Please respect these puzzles: be patient and think for awhile before you click on the answer!
Strange Trip
You travel 100 miles north, 100 miles east, and then 100 miles south. You are at the same point that you started from. Describe all the places on earth this could be, if any. 
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Three Cards
There are 3 cards: one is all red, one is all blue, and the third is blue on one side and red on the other. The cards are shuffled. You pick one at random and it is blue on the side facing you. What are the chances that it is also blue on the other side? 
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Monty Hall Problem
Behind 1 of 3 closed doors is a prize. You pick one of the doors. Monty, knowing where the prize is, opens one of the other doors which is empty. You are given the choice of sticking with your choice or switching to the other unopened door. Should you switch? What are your chances of winning if you do? Assume Monty always opens an empty door. 
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4 Door Monty Hall Problem
Behind 1 of 4 closed doors is a prize. You pick door 1. Monty, knowing where the prize is, opens the 4th door which is empty. You switch your choice to door 2. Now Monty opens another door which is empty: door 3. Given the choice, should you switch back to door 1, and what are your chances of winning if you do? Assume Monty always opens doors that are empty.  Answer 
Monty Fall Problem
Behind 1 of 3 closed doors is a prize. You pick one of the doors. Monty accidentally slips and falls, knocking one of the other doors open at random which happens to be empty. You are given the choice of sticking with your choice or switching to the other unopened door. What are your chances of winning if you switch? 
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Two Envelopes
(Also known as the exchange paradox.) There are two envelopes, one contains twice as much money as the other. You pick one at random and find $100 inside. What is the "expected value" of the amount in the other envelope? Given the option, should you switch? Does it matter how much you found in that first envelope? Does it matter if you open the envelope? 
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Three Envelopes
There are three envelopes with different amounts of money in them. You pick one at random and open it. You then have the option to switch and open a second envelope. Again, you may switch to the third envelope if you'd like. However, if you switch you must discard the opened envelope and you can never switch back to it. Is there a strategy that gives you better than 1/3 chances of getting the best envelope, and if so what are those chances? 
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What's Next?
What is the next figure in this sequence?

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Helium
A helium balloon is in your car. How does it move when you slam on the brakes? 
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Urns with Balls
There are 2 urns filled with 100 ping pong balls total. 50 ping pong balls are white and 50 are black. I reach randomly into one of the urns, stir, and pick one ball without looking. What are the highest possible chances of me picking a white one that you can cause if you arrange the balls in the urns ahead of time? 
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Bean Bag
A bag contains a single bean, known to be either white or black. A new white bean is added to the bag, and it is shaken. A bean is taken back out, and it is white. What are the chances the remaining bean is also white? 
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Apples and Oranges
Three boxes each contain 20 pieces of fruit and are labeled "apples", "oranges", and "apples and oranges". The labels were correct but have been mixed up and are now all on the wrong boxes. What is the minimum number of fruits you need to inspect to learn the correct contents of all three boxes?  Answer 
4 Boxes of Fruit
Four unlabled boxes contain one type of fruit each: apples, oranges, pears, and bananas. Knowing this, 100 people guess which boxes contain which type of fruit. 32 people guess all 4 wrong, 39 guess only 1 fruit correctly, and 22 guess 2 of the fruits correctly. How many guess 3 correctly, and how many guess all 4 of them correctly? 
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Four Trees
A farmer claims to have 4 trees on his land all equidistant from each other. Could this be true? 
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Suicidal Spots
In a far away land, there is an unusual tribe of 300 perfectly logical and perfectly intelligent people. Each member has a visible spot on the back of his or her head, some are red and some are black. Nobody knows the color of their own spot, but they do know the color of everyone else's. If a tribesman ever realizes the color of his own spot it is strict custom that he publicly commit suicide the following morning, so they never mention spot colors, and have no mirrors. But then one day an American tourist visits this land and announces to the entire tribe: "I can see that at least one of you has a red spot." The tourist leaves and returns a year later. What has happened? 
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One Question
You are shipwrecked on an island. There is a fork in the path to the
other side, one way leads to a safe village, the other leads to hungry
cannibals. There are twin brothers who both know which path is which,
but one of the brothers is honest, and the other always lies. You may
ask one of them a single question. What should it be?
Related puzzle: what one question would you ask if there is just one person who is honest or lies but you don't know which?  Answer 
Three Random Hats
Three people are given hats. Each hat is either red or blue, chosen at random. Each person can see the other 2 hats, but not their own. They each must simultaneously either guess their own hat's color, or pass. No communication is allowed, although they can agree on a strategy ahead of time. What strategy will give them the best chances of at least one person guessing right, and nobody guessing wrong? 
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Two Random Hats
Two people are given hats. Each hat is either black or white, chosen at random. Each person can see the other hat, but not their own. They each must simultaneously guess their own hat's color. No communication is allowed, although they can agree on a strategy ahead of time. What strategy will give them the best chances of at least one person guessing right? (In this version there is no penalty for a wrong guess if the other guesses right.) 
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String Around the Earth
Imagine a long string tied tightly around the entire earth. One meter is then added to its total length. The slack is evenly distributed, and the string is somehow made to hover slightly above the ground at the same height all the way around the world. Ignore mountains and oceans, and assume the earth is perfectly round. What is the largest creature that could now fit under the string: ant, cricket, mouse, or cat? 
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Northwest Spiral
Two pilots fly from the Equator to the North Pole. The first flies north in a straight path. The second flies on a spiral path by always heading northwest. How far does the second pilot travel? (relative to the first)  Answer 
Odd Ball
There are 12 equal sized balls. One ball has a slightly different weight (more or less) than the other 11. Can you use a balance scale only 3 times to find the odd ball?  Answer 
Six Balls
You have 6 balls: 2 red, 2 white, and 2 blue. One of each color is slightly heavier, but the 3 heavy ones weigh the same, and the 3 light ones weigh the same. Can you use a balance scale only 2 times to find the 3 heavy balls?  Hint Answer 
Bags of Gold
Ten bags each contain nine pieces of gold. The gold pieces are all supposed to weigh 1 ounce, but the pieces in one bag weigh only .9 ounces. Use an accurate scale just once to find which bag contains the lighter pieces.  Answer 
Fair Cake
When two people want to share a cake fairly, one cuts, and the other chooses. Assuming this is a fair scheme, devise a similar scheme for 3 people and 1 cake. Nobody should get short caked even if the other 2 cooperate.  Answer 
Light Switches
There are 3 incandescent light bulbs in one room and 3 switches for these bulbs in another room. No light from the bulbs can be seen outside of their room. You are allowed to enter the room with the bulbs only once. How can you figure out which switches are connected to which bulbs?  Answer 
Grid of Tiles
There is an empty 8x8 grid, except two opposite corners are missing. Can you tile the rest with 1x2 tiles?  Answer 
1x3 Tiles
Can you cover an 8x8 grid with 1x3 tiles and a single 1x1 tile? If so, in what locations can the 1x1 tile be?  Answer 
Cheese Cubes
A block of cheese is cut into a 3x3x3 grid of subcubes. A mouse starts eating one corner, and moves on to adjacent pieces until they are all eaten. Could he eat the middle piece last? 
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Measuring with Jugs
Using a 5 liter jug, a 3 liter jug, and a hose, can you measure 4
liters of water? How about measuring 1 liter? 
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Burning Fuses
You have 2 lengths of fuse and 2 matches. One fuse will burn from start to end in 10 minutes, and the other in 15 minutes. However, their burn rate is not steady along their lengths. Measure 20 minutes of time. 
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Rope Escape
You have 150 meters of rope and a knife and need to escape from the roof of a 200 meter burning building. There are places to tie the rope to the building only at the roof, and at a ledge halfway down. How can you make it down without jumping?  Answer 
Pocket Change
If all the coins in my pocket except two are pennies, all except two are nickels, and all except two are dimes, how much money do I have?  Answer 
Gloves and Germs
You have 3 cultures of highly contagious and deadly germs. As part of an important experiment you must squeeze each culture once with your entire hand. However, you have only 1 pair of latex gloves. You must not contaminate any culture with another or with germs from your skin. The gloves can be worn on either the left or right hand. How can you complete your experiment without contaminating anything?  Answer 
Mixed Up Liquids
There are two equally filled jars, one contains milk, the other water. A teaspoon of milk goes into the water and is stirred. Then a teaspoon of the mixture goes back into the milk. Is there more water in the milk or milk in the water?  Answer 
Feynman's Sucking Sprinkler
If you take a water sprinkler like the one above and put it under water, it will spin clockwise as it would on land. But what happens if you then reverse the flow so it sucks in water? Would it spin, and if so, in which direction?  Answer 
Train Full of Water
A train car is at rest on a frictionless track. The car is full of water and has a spout pointing downwards on the far right end. The spout is opened and the water pours out. Describe the movement of the car, if any. 
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Superball Battle
Joe and Billy are having a onedimensional battle by shooting at each other through a long frictionless tube. Their guns each fire 10 balls in rapid succession, and all the balls enter the tube before any collide. The balls are perfectly elastic, have equal mass, are are shot at the same speed. Where do the balls end up and how many total bounces occur?  Answer 
Bubbles in Space
Two balls of matter in empty space would move towards each other. What if all space were filled with a frictionless deformable substance, except for two empty bubbles? How would the bubbles move?  Answer 
Flipped Cards
You are blindfolded and given a deck of 52 cards with 10 of the cards flipped upside down at random. Can you divide the deck into two parts that contain the same number of flipped cards? The two parts may have different numbers of cards and you may flip cards over, but you may not look at any cards.  Answer 
Fox in a Hole
There are 5 holes in a row. A fox spends each day in a hole, but always moves to an adjacent hole the next day, either right or left. You want to find the fox but you only get to inspect one hole per day. What is a strategy for finding the fox in the fewest days? 
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Six Chop Sticks
Using 6 equal length chop sticks make exactly 4 equilateral triangles. 
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Stick Boxes
Make 4 equal sized squares out of these 5 by moving only 2 sticks, and leave no extra sticks. 
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Fish Sticks
Point the fish the other way by moving only 3 sticks.  Answer 
Ten Points
Can you arrange 10 points so that 5 lines can each be drawn through 4 points?  Answer 
Connect the Dots
Connect these 9 dots with only 4 connected straight line segments. (Don't lift your pencil.)  Answer 
Four Points and Two Distances
Arrange 4 points in a plane so there are only 2 distinct distances between the 6 pairs of points. How many configurations like this are there? 
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Six Marbles
If you have 2 red, 2 green, and 2 blue marbles, can you arrange them so each one touches all four marbles of a different color? 
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Wire Cube
What is the minimum number of wires needed to make a cube? You can bend, but do not double, the wires. 
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Cube Vision
What is the maximum number of sides of a cube that you can see at once? The cube may be any size. The sides are thin but opaque so you can't see through them, and you can't use mirrors or other reflections. 
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Cube Sides
You have 6 differently colored squares that fit together to make a cube. How many different kinds of cubes could you make with these? 
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Five Triangles
Can you arrage five 1x2 right triangles to make a square? You may cut
only one of the triangles into two pieces. All of the triangle pieces must
be used to fill the square with no overlaps. You can rotate or flip
the triangles but they should remain flat.

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306090 Triangles
Can you cut a 306090 triangle into 3 smaller but equal sized 306090 triangles?
How about into 4 of them? How many ways are possible for each?
For a harder problem: how many ways to cut into 9 of them?  Answer 
Bookworm
A encyclopedia with ten 200 page volumes is sitting on a bookshelf in the usual order. A bookworm starts on the first page and eats in a straight line to the last page. How many total pages does he eat through?  Answer 
Five Pirates
Five pirates of different ages have 100 gold coins, and they decide to split the coins using the following rules: the oldest pirate proposes how to divide the coins, and all pirates vote for or against that plan. If 50% or more of the pirates approve, then the coins will be shared that way. Otherwise, the pirate proposing the plan is thrown overboard, and the process is repeated with the remaining pirates. Assume all the pirates are predictably very intelligent and very greedy. What will happen? 
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100 Pirates
Similar to above but with the quantities flipped: 100 pirates of different ages have 5 gold coins, and they decide to split the coins using the following rules: the oldest pirate proposes how to divide the coins, and all pirates vote for or against that plan. If 50% or more of the pirates approve, then the coins will be shared that way. Otherwise, the pirate proposing the plan is thrown overboard, and the process is repeated with the remaining pirates. Assume all the pirates are predictably very intelligent and very greedy. Also if a pirate figures his vote will not make a difference, he'll act in a bloodthirsty way and vote against the plan. What will happen?  Answer 
Five Hats
Three wise men are lined up in single file, each wearing a white hat. They know there were 5 hats total, three white, and two black, but they can only see the hats on the men in front of them. They don't speak unless they figure out what color hat they have on. Who figures out first?  Answer 
Pop Quiz
A teacher announces there will be a surprise quiz sometime during the week. The students argue it can't be on Friday because if the teacher waits until the last day it won't be a surprise anymore. Once they know it can't be Friday they argue by the same reasoning that it can't be Thursday either. What is wrong with this logic?  Answer 
Darts
You throw two darts at a dart board, aiming for the center. The second lands farther from the center than the first. You then throw another dart at the board, aiming for the center. Assume your skill level is consistent. What are the chances that this third dart also lands farther from the center than the first?  Answer 
Girl Babies
A large tribe obeys a strict reproductive custom. All families continue having children until they have a girl, and then they stop having more children. Assume it is equally likely for a given birth to produce a girl or boy, and assume families can have any number of children so they always do get one girl eventually. In the 10th generation, what is the expected ratio of males to females? Also, what is the expected population size of the 10th generation relative to the 1st?  Answer 
Hotel Bellboy
Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totaling $27. The bellboy has $2, totaling $29. Where is the remaining dollar?  Answer 
Doctor Who
A father and his son are in a car crash. The father is killed instantly but the son is only injured and is taken to the hospital. He is rushed to the operating room, the doctor comes in, looks at the patient on the operating table, and says, "I can't operate on him, he's my son." How can this be?  Answer 
Two Fathers and Two Sons
Two fathers and two sons are in a boat. One person falls overboard, but there are only two people left in the boat. How can this be?  Answer 
Two Boys and a Boat
Two boys wish to cross a river. The only way to the other side is by boat, but the boat can only take one boy at a time. The boat can not return on its own and there are no ropes or similar tricks, yet both boys manage to cross using the boat. How? 
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4 People and a Bridge
A family of four must quickly cross a precarious bridge over a dangerous river at night. They have only one torch and need it for every crossing. No more than two people can be on the bridge at the same time or it will break and they will fall to their deaths. Each person is able to walk at a different speed: they take at least 1 minute, 2 minutes, 7 minutes, and 10 minutes to cross respectively. What is the fastest they can all get safely across? 
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Defying Death
A thief is caught and sentenced to death, but the king allows him to make one last statement which will also determine his method of execution. He is to be hanged if his statement is true, or he is to be fed to lions if his statement is false. Somehow he manages to live. What did he say?  Answer 
NonSelf Containing Sets
What is difficult about the set of all sets that do not contain themselves?  Answer 
Manhole Covers
Why are manhole covers round?  Answer 
Mirrors
Why do mirrors seem to flip things leftright but not updown?  Answer 
Centrifuge
Can you spin 5 samples in a 12hole centrifuge, without it being out of balance?  Answer 
1000 Doors
A thousand doors start closed. Someone walks along and changes the state of each door (opens or closes). A 2nd person changes the state of every 2nd door, and a 3rd person changes the state of every 3rd door. This continues until the 1000th person changes the state of the 1000th door. How can you know if the Nth door is now open or closed? (without simulating the whole thing)  Answer 
Three Dice
You roll three dice, and multiply the resulting numbers together. What are the chances that product is odd?  Answer 
Two Dice at 7
If you roll two dice, what are the chances they add to 7? (This is a warmup for the next problem.)  Answer 
Four Dice at 14
If you roll four dice, what are the chances they add to 14?  Answer 
Meet in the Middle
You are negotiating to buy a Persian rug where they often overcharge tourists. You offer 1/2 the asking price, and the salesman says he can meet you in the middle at 3/4. You then offer to meet him in the middle again (between 1/2 and 3/4) and he does the same back to you again (between 5/8 and 3/4). What price would you arrive at if you continued like this forever?  Answer 
Alien Hats
You are among 10 humans abducted by aliens who will be given an intelligence test to determine if earth is worth saving. You will be lined up single file and each given a white or black hat, at random. Nobody will see the color of their own hat, nor can they see the hats on the people behind them, but they can see the hats on all the people in front of them. Then, one at a time, each person must guess the color of their own hat, starting with the person in the back who sees all the others, and ending with the person in the front who sees nothing. No other communication is allowed except the single guess "black" or "white" from each person. No delays or tone of voice signals are allowed. If anybody except the first person guesses wrong, everyone is killed and earth is destroyed. Fortunately you have some time before the test to discuss and agree on a strategy. Can you save the planet, and if so how?  Hint Answer 
100 Prisoners and 100 Boxes
A room has 100 boxes labeled 1 to 100, containing the names of 100 prisoners, one name per box in a random order. These 100 prisoners visit the room one by one, and each is allowed to inspect up to 50 boxes, one after the other. If all the prisoners somehow each manage to find their own name in a box, they are all released. The prisoners may not change anything in the room or communicate any information to the others after entering the room. However they are allowed to meet ahead of time and devise a plan. Is there a strategy that allows all of the prisoners to find their names with some reasonable probability? 
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Wire Ends
A new undersea cable is laid connecting a remote island to the mainland. The cable contains 36 wires, however the cable company neglected to label or colorcode the wire ends to indicate which wires are which. You have one battery and one light bulb for testing, and plenty of labels to tag each wire on both ends, so they can be properly attached to the equipment the following day. However, there is nobody to help you, and there is only time to travel once from the mainland to the island and back. Is there a strategy that allows you to identify and label the matching ends of all 36 wires in just one round trip? 
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Ball Paths
A ball is dropped into the top of the stack of boxes as shown. The boxes are open on the top and bottom so if there are 2 boxes below, the ball can fall either to the left or right. How many possible paths are there from the top to the bottom box? (The ball never bounces back up, and motion within a box doesn't matter. A path is a unique sequence of boxes that the ball passes through.) 
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Ball Paths 2
Similar to above, a ball is dropped into the top of the stack of boxes and falls down to the bottom box. For each level, when there are 2 boxes below, the ball falls randomly left or right with equal chances. (Assume the direction the ball came from the previous level does not affect the next bounce.) Two of the many possible paths from top to bottom are shown. Which of these paths is more likely, or are they equally likely? 
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Square of Bugs
Four bugs are on the corners of a 1 meter square. Each bug always faces the next bug (on the next clockwise corner). If they all walk forward at the same speed until they meet, how far does each bug travel?  Answer 
Bike Speed
A biker rode a mile in 3 minutes with the wind, and returned in 5 minutes against the wind. How fast could he ride a mile with no wind? 
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A Bee and Two Trains
Two trains are 30 miles apart, and travel towards each other at 5 mph and 10 mph. A bee starts at the slower train and flies at 25 mph to the other train. Each time it reaches a train it turns around and flies back to the other train again. What is the sum of the distances that the bee has flown when the trains meet? 
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Backwards Bee and Two Trains
Two trains start endtoend at the same point and travel away from each other at 5 mph and 10 mph. A bee also starts at the same point and flies back and forth at 25 mph between the ends of the moving trains. After 2 hours, where is the bee? 
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Water Levels
You are on a boat in a small pond. You have a stone and a log in the boat. You throw the stone into the water. Does the water level in the pond rise, fall or stay the same? How about if you throw the log in? 
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Pieces of Stone
A farmer has a 40 lb stone that he uses to measure out bales of hay on a 2 sided balance. He loans it to a friend who accidentally breaks it into 4 pieces. Instead of being angry, the farmer is quite happy. He says to the friend, "you managed to break it into just the right 4 pieces that will now let me weigh any weight between 1 and 40." What are the weights of the 4 pieces? 
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Breaking Balls
You have 2 bowling balls that each breaks when dropped from the same height. You want to find the highest floor of a 100 story building from which these balls can be dropped without breaking. Devise an optimal procedure that can always locate that floor using not more than N drop tests. What is the smallest N can be? 
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Puzzling Scales
Here is a classic old puzzle from Samuel Loyd (18411911). Assume the
3 blocks weigh the same amount as each other, and the 12 marbles weigh
the same amount as each other. How many marbles will balance the top?
 Hint Answer 
Magic Microbes
Count the microbes in the picture below. There are 14.
Now swap the top two rectangular pieces of the image, and count them again.
A 15th microbe has appeared! Where does it come from? Print one of these images and cut along the black lines to make three rectangular pieces. Then you can physically swap the top two rectangles to show the trick. 
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Handshakes
Jack and his wife attend a party with 4 other couples. Each person shakes hands with those they don't already know. Jack then asks each person how many hands they shook, and to his surprise he gets 9 different answers. How many hands did Jack and his wife each shake? 
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ThreeWay Duel
Joe, John, and Jack have an argument and agree to a 3way dual. They will take turns shooting until only one man is left standing. Joe is given the first shot because he is the worst aim and can only hit his target 1/2 of the time. John goes second and is ontarget 3/4 of the time. Jack always hits his target, and will shoot third if he is still standing for his turn. What is the best strategy for Joe's first shot, and who is most likely to win? 
Hint Answer 
Find the Cable
You urgently need to find an underground fiber optic cable that will allow you to listen to enemy communication and save your fleet from destruction. You know this cable is buried 1 meter underground and passes somewhere straight through a 1x1 square kilometer of land that you control. What is the minimum total length of ditches you need to dig to be sure to find the cable? 
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