Old Chestnuts, the Sequel

There are 3 men in a room, all seated in the same direction, so that the in the rear can see the two heads in front of him, the one in the middle can see only the one head in front of him, and the one in the front can see no one. There are no mirrors or obvious tricks involved here.

A man walks into the room with 5 hats. Three of the hats are red and two are green. He tells the men that he will place a hat on each of their heads, and they will have no obvious way of knowing which colour hat they have, i.e. they can't look up and see the colour of the bill etc. He puts a hat on each of the men's heads. Unbeknownst to them, he places a red hat on every head and does not let then see the colour of the two remaining hats.

He walks up to the man in the back and asks him if he knows what colour hat was placed on his head. He thinks a minute and says he has no idea. The man walks to the one in the middle and asks the same. The man thinks a minute and responds with the same, he has no idea. The man walks to the man in front that can see no one. He asks if he knows what colour he placed on his head. The man in front stands up and says that he knows without a doubt, that his hat is red.

Now, assuming that all three men are logical, intelligent reasoning men, how could the one in front have known that his hat really was, indeed, red?

100 Einsteins in jail. They can't communicate with each other. All 100 Einsteins are wearing hats - and while they cannot see the colour of their own hat, they can see everyone else's. Once a day, the chaplain comes in and gives each prisoner the option to leave. If the prisoner is wearing a black cap, he's free to go; if his cap is red, he dies! The chaplain gives the Einsteins only one fact to work with: At least one of you is wearing a black hat! A prisoner will only leave if he is sure he's wearing a black hat!
Will any prisoners leave? If so, how many, and how many days will it take?

A manufacturer makes Gidgets and Gadgets. At least 500 Gidgets and 750 Gadgets need to be produced to meet minimum daily demand. The machinery is capable of producing up to 1200 Gidgets and 1700 Gadgets per day. The combined number of Gidgets and Gadgets that the packaging department can handle is 2600 per day. If the company sells Gidgets for 42 cents each and Gadgets for 57 cents each, how many of each item should be produced each day for maximum daily income? What is the maximum daily income?

Two Dutch cyclists began a training run simultaneously, one starting from Amsterdam, the other from Tilburg. They'd agreed to meet each other. When the riders were 180 miles apart, a fly took an interest. Starting on one cyclist's shoulder, the fly flew ahead to meet the other cyclist. On reaching the latter, the fly at once turned back. The restless fly continued to shuttle back and forth until the pair met. The fly's speed was 3 times the speed of the cyclist from Amsterdam and twice the speed of the cyclist from Tilburg.
How many miles did the fly travel?
(Note: you are not given any absolute speeds.)

A rope over the top of a fence has the same length on each side. The rope weighs one-third pound per foot. On one end hangs a monkey holding a banana, and on the other end is a weight equal to the weight of the monkey. The banana weighs two ounces per inch.

The rope is as long as the age of the monkey. The weight of the monkey in ounces is as much as the age of the monkey's mother. The combined ages of the monkey and the monkey's mother are thirty years. Half the weight of the monkey plus the weight of the banana is a fourth as much as the weight of the weight and the weight of the rope.

The monkey's mother is half as old as the monkey will be when it is three times as old as its mother was when she was half as old as the monkey will be when it's as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was a third as old as the monkey was when it was as old as its mother was when she was THREE times as old as the monkey was when it was a fourth as old as it is now.

How long is the banana?

A column of soldiers one-mile long marches one mile at constant speed. At the moment they set off, the last (rearmost) soldier runs to the front with a message, and then immediately returns to the rear, at constant speed, returning exactly when the march is completed...
The march is completed when the man in front reaches the 1-mile mark and the man in the rear reaches the point where the first man started.

How far did the runner run?

A merchant in a market was selling eggs. A customer walked up and said, "I'll buy half of all your eggs, plus half an egg." The merchant was happy to oblige.

Soon after that another customer came along and said, "I'll buy half of all your eggs, plus half an egg." Once again, the merchant sold the customer what he wanted.

Then a third customer arrived and said "I'll buy half of all your eggs, plus half an egg." Once again the merchant gave what had been asked.

Finally, a fourth customer approached and said, "I'll buy half of all your eggs, plus half an egg."
"Well, that sold me out," the merchant said, as his last customer strolled away happily.

The question is: How many eggs did the merchant have to begin with?

There is a monastery with a hundred monks. They have taken a vow of silence and there is no communication between them. Once a day they all gather in one large room for prayer and such. Then one day the abbot comes to them and tells them that a certain number of them have a disease that turns their face green. If they find out they have it they have to kill themselves that night. They have no mirrors. You know that seven of them have it, but the monks don't. How many days before all the infected ones have killed themselves?

Three logicians, A, B, and C, are wearing hats, which they know are either black or white but not all white. A can see the hats of B and C; B can see the hats of A and C; C is blind. Each is asked in turn if they know the color of their own hat.

Their answers are:
A: "No."
B: "No."
C: "Yes."
What color is C's hat and how does he know?