Mind Puzzles

I do not take credit for coming up with any of these puzzles. I have however stated them in my own words.

Two Fuses (This is my favorite)
You are given two fuses and a lighter. The fuses take one hour to burn. They burn at non-constant unknown rates; meaning it could take 40 minutes to burn half way and then 20 minutes for the other half, you do not know. You are told to make a timer using these fuses that will burn for 45 minutes. You can cut them, tie them in a bow, use them to floss with. . . anything you want.
Hint 1 Hint 2 Solution

Three Prisoners
Three men need to be put into jail. But there is a problem; the jail they need to get into only has room for two of the three. So the prison guard decides to let one of the men go. The prison guard tells the men that he is going to paint either a red or a blue dot on their forehead while they are blindfolded. After he blindfolds them and paints the dots on their heads, he then arranged them in a triangle all facing each other, the reason for this is so when he tells them to take off their blindfolds, they will be able to see both of the other men, but not themselves. So once they are in position, he tells them that as soon as they take off their blindfolds and look at the other prisoners, they must raise their hand if they see a red dot. (So they raise their hand if they see either one or two red dots) Then he tells the men to lower their hands, think, and then guess.
The guard actually painted them all red, but they do no know that. After some thinking one of the men says that he is red, and he is right, how does he know he is red? You may assume that the prisoners are intelligent and that they each know the other two are intelligent.
Hint 1 Hint 2 Solution

Four Cities
Imagine four cities, each located on the corners of a square (perfect square, all sides equal, all interior angles 90 degrees, the square is on a 2-d plane (the effect of the Earth being spherical does not come into play)). One of the cities is like Buffalo and broke, so they do not have much money to waste, especially on roads, and that is just what the four cities need. So the mayors of the cities hire a construction team to make a system of roads between the four cities. In what way should the roads be laid out such that they use the least amount of building material to construct? A line can be used to represent a road. All four cities must at all times be connected. Once you find the solution, try solving for some of the roads dimensions, assume the square has sides of lengths one.
Hint 1 Hint 2 Solution

Three Switches
Imagine a closed room with an incandescent light bulb sitting on a table. The room has a door that allows no lihgt to escape when closed. Outside the room there are three light switches wired to the bulb, onlu one of them actually can activate the bulb. The switches have labeled on/off posistions. If you are allowed to play with the switches as much as you please before you open the door, how can you know for certain which switch controls the light when you open the door?After opening the door you are allowed to enter the room before you state you choice.
Hint 1 Hint 2 Solution

Rock in a boat
Imagine a boat sitting in a tank filled half way with water. You sit in the boat with a rock. If you were to throw the rock into the water would the level of the water with respect to the sides of the tank increase, decrease or stay the same?
Hint 1 Hint 2 Solution

Suicidal Monks
Imagine an island in the middle of the Pacific inhabited only by a small sect of monks. Let the total number of monks that live on the island be equal to some finite number N. Some of the monks have blue eyes, and the rest have brown eyes. There is at least 1 monk with brown eyes. Assume that all monks know there is at least 1 with brown eyes. Their daily activities consist only of waking, eating, meeting together in a circle, praying and sleeping. During their meeting the monks do not talk or gesture to each other, but they can see each others eye color. One day a decree is made-all monks who have brown eyes must kill themselves in their quarters. As said in the decree, all the brown eyed monks kill themselves in private, and the other monks do not know any monk has died until the following day when they meet in the circle. None of the blue eyed monks kill themselves. If their suicide is the only change to their daily routine, and there is no method for the monks to see their own eye color, how do all the monks with brown eyes figure out they have brown eyes?
Hint 1 Hint 2 Solution

9 marbles
You are given 9 marbles and a simple scale. The scale works by measuring some amount against another and tells you which is heavier, like the Egyptian balance scales. You are told that one of the marbles is just ever so heavier than the others. By touch, sight, feel…you cannot tell which marble is the heavier one. How can you find the heavier marble by only using the scale twice?
Solution

100 Lockers
There are 100 lockers all unlocked. To lock and unlock them there is a switch on the front of each locker with a locked and unlocked position. A man goes and starts switching the switches in the following manner. He begins by flipping the switch on every locker. (this will now lock all the previously unlocked lockers) Then he starts at the second locker and switches locker numbers 2,4,6,8,10 . . . 100. Then he starts at the third locker and switches 3,6,9,12 . . . 99. Then he starts at the fourth locker and switches every fourth and so on until he gets to 100 and only switches the 100 th locker. In the end, which lockers will be locked?
Hint 1 Hint 2 Solution