3 fun brain teasers

I learned these recently from friends that had investment banking interviews. I'll put the answers at the bottom. The answers are clever, but don't recuire any "shoot the hostage" kind of out-of-the-box thinking. enjoy:

1. There's a man who owns a stable with 25 horses. He also has a track on which he can race 5 horses at a time. How many races must he hold to determine the 5 fastest horses?
2. There are 100 prisoners who are given the following instructions by a warden, "Tomorrow I will line you up facing in the same direction and make you wear hats. The hats will be either black or white, assigned at random, and you will not know how many there are of each color. You will be able to see the hats of the prisoners in front of you, but you will be unable to turn around. I will ask you what color your hat is. You must answer the question then shut up. If you're right, you live. If you're wrong you die." The prisoners have the night to devise a plan. How many of the 100 can safely survive?
3. There's a round table with a hole in the middle. You're playing a game with a friend where you take turns placing coins on the table. The loser is the first person who must place a coin on top of another coin. If you are going to play this game, would you rather go first or second? [amazingly, it doesn't matter how big the table, hole, or coins are]

OK, here are the answers:

1. The stable owner must hold seven races. Five "heats" with have different horses in each heat. Then he holds a race for the winner of each heat. The winner of this race is the fastest, but who are #2 and #3? Well, let's hold a race with the horse that finished #2 and #3 in the champions race, as well as the two horses that were just behind #2 in his original heat, and the 1 horse that was just behind #3. These are the only horse that could possibly still be in the top 3. Make sense?
2. The first prisoner who the warden asks is screwed. He's got a 50/50 shot, but he can pass along information about the others with his response. I heard someone suggest that the prisoners alter the tone of their voice to indicate the color of the person in front of them. Great idea, for partial credit. Here's the real answer: if there are 99 hats in front of the last man, there must either be an even number of black hats or white hats. The first prisoner counts the hats he sees in front of him, and his answer to the warden is not what he thinks his own hat is, but what color has an even number. Assuming he says "white", the next prisoner counts the white hats, and if he sees an even number too, he knows his own hat must be black. This same logic applies all the way up the line. Using this system, we can save all but the last prisoner, who might still stand a chance if he's lucky.
3. You want to go second in this game. You play your coin each turn on the exact 180º opposite place on the table from your opponent. As long as he has a place to put his coin, you will too, regardless of the dimensions of the table, hole, or coin. Cool, right?