Logic Puzzles

1. The Missing Piece

Below the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?

Where does this hole come from?

2. Four Gallons

You have a three gallon and a five gallon measuring device. You wish to measure out four gallons.

3. The Islanders

There are two beautiful yet remote islands in the south pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.

You are on one of the islands, and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same Island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.

You ask the third Islander whether the other two Islanders are from the same island as him. Can you guess what the third Islander will answer to the same question?

4. Five Gallons

You are mixing cement and the recipe calls for five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four gallon bucket and a seven gallon bucket and nether has graduation marks. Find a method to measure five gallons.

5. Two Strings

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

6. The Cubes

A corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month.

What numbers are on the faces of the cubes to allow this?

Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07".

7. The Pot of Beans

A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.

At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?

8. The Pigeon

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

9. The Lightbulb

There is a lightbulb (incandescent, it's currently off) in an upstairs room. You are downstairs, standing next to a panel of three light switches (all of them in the off position). One of them controls the lightbulb. The other two don't do anything. You must figure out which switch controls the bulb, with some restrictions.

1) You can do whatever you want to the lightswitches, as long as it's either turning them on or turning them off.
2) After fiddling with the lightswitches, you can go upstairs and check the bulb.
3) You cannot see the bulb nor any light shining from it from where you're initially standing.
4) You cannot make multiple trips up and down the stairs.
5) The lamp is in the ceiling and you don't have a ladder.
6) You are a mutant with 15-foot-long arms, so #5 is moot.

So, you fiddle with the switches, you walk upstairs and check the bulb, and then you immediately decide which switch controls the bulb.

How do you do it?

10. On the Top Floor of a Castle Lives a Princess.

A princess occupies the entire top floor of a castle. The floor contains 17 bedrooms arranged in a straight line. Each bedroom has
• an interior door to each adjacent bedroom, and
• an exterior door that opens onto a common corridor.

Every night, just after midnight, the princess moves through an interior door to one of the two neighbouring bedrooms and then spends the entire next day there. She never stays in the same room two nights in a row and she never skips a room.

A prince arrives wishing to marry her. Each morning, before the princess makes her nightly move, he may knock on exactly one exterior door. If the princess is in that bedroom she will open the door and agree to marry him; otherwise nothing happens and the day is lost.

The prince must return to his kingdom after 30 days, so he has at most 30 knocks. Knowing the princess’s routine but not her initial location, can the prince guarantee success? If so, describe an explicit day-by-day strategy.

11.

What costs a dog?

Achmed and Ali are camel-drivers, and on one day they decided to quit their job. They wanted to become shepherds. So they went to the market and sold all their camels. The amount of money (dinars) they received for each camel is the same as the total of camels they owned. For that money, they bought as many sheep as possible at 10 dinars a sheep. For the money that was left, they bought a goat.
On their way home, they got in a fight and decided to split up. When they divided the sheep, there was one sheep left. So Ali said to Achmed, "I take the last sheep, and you can get the goat." "That's not fair," said Achmed, "a goat costs less than a sheep." "Ok," Ali said, "then I will give you one of my dogs, and then we are even." And Achmed agreed.

How much does a dog cost?

12.

A man needs to go through a train tunnel.

A man needs to go through a train tunnel. He starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him. You don't know how far away the train is, or how fast it is going, (or how fast he is going). All you know is that
If the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the train hits him.
If the man keeps running through the tunnel, he will also just barely make it out of the tunnel alive before the train hits him.
Assume the man runs the same speed whether he goes back to the start or continues on through the tunnel. Also assume that he accelerates to his top speed instantaneously. Assume the train misses him by an infinitesimal amount and all those other reasonable assumptions that go along with puzzles like this so that some wanker doesn't say the problem isn't well defined.
How fast is the train going compared to the man?

13.

Line of Geniuses

This question is from my geometry class, it only involves logic not probability. Please help me solve this! It is only middle school, so I don't think it would be TOO hard. Anyways, here it is. Reply as soon as possible, please.
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Three geniuses stand in a line (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat--at random--on the head of each. Then you hide the other two hats and remove the blindfolds.

You then ask each genius to name the color of his hat (which he cannot see).

The rear one says, "I don't know." The middle one says, "I don't know." Then the front one says, "I know."

What color hat is the front genius wearing?????? How does he know with 100% certainty what color hat it is?????

14. Three Lightbulbs.

You are standing outside a basement door, Down the stairs, there are 3 light bulbs.

Next to you, are 3 switches. You cannot see the lights from upstairs, and you must decide which switch controls which lightbulb by going downstairs once.

How do you do this?

15.

The Island of Baal of All the Islands of Knights and Knaves

The Island of Baal
Of all the islands of knights and knaves, the island of Baal is the weirdest and most remarkable. This island is inhabited exclusively by humans and monkeys. The monkey, as well as every human, is either a knight or a knave.
In the dead center of this island stands the Temple of Baal, one of the most remarkable temples in the entire universe. The high priests are metaphysicians, and in the Inner Sanctum of the temple can be found a priest who is rumored to know the answer to the ultimate mystery of the universe; why there is something instead of nothing.
Aspirants to the Sacred Knowledge are allowed to visit the Inner Sanctum, provided that they prove themselves worthy by passing three series of tests. I learned all these secrets, incidentally, by stealth: I had to enter the temple disguised as a monkey. I did this at great personal risk. Had I been caught, the penalty would have been unimaginable. Instead of merely annihilating me, the priests would have changed the very laws of the universe in such a way that I could never have been born!
Well, a philosopher who was searching for the answer to the question, "Why is there something rather than nothing?" arrived on the island of Baal and agreed to try the tests. The first series took place on three consecutive days in a huge room called the Outer Sanctum. In the center of the room a cowled figure was seated on a golden throne. He was either a human or a monkey, and also a knight or a knave. He uttered a sacred sentence, and from this sentence the philosopher had to deduce exactly what he was, whether a knight or a knave, and whether a human or a monkey.
The First Test
The speaker said, "I am either a knave or a monkey." Exactly what is he?
The Second Test
The speaker said, "I am a knave and a monkey." Exactly what is he?
The Third Test
The speaker said, "I am not both a monkey and a knight." What is he?

16. Two Friends, Whom We Will Call Arthur and Robert, Were

Two friends, whom we will call Arthur and Robert, were curators at the Museum of American History. Both were born in the month of May, one in 1932 and the other a year later.

Each was in charge of a beautiful antique clock. Both of the clocks worked pretty well, considering their ages, but one of them lost ten seconds an hour and the other gained ten seconds an hour.

On one bright day in January, the two friends set both clocks right at exactly 12 noon.

``You realize,'' said Arthur, ``that the clocks will start drifting apart, and they won't be together again until---let's see---why, on the very day you will be 47 years old. Am I right?''

Robert then made a short calculation. ``That's right!'' he said.

Who is older, Arthur or Robert?

17.

Brown, Jones & Smith are suspected of income tax evasion.

Brown, Jones & Smith are suspected of income tax evasion. They testify, under oath as follows
Brown: Jones is guilty & Smith is innocent
Jones: If Brown is guilty, then so is Smith
Smith: I am innocent but at least one of the others is guilty.
a) Assuming everybody told the truth who is or are innocent or guilty?
b) Assuming the innocent told the truth & guilty lied who is or are innocent or guilty?

18.

You want to go to a city where everybody always is truthful.

You want to go to a city where everybody always says the truth. On your way there, you reach a crossroad. On one side is the city where everyone says the truth; on the other is a city where everyone lies. There is a man at the crossroad that comes from one of the cities. You do not know from which city the man comes, and you can only ask him one question to find out where the city of truth is. What do you ask him?

19.

There are 2 rooms, one with a gold treasury.

There are 2 rooms, one with a gold treasury and another with deadly snakes. Each room is guarded by a security. Among the two, one always speaks the truth and the other false. You can ask only one question to either of the security to identify the room with gold.

20.

In Ancient Times, Four Mathematicians Discovered a Game of L

In ancient times, four mathematicians discovered a game of logic. The four people were Mr. Macdonald, Mr. Franke, Mr. Kennedy, and Mrs. Sharma. Mr. Kennedy seated the other three people one behind the other so that Mr. Macdonald saw Franke and Sharma and so that Franke and Sharma saw no one.
Mr. Kennedy had 5 hats which he showed to the mathematicians. Three of the hats were grey and 2 white. Mr. Kennedy put a hat on each person's head and hid the remaining two hats in the box. "What colour is your hat, Mr. Macdonald?" asked Mr. Kennedy. Mr. Macdonald did not know. Mr. Franke did not know the colour of his hat either when asked.
Mrs. Sharma, who couldn't see any hats at all, gave the correct answer when asked the colour of her hat. What was the colour of her hat and how did she figure it out?

21. Paying for 7 Days With 2 Cuts

A landlady permitted the students to rent her apartment with the following condition: the student will pay her 7 golden chain for her 7 days stay at her apartment, she is only allowed to cut the chain twice but the student is obliged to pay one chain daily for 7 days. How is it possible?

22. Digit-Wise Subtraction Code

In a secret code, every digit of a number is replaced independently according to a fixed rule. For example:

555555555 → 222222222

Using the same rule, what is the coded form of the number 89898989898?

23. Identify the Lighter Ball

There are 9 similar looking balls with the same weight, but 1 among the 9 balls has relatively lesser weight. You are allowed to use a balance twice. How do you identify the ball with lesser weight?

24. Socks in the Dark Drawer

Ready to go, the light went out, and they have run out of matches to light a candle. Juan still needs to put on his socks. He thinks about taking them and putting them on later in a lit place. He has them in a drawer where there are 20 loose black socks and 20 loose blue socks. How many socks should he take to ensure he has a pair of the same color?

25. Find the Right Switch in One Trip

Near the front door on the ground floor there are three unlabeled switches. One—and only one—of them controls the ceiling light in a room on the fourth floor. You would like to determine which switch it is, but you want to climb the stairs only once.

How can you identify the correct switch with a single trip upstairs?

26. Family Tree Confusion

A man is standing in front of a picture of a man. Then he said Brothers and Sisters have I none but the father of this man (while pointing at the picture) is the son of my father. Who is in the picture?

27. Password Clue at the Club

At a club people were only allowed to enter if you know their password. Fatso wanted to enter but he didn't know the password so he stood just by the corner so that he can get the clue to the password. First person got at the door and the doorman said twelve and he said six and he got in, the next person came and the doorman said six and he said three and he was in. Fatso thought he got the clue and he went to the door. The doorman said ten and obviously Fatso said five and he was kicked out. What do you think was the password and why?

28. Family River Crossing with a 60 kg Boat Limit

Rajan (60 kg), his wife (40 kg) and their son (20 kg) need to cross a river in a small rowing boat. There is no boatman: anyone in the boat must do the rowing.

The boat can carry at most 60 kg at a time.

How can all three family members reach the opposite bank without exceeding the weight limit at any point?

29. Measuring One Gallon

A milkman has 2 empty jugs: a 3-gallon jug and a 5-gallon jug. How can he measure exactly one gallon without wasting any milk?

30. Identifying Hidden Numbers on Cards

You are shown five cards lying on a table (so you can only see one side of each of the five cards). Each card has a single positive integer printed on each side of the card (they may or may not be repeated). The numbers that you can see are: 1, 2, 3, 4, and 5. How many cards must you turn over to completely verify the statement any card that has a 2 on one side has a 5 on the opposite side?

31. Finding the Lighter Iron Ball

There are 4 iron balls, one with a comparatively little less weight than others which we cannot find by carrying it on the hand. When a beam balance (common balance) is given and only 2 chances are given to find the less weight ball. How will you do it?

32. Ring Movement Puzzle

I have 7 pegs on a board, 3 to the left hand blue rings and three to the right have red rings, the centre peg is empty. How I can get the 3 blue and the 3 red to opposite ends if the board. You cannot move backwards.

33. Race Position Riddle

I am in a race and I overtake the second person. What place am I in now?

34. How Far Is the Fall?

In a hotel each story is exactly 10 feet high. From ground level to the floor of the 3^rd story is therefore 30 feet, and from ground level to the 10^th story is 100 feet.

Using the same measurement, how far is it from the ground to the floor of the 20^th story?

35. Surviving Two Hours in a Submerged Car

A man was driving alone when he lost control of his car at high speed. The vehicle crashed through a fence, tumbled down a steep ravine, and finally splashed into a fast-flowing river. With one arm broken, the driver was unable to release his seat belt and escape before the car sank to the bottom.

Rescuers arrived two hours later and hauled the car to the surface. To their surprise, the man was still inside—and still alive. How did he manage to survive two hours underwater?

36. Dividing Eggs Among Sons

A man has three sons but he wants to have a daughter, however, in order to give him a daughter, God asks him how to divide seven eggs equally to three sons.