## Logic Puzzles

### June 7, 2013

### http://arthurjohnkyriazisgoogleblog.blogspot.com/2013/06/logic-puzzles.html

1. The Missing PieceBelow 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?

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

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### 3. The IslandersThere 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.

Can you guess what the third Islander will answer to the same question?

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### 4. Five GallonsYou 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.

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### 5. Two StringsYou 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?

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### 6. The CubesA 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”.

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### 7. The Pot of BeansA 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?

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### 8. The PigeonTwo 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?

Guess: Guess | Show Hint Show Solution

### 9. The SocksThere 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?

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1. The CamelsFour tasmanian camels traveling on a very narrow ledge encounter four tasmanian camels coming the other way.

As everyone knows, tasmanian camels never go backwards, especially when on a precarious ledge. The camels will climb over each other, but only if there is a camel sized space on the other side.

The camels didn’t see each other until there was only exactly one camel’s width between the two groups.

How can all camels pass, allowing both groups to go on their way, without any camel reversing?Show Hint Show Solution

### 2. The WaiterThree men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14…..where has the other $1 gone from the original $15?

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### 3. The Boxes

#### There are three boxes. One is labeled “APPLES” another is labeled “ORANGES”. The last one is labeled “APPLES AND ORANGES”. You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?

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4. The CannibalsThree cannibals and three anthropologists have to cross a river.

The boat they have is only big enough for two people. The cannibals will do as requested, even if they are on the other side of the river, with one exception. If at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them.

What plan can the anthropologists use for crossing the river so they don’t get eaten?

Note: One anthropologist can not control two cannibals on land, nor can one anthropologist on land control two cannibals on the boat if they are all on the same side of the river. This means an anthropologist will not survive being rowed across the river by a cannibal if there is one cannibal on the other side.

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5. The FatherA mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.

Where’s the father?

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6. The Double Jeopardy DoorsYou are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don’t know which is which.

There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.

You can, however, ask one robot one question. The problem is one robot always tells the truth ,the other always lies and you don’t know which is which.

What is the question you ask?

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7. The FrogA frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

Guess: Guess | Show Hint Show Solution

8. The BobberYou can paddle your canoe seven miles per hour through any placid lake. The stream flows at three miles per hour. The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you.

How many hours does it take for you and the bobber to meet?

Guess: Guess | Show Hint Show Solution

9. The SocksCathy has twelve black socks and twelve white socks in her drawer.

In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?

Guess: Guess | Show Solution

10. There is something about MaryMary’s mum has four children.

The first child is called April.

The second May.

The third June.

What is the name of the fourth child?

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11. Petals around the roseThe name of the game is Petals Around the Rose, and that name is significant. Newcomers to the game can be told that much. They can also be told that every answer is zero or an even number. They can also be told the answer for every throw of the dice that are used in the game. And that’s all the information they get.

The person who has the dice and knows the game, rolls five dice and remarks almost instantly on the answer. For example: in Roll #1 the answer is two.

Roll #1.

“The answer is what?” says the new player.

“Two.”

“On that roll?”

“Yes.”

“Would it still be two if I moved the dice without turning any of them over, just rearranging the pattern?”

“I can tell you only three things: the name of the game, the fact that the answer is always even, and the answer for any particular throw. In this case the answer is two.”

“So that’s how it is. What am I supposed to do?”

“You’re supposed to tell me the answer before I tell you. I’ll give you all the time you want, but don’t tell me your theory, just the answer. If you figure it out, you don’t want to give the idea away to these other jokers around you. Make them work for the answers, too. If you get the answer right on six successive rolls, I’ll take that as prima facie evidence that you understand the game.”

“OK, roll again.”

Roll #2.

“I give up. What’s the answer?”

“The answer is eight.”

“Roll again.”

Roll #3.

The answer is fourteen.

Roll #4.

The answer is zero.

Roll #5.

The answer is four.

Roll #6.

The answer is… Guess |

An integral part of the puzzle is that those who have solved it are urged to keep the solution a secret, so there is no solution posted here. It is not a hard puzzle to figure out however.

A claim that often accompanies these instructions is that the smarter an individual, the greater amount of difficulty the individual will have in solving it. If such a statement is true, it may be attributed to the fact that “smarter” people tend to be more knowledgeable in a wide range of information which they may unnecessarily attempt to draw upon to solve the puzzle.