for 30 more minutes without lighting the second end), completing the 45 minutes.

A woman who lived in Germany during World War II wanted to cross the German/Swiss border in order to escape Nazi pursuers. The bridge which she is to cross is a half mile across, over a large canyon. Every three minutes a guard comes out of his bunker and checks if anyone is on the bridge. If a person is caught trying to escape German side to the Swiss side they are shot. If caught crossing the other direction without papers they are sent back. She knows that it takes at least five minutes to cross the bridge, in which time the guard will see her crossing and shoot her. How does she get across?

She waits until the guard goes inside his hunt, and begins to walk across the bridge. She gets a little more than half way, turns around, and begins to walk toward the german side once more. The guard comes out, sees that she has no papers, and sends her "back" to the swiss side.

You have 3 jars that are all mislabeled. One jar contains Apples, another contains Oranges and the third jar contains a mixture of both Apples and Oranges.
You are allowed to pick as many fruits as you want from each jar to fix the labels on the jars. What is the minimum number of fruits that you have to pick and from which jars to correctly label them?

Let's take a scenario. Suppose you pick from jar labelled as Apples and Oranges and you got Apple from it. That means that jar should be Apples as it is incorrectly labelled. So it has to be Apples jar.
Now the jar labelled Oranges has to be Mixed as it cannot be the Oranges jar as they are wrongly labelled and the jar labelled Apples has to be Oranges.
Similar scenario applies if it's a Oranges taken out from the jar labelled as Apples and Oranges. So you need to pick just one fruit from the jar labelled as Apples and Oranges to correctly label the jars.

Four people come to an old bridge in the middle of the night. The bridge is rickety and can only support 2 people at a time. The people have one flashlight, which needs to be held by any group crossing the bridge because of how dark it is.
Each person can cross the bridge at a different rate: one person takes 1 minute, one person takes 2 minutes, one takes 5 minutes, and the one person takes 10 minutes. If two people are crossing the bridge together, it will take both of them the time that it takes the slower person to cross.
Unfortunately, there are only 17 minutes worth of batteries left in the flashlight. How can the four travellers cross the bridge before time runs out?

The two keys here are:
You want the two slowest people to cross together to consolidate their slow crossing times.
You want to make sure the faster people are set up in order to bring the flashlight back quickly after the slow people cross.
So the order is:
1-minute and 2-minute cross (2 minute elapsed)
1-minute comes back (3 minutes elapsed)
5-minute and 10-minute cross (13 minutes elapsed)
2-minute comes back (15 minutes elapsed)
1-minute and 2-minute cross (17 minutes elapsed)