Timepieces

A sundial is a timepiece that has the fewest number of moving parts. Which timepiece has the most moving parts?

Answer
An Hourglass

Band Camp

Mogmatt's marching band played their show and then listened to it. They played the show almost perfectly and yet when they listened to it, it was all messed up. How could that have happened?

Ans

The band was hearing their echo. Because they were marching at the time, they were all different distances from the wall and their echoes played at different times.

Bird on the Moon

If a light oxygen tank were tied to a bird so that it can breathe on the moon, would the bird fly faster, slower or the same speed as it does on earth? (Remember that there is less gravity on the moon)

Ans

A bird cannot fly on the moon because there is no air to suspend it.

Water in the Cup

A man in a restaurant asked a waiter for a juice glass, a dinner plate, water, a match, and a lemon wedge. The man poured enough water onto the plate to cover it.
"If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon to do this."
A few minutes later, the waiter walked away with $100 in his pocket. How did the waiter get the water into the glass?

Ans
First, the waiter stuck the match into the lemon wedge, so that it would stand straight. Then he lit the match, and put it in the middle of the plate with the lemon. Then, he placed the glass upside-down over the match. As the flame used up the oxygen in the glass, it created a small vacuum, which sucked in the water through the space between the glass and the plate. Thus, the waiter got the water into the glass without touching or moving the plate.

Trapdoors

There are five doors, one leads to the exit, the others lead to traps. They are in a line. The clues tell you which position the doors are in the line and where the door to freedom is. All the clues are true. Each door has a clue written on it. The clues read:

The blue door: This door is two spots away from the door to freedom.
The red door: This door is at the far right, and is two spots away from the blue door.
The purple door: This door is not next to the door to freedom.
The green door: This door is left of the blue door.
The orange door: This door is not next to the red or blue doors.

Which door leads to freedom?

Ans

The orange door leads to freedom.

Tinman's Pick

Puzzle

Tinman was in quite a pickle. He was choosing a vehicle that he had to drive for the next 7 years, and he had to make the best decision possible. He had only five choices to choose from, and the choices each had different qualities that made them better or worse.

If the third choice was worse than the first choice and the second choice as good as the fifth, but the fifth choice was only as good as the worst choice leaving the fourth choice a little better than the third but not as good as the first, and the second was the worst choice to go with, which choice should Tinman go with if he wanted the best vehicle?

Answer

Tinman should go with the first choice. In order from worst to best, the choices are:

5th/2nd, 3rd, 4th, 1st.

Five Cards

Puzzle:

I was playing a game of five card draw poker with a bunch of logicians. By the time we had finished bidding and were just about to reveal our cards, I was pretty confident I would win of the four of us remaining. I had three nines, some face card (I can't remember what suit or even whether it was a jack, queen, or king) and a four. (Or was it a five? I can't remember.)

I was even more sure when two of my opponents laid down their cards. One had a pair of fours and a pair of sevens, the other had a pair of twos and a pair of eights. My third opponent, however, laid down his five cards face down in a row. He said, "I have a straight, and the cards are, from lowest to highest: a ten, a jack, a queen, a king, and an ace. I have at least one card of each of the four suits: clubs, spades, hearts, and diamonds. I am fairly certain that this is the winning hand, but I'm feeling generous today, and I will give a third of the pot to whoever can determine which suit I have two cards of.

Now I know you can't figure it out without some clues. Here they are:

1. The king is next to at least one diamond.
2. The queen is next to exactly one heart.
3. The jack is next to at least one spade, but is not next to any hearts.
4. The ten is next to at least one club.
5. The ace does not border any black cards, nor does it border any diamonds.
6. My two cards of the same suit are not next to each other.
7. Of the ten possible pairings of cards, only one pair, when removed, leaves three cards in ascending order from left to right.
8. My ace is not the card on the far left."

There was a minute's silence. One of the other logicians said, "I give up! There's no way to figure that out!"
The other agreed. But I didn't. I had just figured out which suit he had two of.

Which suit is it?

Solution:

The two cards on the ends and the card in the middle border a combined number of two suits. So at least one pair of them should be listed as bordering a card of the same suit in clues 1-5. Of the five, only the ace and the queen meet this criterion, so they must be two cards apart. One of them must be in the center, but it can't be the ace (the two cards on the ends would only border hearts - and one of them has to be bordering something else from clues 1-4), so it must be the queen. The ace is not on the left end from clue 8, so it must be on the right end, and the card next to it must be a heart. So far we have this(X represents unknown):
X X Q X A
X X X H X
At least one of the two cards to the left of the queen is lower than the queen (two of the remaining cards are lower, and only one can be right of the queen), so the triplet that is in ascending order is the queen, the ace, and the single card to the left of the queen that is lower than the queen. That means the king is left of the queen, and is also left of both the jack and the ten (otherwise, jack king ace or ten king ace would be a second triplet), so it must be on the far left. The jack must be left of the ten (or else ten jack ace would be a second triplet), so it must be second from the left, and the ten must be second from the right. The only card next to the king is the jack of diamonds (it's a diamond from clue 1). So far we have(T is ten):
K J Q T A
X D X H X
Now we seem to be stuck. We don't have any more clues that can be used. So how did I figure it out?
I held a face card (I said so myself in the intro). I must have known it cannot be that card and deduced the correct answer from there.
But which card did I have? We already know the suit of the jack, so my holding a jack would not help. Could I have held a queen? No, because I know the queen to either be a spade or club (clue 6), so one of the cards next to the queen would have its clue satisfied (see clues 3 and 4), and I could not determine the suit of the card on the other side of it.
Therefore, I must have held a king. But which king? I know the king is not a diamond (clue 6) or a heart (clue 3). If I held the king of clubs, then the king next to the jack would have satisfied the jack's clue, and I could not have determine the suit of either card next to the ten.
Therefore, I held the king of spades. The king of clubs must have been on the far left (only suit available), so the only card next to the jack that could be a spade is the queen, so the only card next to the ten that could be a club is the ace. In summary:
K J Q T A
C D S H C
Therefore there are two CLUBS.

Spirit Search

Puzzle:
You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: It's behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

Answer:

The spirit lies behind Door D.

If the spirit is behind Door A, then both B and D are true.

If the spirit is behind Door B, then both A and D are true.

If the spirit is behind Door C, then A, C, and D are all true.

If the spirit is behind Door D, then the statements on all the doors are false, except for that on Door B. This matches the rules, and therefore, the resort hotel spirit lurks behind Door D.

Marbles, Coin and Die

Puzzle

If I have:
a normal coin with a heads and tails;
a 6-sided die;
and a bag containing 4 blue and 2 red marbles,
what is the probability of me flipping a heads, rolling a 4, and picking out a red marble?

Solution

Probability of flipping a heads: 1/2
Probability of rolling a 4: 1/6
Probability of selecting a red marble: 2/6

Then multiply the results, so:
1/2 x 1/6 x 2/6= 1/36 or 0.027 to 3 decimal places

The Gardner Sisters

Puzzle:

Gretchen and Henry invited the four Gardner sisters over to their house for an afternoon tea. Henry went to the cabinet to take out some plates (they have both blue and green plates in the cabinet), and the first two plates he took out were blue. "What are the odds?" asked Martina Gardner, the youngest.

Henry thought for a moment, and then replied, "Knowing how many plates of each color I have, the probability that I would pull out two blue ones is exactly 1/2!" Martina then asked if Henry could feed two dozen people if he used all of his plates. "Not quite," he replied.

She then told him how many plates he had. What number did she say?

Solution:

Henry has 21 plates, and 15 of them are blue.

This makes the probability of drawing two plates (15/21) * (14/20), which equals 1/2.

Martina had to ask if he could feed two dozen people because there are other (larger) numbers that work. For example, if he had 85 blue plates out of 120 total, the probability that he would pull out two blue ones would have been (85/120) * (84/119), or 1/2. Other numbers work, as well, but all are greater than 120.

Another Game of Dice

Puzzle
Your friend offers to play a game of dice with you. He explains the game to you.

"We each get one die, the highest die wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll again. If you get a one the second time you have to keep it."

What is each person's probability of winning?

What are the probabilities of winning if you can keep rolling until you get something besides a one?

Solution
In the first game the probabilities of winning are 37/72 for your friend and 35/72 for you. In the second game each player has a 50% probability of winning.

There are 36 combinations (6 x 6) for your die and your friend's die on the first roll. In the first game if you don't roll a one on the first roll then that roll is equally likely to be a 2, 3, 4, 5 or 6, which can beat 1, 2, 3, 4, 5 different numbers, respectively. That gives a

(1+2+3+4+5)/36 = 15/36

probability of winning on the first roll. There is a 1/6 chance of rolling a one, in which case you have a 15/36 probability of winning on the second roll, which gives a

1/6 * 15/36 = 15/216 = 5/72

probability of winning on the second roll for a total probability of winning of

15/36 + 5/72 = 30/72 + 5/72 = 35/72 = .486111...

In the second game we never keep a one, so there are only 30 combinations (5 x 6) for the final roll. As shown above, there are 15 ways to win, which gives a probability of

15/30 = 1/2

of winning the second game.

Duplicate Lottery Picks

Puzzle
In the Massachusetts Megabucks lottery, six different numbers from 1 to 42 (inclusive) are selected. When you buy a ticket, you can ask for a "quick pick" in which the computer chooses the numbers for you, and you can purchase up to five games on a single ticket. We'll assume that the computer's random number generator is fair, giving each possible combination an equal probability of being chosen.

1. If I "quick pick" for two games, what are the chances that the two games have the same combination of numbers?

2. If I "quick pick" for five games (one five-game ticket), what are the chances that there are two games on that ticket with the same combination?

3 (The toughie). How many five-game quick-pick tickets would I have to buy in order to have a greater than 50% chance of having at least one ticket with two games on it that match exactly?

Solution
1. 1/5245786. The first game on the ticket will be some combination. Then you just calculate the chances that the second game on the ticket will match it. This number of combinations is (42 choose 6) or

42! / 6! (42-6)! = 5245786

So the chances that they match is 1 over this number.

2. For this sort of problem, where you are asking what are the chances of something happening at least once out of several opportunities to happen, you first calculate the opposite -- the chances of it NOT happening in all the tries -- and subtract from 1. So, what are the chances that the 5 games on the ticket are all different?

We know that there are 5245786 possibilities for any one game. In the first game, we choose one of them. The second game now has a 5245785 / 5245786 chance of being different from that first one. Now the third game has a 5245784 / 5245786 chance of being different from either of the first two; and the fourth has a 5245783 / 5245786 chance of being a new selection. When you have the chances of individual events occurring, and you want to know the chance of them ALL occurring, you just multiply. We multiply the chances of all these events occurring (that is, each choice being different) to get:

(5245785 * 5245784 * 5245783 * 5245782) / 5245786 ^ 4

This equals

0.99999809370925005714289758986902

Remember, this is the chance of all of the games on a five-game ticket being different. So the chance of at least two of them being the same is 1 minus this number, or

0.0000019062907499428571024101309848736

which is a really tiny number.

3. We take a similar approach with this calculation that we took before: figure out the chance of it not happening for N tickets, and subtract that value from 1. Then we set that chance to 0.5 and solve for N.

We already know the chance of it happening in one try: the tiny number above, which, for now, we'll call p. So the chance of it NOT happening in one try is (1-p). The chance of it NOT happening in n tries is (1-p)^n, so the chance of it happening at least once in n tries is [1 - (1-p)^n]. We set this formula to 0.5 and solve for n.

Of course, solving for n is tricky, unless you are comfortable with logarithms. I start with the equation

0.5 = [1 - (1-p)^n]

Simplify
0.5 = (1-p)^n

Take natural logarithm of both sides
ln(0.5) = ln( (1-p)^n)

Use logarithm magic
ln(0.5) = n * ln(1-p)

Divide both sides by ln(1-p)
n = ln(0.5) / ln(1-p)

Plug in the number (which we already know) for p and let the calculator do what it's good at
n = 363610.07359999192796640483226154

which is how many tickets we would have to buy to have a 50% chance of seeing one ticket with a match. Since we can't buy fractional tickets, we round up, to make sure we have a greater than 50% chance.

So we need to buy 363611 five-game tickets to have a better than 50% chance of having at least one ticket on which two games match exactly.

St. Petersburg Paradox

Puzzle:
You are offered a game to play with a single fair coin. It costs 20 dollars to play this game, but you can win much more than that. The way it works is that you continue to flip the coin until you get tails. For every heads you get before that, your payoff doubles. For example, if you get:
Heads
Heads
Tails, then you would earn 4 dollars.
In other words, you get: 2^heads dollars after you play. The question is: would you come out with more or less money after you played this game an INFINITE number of times? Remember, each game costs 20 dollars!

Solution
Neither!
You would come out with an INFINITE amount of money! Here's why:

The way to calculate an expected value of a game=(the probability of event1)*(the payoff from event1)+(the probability of event2)*(the payoff from event2)...

Let's say:
event1=Tails
event2=Heads,Tails
event3=Heads,Heads,Tails, and so on.

The probability of these events are:
event1=1/2
event2=1/2*1/2=1/4
event3=1/2*1/2*1/2=1/8, and so on.

The payoff of these events are:
event1=1
event2=2
event3=4
event4=8, and so on.

Plugging this into the expected value formula, we get:
EV=(1/2*1)+(1/4*2)+(1/8*4)+(1/16*8)...

This simplifies to:
EV=1/2+1/2+1/2+1/2...
Any number added an infinite number of times will sum to infinity, so your expected value of this game is infinity.

100 Prisoners in Solitary Cells

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say “Every prisoner has been in the special room at least once”. If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

Trailing Zeros in 100 Factorial

How many zeros are there in 100! (100 factorial)?

Apples and Oranges?

You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. However, each of these labels is always placed incorrectly. How would you pick only one fruit from a basket to place the labels correctly on all the baskets?

5 Pirates Fight for 100 Gold Coins

Five pirates discover a chest containing 100 gold coins. They decide to sit down and devise a distribution strategy. The pirates are ranked based on their experience (Pirate 1 to Pirate 5, where Pirate 5 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is his plan?

How Strong is an Egg?

You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum number of tries needed to find out the solution?

What’s Your Eye Color?

On a certain island there are people with assorted eye colors. There are 100 people with blue eyes and 100 people with brown eyes. Since there are no mirrors on this island, no person knows the color of their own eyes. The people on the island are not allowed to talk or communicate with each other in any way. They are also NOT aware of the number of blue or brown eyed people on the island. For all they know, they could have red eyes too. But they are allowed to observe other people and keep count of the number of people with a certain eye color. There is a rule that the people on the island have to follow – any person who is sure of their eye color has to leave the island immediately.

One day, an outsider comes to the island and announces to the people that he sees someone with blue eyes. What do you think happens?

Bulb Or No Bulb?

There are 100 bulbs arranged in a row. Each bulb has its own switch and is currently turned off. In the first round, you turn every switch on. In the second round, you flip the switch of every second bulb (i.e. bulb 2, 4, 6, 8 and so on). In the third round, you flip the switch of every third bulb and so on. What is the state of bulb 9 after 100 rounds? Also, how many bulbs are on after 100 rounds?

6 Pirates Fight for 1 Gold Coin

Six pirates discover a chest containing 1 gold coin. They decide to sit down and devise a distribution strategy. The pirates are ranked based on their experience (Pirate 1 to Pirate 6, where Pirate 6 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 6 devises a plan which he knows will keep him alive. What is his plan?

Chess Squares

ow many squares are on a chess board?

9 Minutes

You are given two hourglasses. One measures 4 minutes and one measures 7 minutes. How would you measure exactly 9 minutes?

Three Switches

You are standing outside a room next to three switches, all of which are off. Each switch operates a different light bulb in the room. The room door is closed, so you cannot see which switch operates which bulb. You are only allowed to go into the room once. Determine which switch operates which bulb.

Farmer’s Dilemma

A farmer bought a goat, a wolf and a cabbage from the market. On his way home, he has to cross a river. He has a small boat which only allows him to take one thing with him at a time. The farmer cannot leave the cabbage and the goat together (the goat would eat the cabbage) nor can he leave the goat and the wolf together (the wolf would eat the goat). How does he cross the river without losing any of the things he bought?

Tunnel Trouble

A man needs to go through a train tunnel to reach the other side. He starts running through the tunnel in an effort to reach his destination as soon as possible. When he is 1/4th of the way through the tunnel, he hears the train whistle behind him. Assuming the tunnel is not big enough for him and the train, he has to get out of the tunnel in order to survive. We know that the following conditions are true.

1. If he runs back, he will make it out of the tunnel by a whisker.
2. If he continues running forward, he will still make it out through the other end by a whisker.

What is the speed of the train compared to that of the man?

Clock Hands

How many times a day do the minute and hour hands of a clock overlap?

Globe Walker

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

Trains and Birds

A train leaves City X for City Y at 15 mph. At the very same time, a train leaves City Y for City X at 20 mph on the same track. At the same moment, a bird leaves the City X train station and flies towards the City Y train station at 25 mph. When the bird reaches the train from City Y, it immediately reverses direction. It then continues to fly at the same speed towards the train from City X, when it reverses its direction again, and so forth. The bird continues to do this until the trains collide. How far would the bird have traveled in the meantime?

Burning Sticks

You have two sticks and matchbox. Each stick takes exactly an hour to burn from one end to the other. The sticks are not identical and do not burn at a constant rate. As a result, two equal lengths of the stick would not necessarily burn in the same amount of time. How would you measure exactly 45 minutes by burning these sticks?

The Fox and The Duck

A duck that is being chased by a fox saves itself by sitting at the center of circular pond of radius r. The duck can fly from land but cannot fly from the water. Furthermore, the fox cannot swim. The fox is four times faster than the duck. Assuming that the duck and fox are perfectly smart, is it possible for the duck to ever reach the edge of the pond and fly away to its escape from the ground?

Chasing Dogs

There are four dogs each at the corner of a unit square. Each of the dogs starts chasing the dog in the clockwise direction. They all run at the same speed and continuously change their direction accordingly so that they are always heading straight towards the other dog. How long does it take for the dogs to catch each other and where?

Boxes of Money

You are given b boxes and n dollar bills. The money has to be sealed in the b boxes in a way such that without thereafter opening a box, you can give someone a requested whole amount of dollars from 0 to n. How should b be related to n for this to happen?

One train leaves Los Angeles

One train leaves Los Angeles at 15 MPH heading for New York . Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?

Sheriff in a town that caught three outlaws

There was a sheriff in a town that caught three outlaws. He said he was going to give them all a chance to go free. All they had to do is figure out what color hat they were wearing. The sheriff had 5 hats, 3 black and 2 white. Each outlaw can see the color of the other outlaw’s hats, but cannot see his own. The first outlaw guessed and was wrong so he was put in jail. The second outlaw also guessed and was also put in jail. Finally the third blind outlaw guessed and he guessed correctly. How did he know?

Fuse ropes

You are given two 60 minute long fuse ropes (i.e. the kind that you would find on the end of a bomb) and a lighter. The fuses do not necessarily burn at a fixed rate. For example, given an 8 foot rope, it may take 5 minutes for the first 4 feet of the fuse to burn, while the last 4 feet could take 55 minutes to burn (a much slower rate) (5+55=60 minutes). Using these two fuses and the lighter, how can you determine 45 minutes? HINT: You can use the lighter any number of times

Three wise men in a room

There are three wise men in a room: A, B and C. You decide to give them a challenge. Suspecting that the thing they care about most is money, you give them $100 and tell them they are to divide this money observing the following rule: they are to discuss offers and counter-offers from each other and then take a vote. The majority vote wins. Sounds easy enough... now the question is, assuming each person is motivated to take the largest amount possible, what will the outcome be?

5 houses in 5 different colors

This puzzle was apparently written by Einstein in the last century.
He said that 98% of the people in the world cannot solve the quiz. See if you can...

Facts:

1: There are 5 houses in 5 different colors
2: In each house lives a person with a different nationality.
3: These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.
4: No owner has the same pet, smoke the same brand of cigar or drink the same drink.



Hints:

1: The British lives in a red house.
2: The Swede keeps dogs as pets
3: The Dane drinks tea
4: The green house is on the left of the white house (it also means they are next door to each other)
5: The green house owner drinks coffee
6: The person who smokes Pall Mall rears birds
7: The owner of the yellow house smokes Dunhill
8: The man living in the house right in the center drinks milk
9: The Norwegian lives in the first house
10: The man who smokes Blend lives next to the one who keeps cats
11: The man who keeps horses lives next to the man who smokes Dunhill
12: The owner who smokes Blue Master drinks beer
13: The German smokes Prince
14: The Norwegian lives next to the blue house
15: The man who smokes Blend has a neighbor who drinks water.

The question is: who keeps the fish?

5 Jars of pills

You have 5 jars of pills. Each pill weighs 10 grams, except for contaminated pills contained in one jar, where each pill weighs 9 grams. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?

One gold bar

You have someone working for you for seven days and you have one gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

Cross a bridge

There are four people who need to cross a bridge at night. The bridge is only wide enough for two people to cross at once. There is only one flashlight for the entire group. When two people cross, they must cross at the slower member's speed. All four people must cross the bridge in 17 minutes, since the bridge will collapse in exactly that amount of time. Here are the times each member takes to cross the bridge:

Person A: 1 minute

Person B: 2 minutes

Person C: 5 minutes

Person D: 10 minutes

If Person A and C crossed the bridge initially, 5 minutes would elapse, because Person C takes 5 minutes to cross. Then Person A would have to come back to the other side of the bridge, taking another minute, or six minutes total. Now, if Person A and D crossed the bridge next, it would take them 10 minutes, totaling to 16 minutes. If A came back, it would take yet another minute, totally 17. The bridge would collapse with A and B on the wrong side. How can all four people get across the bridge within 17 minutes? Note: there is no trick-answer to this problem.

Rectangular cake

If given a rectangular cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?

Life or Death? The Emperor's Proposition

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?

Birthday Line

At a movie theater, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, that birthdays are distributed randomly throughout the year, etc., what position in line gives you the greatest chance of being the first duplicate birthday?

Russian Roulette

You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?

Shared Puzzle

If you have any puzzle to share please, do so by posting a comment to this post.

[Microsoft] 500 men are arranged in an array

500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to come out. And the shortest among them is A. Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B. Now
who is taller A or B ?

Glove selection

There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the dark and can check them only after a selection has been made. What is the smallest number of gloves you need to select to have at least one matching pair in the best case? in the worst case?

There are four people who want to cross a bridge

There are four people who want to cross a bridge; they all begin on the same side. You have 17 minutes to get them all across to the other side. It is night, and they have one flashlight. A maximum of two people can cross the bridge at one time. Any party that crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown, for example. Person 1 takes 1 minute to cross the bridge, person 2 takes 2 minutes, person 3 takes 5 minutes, and person 4 takes 10 minutes. A pair must walk together at the rate of the slower person’s pace. For example, if person 1 and person 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If person 4 returns the flashlight, a total of 20 minutes have passed and you have failed the mission.

Crazy Guy on the Plane

A line of 100 airline passengers is waiting to board a plane. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let's say that the nth passenger in line has a ticket for the seat number n.)
Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random.
What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?

Sum It Up

You are given a sequence of numbers from 1 to n-1 with only one of the numbers repeating once. (example: 1 2 2 3 4 5) how can you find the repeating number?