You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die." How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?
HINT: The answer does not guarantee 100% you will chose a white marble, but you have a much better chance.
Place 1 white marble in the bowl, and place the rest of the marbles in the other bowl (49 whites, and 50 blacks). This way you begin a 50/50 chance of choosing the bowl with just one white marble, therefore life! BUT even if you choose the other bowl, you still have almost a 50/50 chance at picking one of the 49 white marbles.
A man while looking at a photograph said, "Brothers and sisters have I none. That man's father is my father's son."
Who was the person in the photograph?
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don't know which is which. So, What do you ask?
You ask each twin "What would your brother say?"
This works because.... Well let's say the correct path is on the left side. So say you asked the liar "What would your brother say?" Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left.
There are 1 million closed school lockers in a row, labeled 1 through 1,000,000.
You first go through and flip every locker open.
Then you go through and flip every other locker (locker 2, 4, 6, etc...). When you're done, all the even-numbered lockers are closed.
You then go through and flip every third locker (3, 6, 9, etc...). "Flipping" mean you open it if it's closed, and close it if it's open. For example, as you go through this time, you close locker 3 (because it was still open after the previous run through), but you open locker 6, since you had closed it in the previous run through.
Then you go through and flip every fourth locker (4, 8, 12, etc...), then every fifth locker (5, 10, 15, etc...), then every sixth locker (6, 12, 18, etc...) and so on. At the end, you're going through and flipping every 999,998th locker (which is just locker 999,998), then every 999,999th locker (which is just locker 999,999), and finally, every 1,000,000th locker (which is just locker 1,000,000).
At the end of this, is locker 1,000,000 open or closed?
Locker 1,000,000 will be open.
If you think about it, the number of times that each locker is flipped is equal to the number of factors it has. For example, locker 12 has factors 1, 2, 3, 4, 6, and 12, and will thus be flipped 6 times (it will end be flipped when you flip every one, every 2nd, every 3rd, every 4th, every 6th, and every 12th locker). It will end up closed, since flipping an even number of times will return it to its starting position. You can see that if a locker number has an even number of factors, it will end up closed. If it has an odd number of factors, it will end up open.
As it turns out, the only types of numbers that have an odd number of factors are squares. This is because factors come in pairs, and for squares, one of those pairs is the square root, which is duplicated and thus doesn't count twice as a factor. For example, 12's factors are 1 x 12, 2 x 6, and 3 x 4 (6 total factors). On the other hand, 16's factors are 1 x 16, 2 x 8, and 4 x 4 (5 total factors).
So lockers 1, 4, 9, 16, 25, etc... will all be open. Since 1,000,000 is a square number (1000 x 1000), it will be open as well.
A man is found dead in the desert. He is wearing only his underwear. Half of a straw is found nearby.
How did this man die?
The man was flying in a hot-air balloon with another man over the desert. The balloon started to go down because of excess weight. Both men would die if they ended up stranded in the desert, so they stripped down to their underwear and threw their clothes off the balloon to try to reduce the weight. Unfortunately, that didn't work well enough. So they drew straws to decide who would jump. The dead man pulled the short straw and jumped out of the balloon.
