Logic Puzzles


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1. The Camels

Four 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?

Hint:

Use match sticks or coins to simulate the puzzle.

Solution:

First a camel from one side moves forward, then two camels from the other side move forward, then three camels from the first side move forward etc...

 

 

 

 

 

 

 

 

etc...


2. The Waiter

Three 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?

Solution:

The payments should equal the receipts. It does not make sense to add what was paid by the men ($12) to what was received from that payment by the waiter ($2)

Although the initial bill was $15 dollars, one of the five dollar notes gets changed into five ones. The total the three men ultimately paid is $12, as they get three ones back. So from the $12 the men paid, the owner receives $10 and the waiter receives the $2 difference. $15 - $3 = $10 + $2.


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?

Solution:

Pick from the one labeled "Apples & Oranges". This box must contain either only apples or only oranges.

E.g. if you find an Orange, label the box Orange, then change the Oranges box to Apples, and the Apples box to "Apples & Oranges."


4. The Cannibals

Three 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.

Solution:

First, two cannibals go across to the other side of the river, then the rower gets called back. Next, the rowing cannibal takes the second across and then gets called back, so now there are two cannibals on the far side.

Two anthropologists go over, then one anthropologist accompanies one cannibal back, so now there is one anthropologist and one cannibal on the far side.

The last two anthropologists go over to the far side, so now all the anthropologists are across the other side, along with the boat and one cannibal.

In two trips, the cannibal on the far side takes the boat and ferries the other two cannibals across the river.


5. The Father

A 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?

Solution: With the mother. If you do the math, you find out the child will be born in 9 months.

6. The Double Jeopardy Doors

You 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?

Hint:

The two robots know each others personality. That they talk when they're bored, lonely, etc. Try to get the two robots to cancel their evil & good ways out.

Solution: Ask one robot what the other robot would say, if it was asked which door was safe. Then go through the other door.

7. The Frog

A 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.

Hint:

Try to think the problem through for a five meter well. Now what is the solution for the 30 meter well?

Solution:

28

Each day he makes it up another meter, and then on the twenty eighth day he can leap three meters and climb out.


8. The Bobber

You 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?

Hint:

Assume the stream moves at a perfectly constant three miles an hour.

Solution:

2

Ignore the speed of the stream, as the cork will be carried along at three miles per hour as will you. It takes two hours to travel fourteen miles, at a rate of seven miles per hour.


9. The Socks

Cathy 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?

Solution:

3

Socks do not come in in left and right, so any black will pair with any other black and any white will pair with any other white. If you have three socks and they are either colored black or white, then you will have at least two socks of the same color, giving you one matching pair.


10. There is something about Mary

Mary'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?

Solution:

Mary.

Mary's mothers fourth child was Mary herself.


11. Petals around the rose

The 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. 4 1 6 3 6

"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. 5 6 5 4 4

"I give up. What's the answer?"

"The answer is eight."

"Roll again."

Roll #3. 3 5 5 5 6
The answer is fourteen.

Roll #4. 2 6 2 1 4
The answer is zero.

Roll #5. 4 3 2 1 3
The answer is four.

Roll #6. 6 5 6 2 2

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.

Solution: We used to not publish an answer to this classic problem, now with the advent of Generative AI, the answer is easily obtained, so we now publish the solution for all who are interested...

The answer is determined by the number of dots on the dice that show a value of 2, 4, or 6, as these values contribute to the 'petals' around the 'rose' (the center dot of a 5). The answers for the rolls correspond to the total number of these petals: Roll #1 has 2 petals, Roll #2 has 8 petals, Roll #3 has 14 petals, Roll #4 has 0 petals, and Roll #5 has 4 petals.


12. Watson's Selection

You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown.
Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?

4

Hint:

A response that identifies a card that need not be inverted, or that fails to identify a card that needs to be inverted, is incorrect. The original task dealt with numbers (even, odd) and letters (vowels, consonants).

Solution: The correct response is to turn over the 8 card and the brown card.

The rule was "If the card shows an even number on one face, then its opposite face is red." Only a card with both an even number on one face and something other than red on the other face can invalidate this rule:

If the 3 card is red (or brown), that doesn't violate the rule. The rule makes no claims about odd numbers.

If the 8 card is not red, it violates the rule.

If the red card is odd (or even), that doesn't violate the rule. The red color is not exclusive to even numbers.

If the brown card is even, it violates the rule.

101. Bad School Boys

During the lunch hour at school, a group of five boys from Miss Jones home room visited a nearby lunch wagon. one of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:
1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are lying."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Jones is correct, can you determine who took the candy bar?

Solution:

Abe took the candy bar.


102.

Oil Wells

You are an oil mogul considering the purchase of drilling rights to an as yet unexplored tract of land.
The well's expected value to its current owners is uniformly distributed over [$1..$100]. (I.E., A 1% chance it's worth each value b/w $1..$100, inclusive).
Because you have greater economies of scale than the current owners, the well will actually be worth 50% more to you than to them (but they don't know this).
The catch: although you must bid on the well before drilling starts (and hence, before the actual yield of the well is known), the current owner can wait until *after* the well's actual value is ascertained before accepting your bid or not.
You want to maximize your profits. You didn't get rich by scoffing at small dollar amounts. A dollar is a week's wages.
Bids must be in even rounded dollar values. How many dollars should you bid?

Hint:

The seller will only sell to you if you bid either a fair price, or if you bid more than the well is worth to him.

Solution:

Bid $1 for a certain profit of 50 cents, assuming the seller will sell the well at a fair market price. If you bid $2 you may lose 50 cents or you may gain $1, and the average expected profit is only 25 cents. If you bid $3, you might break even, or you might lose $1.50 or you might gain $1.50, so the average expected profit is nothing. All other bids are losing propositions. The classic “winner’s curse” version often assumes values are continuous from $0 to $100. In that version, the right answer is bid $0, because every accepted bid has negative expected value.


105. You Are on Your Way to Salalalah

You are on your way to Salalalah and it is midnight and you are in the middle of the dessert, when your tire goes flat. You remove the four bolts of your tire and keep them on the side of the road. Suddenly, a truck passes by at a very high speed and your bolts just go flying all over and you can't find them. What do you do to replace the tyre? You know there is a Tyre Repair Shop (equipment supplied by TTC ) about 20 KM away. As it is midnight no one will stop to help you. There are no camels around that you can ride and if you are thinking of using a flash light or wait till the sun rises hmmm its not the answer .

Solution:

Remove one bolt from each of the other tires and use them to secure the spare tire.


106. I Have a Bag, With Some Balls in it

I have a bag, with some balls in it. All but 4 are blue, all but 4 are green, and all but 4 are red. How many balls do I have in total?

Solution:

The total number of balls in the bag is 6. You can have 2 blue, 2 green, and 2 red balls. This configuration satisfies the conditions that all but 4 are blue, all but 4 are green, and all but 4 are red.


107. Two Fathers Gave Their Two Sons Some Money.

two fathers gave their two sons some money.one gave his son 150 pesos and other father gave 100 pesos to his son.when the two sons counted their money,they found that all together they had become richer by only 150 pesos.how come?

Solution:

The two fathers are actually a grandfather and a father. The grandfather gives 150 pesos to his son (the father), and then the father gives 100 pesos to his son (the grandson). Although the total amount given is 250 pesos, the increase in wealth is only 150 pesos because the father is also a son, and his original amount is not counted twice.


108. There is the Enterance of the Place Where Two Guards Are the

there is the entrance of the place where two guards are there outside,one guard is facing north and another south, the one on the north smiles and the another one asks why ? how ?

Solution:

The two guards are facing each other, with one guard facing north and the other facing south. The guard facing north smiles because he is looking at the other guard, while the guard facing south is looking directly at him.


109. Four People Meet in a Room. Each Person Shakes Hands

Four people meet in a room. Each person shakes hands once with each other person.

How many hand shakes are there in all?

Solution:

In a group of four people, each person shakes hands with three others. Since each handshake involves two people, the total number of unique handshakes can be calculated using the formula n(n-1)/2, where n is the number of people. Thus, the total number of handshakes is 4(4-1)/2 = 6.


111. Arrange 10 Balls in 5 Lines

Arrange 10 balls in 5 lines in such a way that each line contains 4 balls and only 4 balls.

Solution:

Arrange the balls in the shape of a pentagonal star, placing 4 balls at each of the intersecting points of the 5 lines. Each line formed by connecting the points of the star contains exactly 4 balls.


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

On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the outside corridor. The princess sleeps in a different bedroom each night by opening the door to an adjoining bedroom and spending the night and the next day in that room.

One day a prince arrives at the castle and is desirous of marrying the princess. The guardian angel at the castle tells him of the princess sleeping patterns and informs him that each morning he may knock on one of the outside doors. If the princess happens to be behind that door, she will open it and consent to marry him. The prince also has a return ticket to his kingdom in 30 days; so he can make at most 30 attempts. Can the prince win the hand of the princess and if so, what is his strategy?

Solution:

The prince should knock on door 9 every day. This strategy ensures that he will eventually find the princess regardless of her movement pattern, as she can only move to adjoining rooms. By starting at the middle door, he maximizes the chances of encountering her within the 30 days.


113. Where Must Dracula Be

There is one and only one Dracula
This Dracula is locked in three and only three caskets
One is solid red, one is solid yellow, one is solid blue
The caskets have inscriptions
Red says, Dracula is here (meaning inside the casket)
Yellow says, Dracula is not here (not inside the casket)
Blue says, Dracula is not in the red casket
At most one inscription is true

Where must Dracula be

Solution:

Dracula must be in the yellow casket. If the red casket's inscription is true, then Dracula is in the red casket, which would make the blue casket's inscription true as well, violating the rule that at most one inscription can be true. If the blue casket's inscription is true, then Dracula cannot be in the red casket, leaving the yellow casket as the only option where Dracula can be. Therefore, the only consistent scenario is that the yellow casket's inscription is false, confirming that Dracula is in the yellow casket.


114. A Man in a Cave

theres a man in a cave, staring at a blank wall. behind him is a large fire. all the sudden the man exclaims "i see a book." without turning around, what is he talking about?

Solution:

The man is likely referring to the shadows cast on the wall by the fire behind him, which can create shapes that resemble a book.


115. Spider on the Wall

There are 5 girls over for a sleep over, one of the girls gasps and yells "OMG there's a spider on the wall" the other girls scream and yell "kill it." Yet the spider makes it outside alive. How is this?

Solution:

The spider was already outside, and the girls were reacting to its shadow or simply panicking without any real threat to the spider.


116. A Bag of Gold Coins

I have 10 bags filled with 10 gold coins a piece, which equals 100 gold coins. 9 bags, are filled with counterfeit coins (90 total coins), while only 1 bag is filled with real coins (totaling 10 coins). They appear the same in shape, color, texture, and size. The only difference is their weight. Counterfeit coins weigh 1oz, while the real coins weigh 1.1 oz. Using a scale, only once, how would I determine which bag was filled with real coins?

Solution:

Take 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3, and so on, until you take 10 coins from bag 10. Weigh all the coins together. The total weight will be 100 oz if all coins were counterfeit. For each bag, the excess weight over 100 oz will indicate the bag with real coins; for example, if the weight is 100.3 oz, then bag 3 has the real coins.


117. Dead Man

A man is found, hanging, in a room. There are no windows, the door is locked from the inside. There is NOTHING in the room. All that is found is the man hanging, and a puddle of WATER underneath him. How did he hang himself?

Hint:

He wasn't murdered, and there was no chair for him to get up and hang himself.
:?:

Solution:

The man stood on a block of ice to hang himself. Once he had hung himself, the ice melted, leaving only a puddle of water underneath him and no means for him to have stood on anything else.


118. Ducks....

There are several ducks in a row:
-two at the front
-two at the back
-one in the middle.

How many dicks are there in total?

Solution:

5


119. The Ghost People

A man is sleeping about 8pm until a loud noise awakes him. When he look outside, he saw many people and police in his neighbor. He went there and he saw his neighbor Jaylord dead. He was shocked. And then a second later he heard some voice calling him. He find and follows where the voice is coming. He follows the voice until he goes in 2nd floor. But all there is nothing. The voice calling him again and he follows it up to 3rd floor. He saw a girl at the window looking at him. The boy heard a noise in his back but its just only a mouse. When he looks again at the window, the girl was gone. The boy was scared so he goes downstairs. But all the people and police and even the corpse are gone but still, he is hearing the noise of the people. Where are them?

Solution:

The man is experiencing a hallucination or a dream. The loud noise that woke him up may have caused him to imagine the events he witnessed, including the dead neighbor and the girl at the window. The girl likely fell from the window while he was distracted by the noise, which is why she disappeared. When he went downstairs, he heard the noise of people returning to see her corpse, explaining why he could still hear them despite not seeing anyone.


120. Sunny Day

A man stays in a room that has no windows or doors, the only thing in there are a very small holes and an open light bulb. The question is.... how does the man knows if it is already night or night will coming??? without looking outside through the holes.

Solution:

The man can determine if it is night or day by observing the light bulb and the small holes in the room; if the light bulb is on, it indicates daytime, while if it is off and no light comes through the holes, it suggests nighttime.


121. You Are Shown a Set of Four Cards Placed on a Table

You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?

Solution:

You must turn over the card showing 8 to verify that it has red on the other side, as it is an even number. Additionally, you must turn over the brown card to ensure that it does not have an even number on the opposite side, which would violate the proposition. Turning over the card showing 3 or the red card is unnecessary, as they do not provide relevant information to test the proposition.


122. Mathematics....

Three 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? :idea: :?: :?: :!: :?: :!: :!: :twisted: :evil:

Solution:

The confusion arises from the incorrect addition of the amounts. The three men paid a total of $12 after receiving $3 back ($1 each), and the waiter kept $2. The correct way to account for the money is to consider the total cost of the meal ($15) as $12 (paid by the men) plus $3 (returned to them), which equals $15. Therefore, the chef has $10, the waiter has $2, and the men received $3 back, with no dollar missing.


123. You Have 2 Eggs.

You have 2 eggs. You are on a 100 floor building. You drop the egg from a particular floor. It breaks or survives. If it survives you can throw the same egg from a higher floor. How many attempts do you need to identify the max floor at which the egg doesn't break when thrown down?

Solution:

14


128. Brother's Age Difference

You are 5 years old. Your brother is 15 years older than you. How old is your brother?

Hint:

Add the age difference to your current age.

Solution:

Your brother is 5 + 15 = 20 years old.


129. Mary's Fourth Child

Mary's mum has four kids, one of them is called March, another is called April, and another one is called May, what's the name of the fourth child?

Hint:

Pay attention to the first part of the question.

Solution:

Mary


131. The Truth-Telling Robot Dilemma

There are two doors: one that you can live if you go through, and one that you die with robots in front of them. One robot tells the truth and one lies. You get to ask one robot one question. What robot would you ask, and what question?

Hint:

Ask a question that reveals the truth about the doors regardless of which robot you ask.

Solution:

You should ask either robot: 'If I were to ask the other robot which door leads to life, what would they say?' Then choose the opposite door.


132. Counting the Surviving Pigs

A farmer has 18 pigs, all but 7 died. How many left?

Hint:

Consider the phrase 'all but 7'.

Solution:

7 pigs are left.


134. Frogs in the Well

There are 6 frogs in the well, 4 died. How many are there now?

Hint:

Consider whether the dead frogs are still counted as part of the total.

Solution:

There are still 6 frogs in the well, as the dead frogs are still present.


135. Argots and Knicks Relationship

Are all argots also knicks?

1) All argots are drones

2) All drones are knicks

Solution:

Yes, all argots are knicks.


136. Aging Backwards in Time

Kiran was 20 years old in 1980 but only 15 years old in 1985. How come?

Hint:

Consider the possibility of different calendars or systems of measuring time.

Solution:

Kiran was born in 1960 B.C. In 1980 A.D., he would be 20 years old, and in 1985 A.D., he would be 15 years old.


137. Identifying the Fifth Daughter

Rachels dad had five daughters lala, lolo, sarah, carcar, and dardar who is the fith daughter?

Hint:

Pay attention to the wording of the question.

Solution:

Rachel


138. Ensuring Two Black Socks

A bag contains 12 white and 12 black socks. How many socks should be withdrawn from the bag to be sure exactly two of the socks taken out are black?

Solution:

14


314. Where is the Two Rupees?

Three persons went to buy a clock worth Rs.60. Each gave Rs.20. When the shop owner realized the clock was only worth Rs.50, he returned Rs.10. He took Rs.4 for himself and returned Rs.2 to each person. Now, the persons paid Rs.54 for the clock and the shopkeeper took Rs.4. Where is the two rupees?

Solution:

The confusion arises from miscalculating the total. The three persons paid Rs.54, which includes the Rs.50 for the clock and Rs.4 kept by the shopkeeper. The Rs.2 returned to each person is part of the Rs.54, not an additional amount. Therefore, there is no missing Rs.2.


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