Poisoned Wine

So there's this king. Someone breaks into his wine cellar where he stores 1000 bottles of wine. This person proceeds to poison one of the 1000 bottles, but gets away too quickly for the king's guard to see which one he poisoned or to catch him.

The king needs the remaining 999 safe bottles for his party in 30 days. The king has 10 servants who he considers disposable. The poison takes 30 days to take effect (right before the party), and any amount of it will kill whoever drinks it. How can he figure out which bottle was poisoned in time for the party?

Einstein Logic Puzzle

There are 5 houses in a row, each with a different color. Their owners, each with a unique heritage, drinks a certain type of beverage, smokes a certain brand of cigarette, and keeps a certain variety of pet. None of the owners have the same variety of pet, smoke the same brand of cigarette or drink the same beverage.

Clues:

• The Brit lives in the red house.
• The Swede keeps dogs as pets.
• The Dane drinks tea.
• Looking from in front, the green house is just to the left of the white house.
• The green house's owner drinks coffee.
• The person who smokes Pall Malls raises birds.
• The owner of the yellow house smokes Dunhill.
• The man living in the center house drinks milk.
• The Norwegian lives in the leftmost house.
• The man who smokes Blends lives next to the one who keeps cats.
• The man who keeps a horse lives next to the man who smokes Dunhill.
• The owner who smokes Bluemasters also drinks beer.
• The German smokes Prince.
• The Norwegian lives next to the blue house.
• The man who smokes Blends has a neighbor who drinks water.

Who owns the pet fish?

100 Prisoners and a Lightbulb

There are 100 prisoners in a jail, each in an isolated cell. In the lobby of the jail is a room with a light and a lightbulb (starts in the off position), which can only been seen from the lobby. Each day, the warden will take 1 random prisoner down to the lobby. The prisoner can flip the switch (either turning the bulb off it was on or on if it was off), or the prisoner can do nothing, or the prisoner can say "each prisoner has been to the lobby at least once." If the prisoner who says this is correct, they all go free. If he is incorrect, they are all killed. The prisoners can get together at the very beginning to discuss a strategy, but can not communicate with one another ever again until the exercise is over. What strategy can the prisoners use to guarantee that they all survive?

1 Million Lockers

There are one million numbered lockers in a row. They all start out closed. On your first pass, you flip every locker, so each one is open. On your second pass, you flip every locker divisible by 2, so you close lockers 2, 4, 6, etc. On the third pass, you flip every locker divisible by 3, so locker 3 becomes closed, locker 6 becomes open, etc. You continue this pattern until the millionth pass, flipping only the millionth locker on the last pass. At the end, is the millionth locker open? What do all the open lockers have in common? Why?

Trains

There are two trains traveling 60 mph towards each other. When they are 120 miles apart, a fly leaves one train heading towards the other at 100 mph. As soon as it reaches the other train, it immediately flies back towards the first train. It continues doing this until the trains collide. How much distance does the fly cover before the trains collide?

Cards in the Dark

You are in a completely dark room with a deck of 52 cards. 12 of the cards are face up, but they are randomly distributed throughout the deck. You need to put the cards into two piles (not necessarily of the same size) so that each pile has the same number of face up cards. There are no markings on the cards that would help you identify the face up cards in any way. You can also flip cards to upside down if you want (changing the number of total face up cards). How do you do it?

25 Horses

You have 25 horses. You need to find out which 3 are the fastest. Only 5 horses can race at a time. You are only given the order in which the horses finish the races, not their actual times. What is the fewest number of races you need to find the 3 fastest?

Gameshow and Urns

You are on a game show. You have 50 Red and 50 Green balls and 2 urns. You are free to distribute the balls among the 2 urns anyway you want. The host then randomly picks an urn and then randomly picks a ball from that urn. A Green ball means you win $1 MM, a Red ball or no ball means you win nothing. How should you distribute the 100 balls?

7 Days of Work

You have one block of gold, weighing 7 pounds. You also have a worker, who is going to work for you for 7 days. You need to pay him 1 pound of gold a day. You can only make 2 cuts into the block of gold. How would you make the cuts so that you can pay 1 pound of gold for each day worked?

50 Prisoners and Hats

A king has fifty prisoners. He decides to play a game to give them a chance to win their freedom. The next day, he will line up the prisoners in a straight line, all facing the same direction. He will then place either a white hat or a black hat on each of their heads. There is no pattern to how he will place the hats and there is no known set number of each color hat. He could choose any number of black hats and any number of white hats, as long as each prisoner has a hat on his head. Once in a line, the prisoner at the back can see all the hats in front of him, and the prisoner in the front can not see any of the hats. The king will start at the back and allow the last prisoner to guess his hat color. He can only say "white" or "black", and he can not signal with timing, pitch, hand motions, etc. Only "white" or "black" in a monotone voice, or they will all be killed. If the prisoner guesses correctly, he will be set free. If not, he will be killed and the king will move forward to the next prisoner in line. He will continue this way all the way down until all the prisoners have attempted to guess their hat color. During the exercise, each prisoner can hear what happens to all the prisoners behind him (whether each lives or dies). The night before, the prisoners meet together and come up with a strategy where at MOST, one of them will die. What is this strategy that guarantees to save at least 49 of them?

Pirates and Treasure

Five pirates stumble across 1000 gold coins. They decide to divide up the coins amongst themselves in the following way. The first pirate will suggest a distribution of the coins. Let's say he suggests: 100 for pirate 5, 100 for pirate 4, 100 for pirate 3, 100 for pirate 2, and 600 for himself. After making a suggestion, all the pirates will vote on whether they agree to the distribution. If a CLEAR majority agree with the distribution, this distribution stays and the game is over. If not, then the pirates kill the first pirate, and the second pirate suggests a distribution for the remaining four pirates. Once again all the pirates vote and only if there is a clear majority does the second pirate live and the distribution stay. Note that a clear majority means over 50%, so if there are four pirates total then three half to agree for the pirate making the suggestion to live. This continues until a distribution is agreed on by a majority of the pirates. In addition to this set-up, all of the pirates have the same list of priorities. First, each is interested in self-preservation, meaning he will vote yes for a plan if he believes the alternative would result in him eventually dying. Second, the pirates are greedy, meaning that they will vote against a plan if they believe they can get more coins later on. Finally, all the pirates are bloodthirsty. This means that if they believe they can live and get the same number of coins later on, they would rather see another pirate die. Given these rules, what is the most number of coins that the first pirate can suggest for himself to guarantee that the distribution is accepted and he lives?

Duck in Pond

A duck starts off in the center of a perfectly circular pond with radius r. On the edge of the pond is a cat. The cat can run four times as fast as the duck can swim, but can not enter the water. Is it possible for the duck to reach any edge of the pond without the cat being there to catch it? If no, provide a proof as to why it can not be done. If yes, provide the strategy that the duck must use.

2 Ropes

You are given two ropes, each of which burn in one hour. However, the ropes do not burn linearly, so simply because one is half way through based on distance does not mean that thirty minutes have passed. The ropes also do not necessarily burn in the same way as each other. Using these two ropes, how can you measure exactly 45 minutes of time?

Two Coin Flippers

Two people are standing across from each other with a solid wall in between, so they can not see each other. Each has a fair coin. At each turn of the game, each will flip his coin and allow it to land on the floor. At the same time, each will try to guess out loud whether the other person's coin is heads or tails. What is a strategy that maximizes the probability that BOTH players are correct, and what is this probability?

Gameshow

You are on a gameshow. The host shows you three closed doors. Behind one of the doors is $1 million. Behind the other two doors is nothing. You begin the game by choosing one of the doors. It remains closed, but the host opens one of the other two doors and shows you that there is nothing behind it. In order to maximize your chances at winning the money, is it best for you to keep the door you originally chose, switch to the other closed door, or does it not make any difference?

10 Machines and 1 Weigh

You have ten machines that produce identical looking and feeling coins. Nine of the machines produce coins that weigh one ounce. However, one of the machines produces coins that weigh 0.9 ounces. You also have a scale with you (a digital scale, not the Libra kind). You can use the machines to produce any number of coins from each of them. Using only ONE weigh, how can you identify the machine with the lighter coins?

3 Prisoners and Hats

A king has three prisoners. He decides to give them a chance to earn their freedom. He has a total of three white hats and two black hats. The prisoners know that the king has these five hats total. The next day, the king says he will blindfold all three prisoners and place a colored hat on each of their heads. He will then remove the blindfold from the first prisoner and let him look around at the other two hats. If the prisoner can guess his hat color with 100% certainty, the king will let them all go free. If not, the king will put the blindfold back on the first prisoner and remove the blindfold from the second prisoner. The second prisoner now has a chance to see the other two hats and if he guesses his own hat color with 100% certainty, the king will let them all go free. If not, the king puts the blindfold back on the second person and allows the third person to guess his own hat color (without ever removing the blindfold). When the game is played, the first prisoner does not make a guess. The second prisoner, knowing the first did not guess, does not make a guess. When it gets to the third prisoner, who knows the first two did not guess, he is 100% sure what his hat color is and guesses it correctly, setting all the prisoners free. What is the third prisoner's hat color and how did he know it for sure?

Twelve Marbles

You have twelve marbles that look and feel identical. Eleven of the marbles weigh exactly one ounce. One of the marbles weighs a different amount, and you do not know it is lighter or heavier than the others. You also have a scale (the Libra kind, not the digital kind.) Using no more than THREE weighs, how can you guarantee to find the defective marble?

Fork in the Road

You are traveling through the woods and you come across a fork in the road. One of the paths leads to your destination, and the other path leads you into a trap. At the fork, you see two men. One always tells the truth, and the other always tells lies. However, you do not which man tells the truth and which one tells lies. What is ONE question you can ask that, regardless of which one answers, you will be able to know which path will take you to the destination?