Can You Solve These Logic Problems?

By: Deborah Beckwin
Image: Colin Anderson Productions Pty Ltd / DigitalVision / Getty Images

About This Quiz

When you hear the word "logic," you may think of a number of things. It's the name of a musical artist. It's a certain way of understanding or thinking about something. In the dictionary, the first definition refers to a science which deals with the principles of reasoning. And that's what this quiz is about.

You'll come across logic in mathematics and in philosophy, and it goes all the way back to Aristotle, branching into a number of fields including informal logic, formal logic, symbolic logic and mathematical logic. 

But logic puzzles use a part of mathematics involving deduction, and author Charles Lutwidge Dodgson, better known under his pen name and author of Alice in Wonderland, Lewis Carroll, created logic puzzles in his book, The Game of Logic

Mathematician Raymond Smullyan created some famous logic problems in his books To Mock a Mockingbird and The Lady or the Tiger. He had a series of puzzles dealing with "knights and knaves", where knights always tell the truth and knaves always lie. You'll see variations of these logic problems in this quiz.

Premises like one party always does this, or another party sometimes does that – that's at the heart of figuring out many logic problems. By deducting what can't be the possible answer, you're able to get closer to the right answer. 

So are you ready to put on your thinking cap and ace these logic problems? Show off your smarty pants and take this quiz! Good luck and have fun! 

What is strange about this sentence? "Was it a car or a cat I saw?"

"Was it a car or a cat I saw?" is what is called a palindrome, a word, number or sentence that reads the same forward or backward. Noon and 2002 are shorter examples.

Tina is two years old, Shirley is also two years old, and Andrea is three years old. How old is Anastasia?

By counting the number of vowels in each name, you can get their age. Anastasia has five vowels her name which makes her five years old.

What is the next letter in the sequence: NWHOIIE_?

So what is this sequence of letters, NWHOIIE_? They are the second letters of number words: oNe, tWo, tHree, fOur, Five, Six, Seven ... which would make the next number eIght, whose second letter is I.

So what about this sequence, what is the next letter? EGBD_?

If you've ever taken piano lessons, you should recognize this sequence. EGBD_ are the line notes on a treble staff, so F would be the next note. "Every good boy does fine" is one mnemonic device that piano students use to remember the order of notes.

Two mothers and two daughters went hiking in a forest and found three orchids. They were able to divide the orchids evenly between themselves, each receiving an orchid. How?

Three generations of women are on the hike, a grandmother, a mother and a daughter. The mother can be both a daughter to the grandmother and a mother to the daughter. So three people were hiking, so three people took three orchids.

A yacht is at anchor, and over the side of it is an eight-foot-high ladder with rungs one foot apart. The tide rolls in at 18 inches per hour. In how many hours will the yacht be overcome by the tide?

So why is the answer never? It's because a yacht floats and even though it is at anchor, it doesn't mean it's sinking as the tide rolls in.

In any calm body of water, you can paddle your kayak at six miles an hour. You're in a stream that flows at two miles an hour. As soon as you paddle upstream, someone loses their hat 18 miles ahead. How long will it take for you to get to the hat?

One way to solve this problem is to ignore the stream's rate of flow. Eighteen miles divided by the six miles per hour it takes you to paddle equals three hours.

"That Jim is a rich guy!" says Frank. "In fact, he owns 1,000 cows or more." Jack interjects, "Now hold on. I know that he owns fewer than 1,000 cows." Sarah pipes up and says "That's not what I heard. Jim owns at least one cow." Only one of these statements can be correct, so how many cows does Jim own?

For Frank's statement to be true, Jim can own 1,000 or more cows, but for Sarah's statement to be true, Jim can own at least one cow, and that means both Frank and Sarah have true statements. But Jack's statement can't be true with neither Frank's (fewer than 1000 cows is less than 1000 cows or more) nor Sarah's (fewer than 1000 can be zero, but Sarah's statement means that Jim has to have at least one). So Jack's statement is the only one which can be true.

A person is trapped in an empty room with only two possible exits. Through door #1 is a room made with magnifying glass. Anything or anyone who enters that room is immediately burned up by the sun's magnified rays. Through door #2 is a room that immediately fills up with poisoned gas, killing anyone upon entry. How does this person escape?

There's no way to get through a room with poison gas, but there is a way of escape. The sun eventually will set and then the person can go through door #1 with any problems.

Darla has 12 green earrings and 12 red earrings in her jewelry box. In total darkness and without looking, how many earrings must Darla take to be sure that she can get a matching pair?

This has to do with probability. If Darla first chose a red earring and then a green earring, then the next earring has to be a match, no matter the color.

There are three boxes of berries, but they have all been mislabeled. The first box is labeled "Strawberries," the second box is labeled "Blueberries" and the third box is labeled "Strawberries & Blueberries." You can only pick one berry from one box to help you label these boxes correctly. Which box will you choose?

Since all boxes are labeled incorrectly, then you know the "Strawberries & Blueberries" box only contains strawberries or blueberries. For example, if you find a strawberry in this box, you will relabel it "Strawberries," the "Blueberries" box must contain strawberries and blueberries, and the "Strawberries" box must contain blueberries.

Donna and Debbie were identical twins born in Oklahoma City in 1992. Debbie was born before Donna, but on their birth certificates, it shows Donna is older than Debbie. What's the explanation?

Debbie was born at 1:50 a.m., right before Daylight Saving Time ended. Then Donna was born 15 minutes later, but it would be shown as 1:05 a.m. on her birth certificate.

A slug is at the bottom of a 33-foot well. During the day, it slithers up three feet, but at night as it sleeps, it slides down two feet. How many days will it take for the slug to finally reach the top of the well and slither to freedom?

The net gain of each day is one foot. On the 29th day, the slug will have reached the top by the end of the day without slipping down again.

A woman looks at a photo of someone, and her friend asks her who that person is. The woman responds, "I don't have any siblings. But that woman's mother is my mother's daughter." So who is she looking at?

"That woman's mother" is the woman looking at the picture. "My mother's daughter" is also the woman looking at the picture. So the "woman" is the daughter of the woman looking at the picture.

A dealer buys a car for $500, sells it for $600, buys it back for $700 and sells it for $800. How much was his profit?

The total profit from these four sales is $200. The dealer made a profit of $100 when they sold the car the first time, and the dealer made another $100 when they sold it a second time.

You're trapped in a room with two doors. One door will lead to your freedom while the other will lead to a lifetime of imprisonment. Two androids are by these doors and will let you choose one door, but you must go through it after you ask your decision. You can only ask one android one question, but one android always lies and the other always tells the truth. You don't know who is honest and who is the liar. So what question would you ask?

If you ask the lying android what the truthful android would say, they would be lying, so you can choose the other door. If you ask the truthful android what the lying android would say, they would truthfully state the lie the lying android would tell you, and you can choose the other door. No matter which android you choose, the lying android should be your focus here and their lie will point you to freedom, allowing you to choose the other door.

Two friends plan to get together and start riding their scooters toward each other, riding at a speed of five miles per hour and living 30 miles apart. One of them has a pet dragon that flies at a rate of 15 mph, back and forth until they meet. How many total miles does the dragon fly?

It takes three hours for the friends to meet in the middle, since they are moving at the same rate, i.e., 15 miles divided by five miles per hour equals three hours. So you would take the dragon's flight speed of 20 mph and multiply it by the length of time it took for the friends to meet up. You would get the total distance of 60 miles.

You randomly ask people if they have two children and if one was a girl born on a Friday. After some searching, you find someone who can answer yes to both questions. What is the probability that this person has two girls? You can assume there's a 50/50 chance of giving birth to either sex and that there's an equal probability for giving birth on any day of the week.

So to solve this, you have to look at the possible sex combinations of two children – boy boy, boy girl, girl boy and girl girl, so that's seven times two squared, which is 196 possible combinations. Then you focus on all the combinations with a girl born on a Friday, leaving you with 27 combinations left. Then focusing on the girl girl combinations, you subtract the boy girl combinations (14), and you're left with 13.

You have two candles of varying lengths and thickness, but each burns in exactly two hours. But you don't know what the burn rate is. How can you start to measure 90 minutes without a watch or clock and only matches and candles?

After the one lit at both ends has been completed, you know that is 60 minutes. After that, the second candle that has been burning at one end, you light the unlit end. Because you've now cut this candle's burn rate in half, it will only take 30 minutes for this candle to burn down, with a total of 90 minutes expired.

Katherine walks through a meadow and finds a frog and a grasshopper. The frog lies on Mondays, Tuesdays and Wednesdays, but tells the truth during the other days of the week. The grasshopper lies on Thursdays, Fridays and Saturdays, but tells the truth during on the other four days. The frog tells Katherine, "Yesterday, I was lying." The grasshopper adds, "So was I." On what day were these things said?

You have to assume that one of these animals is lying, because both animals speak the truth on Sundays, so it's not Sunday. The only day the grasshopper could tell the truth about lying yesterday would be Sunday. And for the frog, the only other day they could tell the truth about lying the day before would be Thursday.

Dave asks his friend Sheila when her birthday is. Shelia replies, "I was 40 the day before yesterday, and next year, I will be 43." When is Sheila's birthday?

Sheila's birthday is Dec. 31. When she was talking to her friend Dave, it was Jan. 1 (the following day), so she is now 41 years old – but the day before yesterday, she was still 40. Her 42nd birthday will be on Dec. 31 of the year they're speaking in, and she will turn 43 in the following year.

A nature photographer walks out their front door, walks a mile south, walks a mile east, sees a bear and tries to take its picture. The bear gets up on its hind legs and roars. The photographer runs a mile north and ends up in front of their home. What color is the bear?

The photographer sees a polar bear, putting the hunter's home at the north pole (where polar bears live). Nearer the poles, because the earth is a globe, the latitudes are shorter, which means paths don't go in a straight line and have more curve to them. That's how the photographer ended up back at their home.

A boutique ran a promotion giving away a free pair of khakis. All you had to do was you had to try on a pair and put your right hand in the left pocket and your left hand in the right pocket, with both hands reaching the bottom of both pockets at the same time. People in the store found this impossible until someone walked in and was able to do it. Which of the following answers best describes how they got their free pair of khakis?

By turning the khakis inside out, the pockets switch places, so the left pocket was on the right side and the right pocket was on their left side. He put his hands in the pockets without having to do anything to his hands or having extra long fingers. Another option would be that he tried on the khakis backward.

You've moved in a new town and you need to get a manicure. There are only two manicurists in town. The first manicurist has a messy shop and ugly nails. The other manicurist has a clean store and has beautiful nails. So which one would you choose and why?

Most likely, but not always, a beautician has to go to another beautician to get their nails done. So the person with the best nails probably got them from someone else, so you should check out the messy manicurist since they probably provided the neat manicurist with their manicure.

You go with your partner, who is a bus driver, to a party for bus drivers and truck drivers. From living with your partner, you've learned that bus drivers always tell the truth about everything, but truck drivers are always lying about something. Two people, Shawn and Dylan, come to your table. Shawn says, "I'm a truck driver, but Dylan is a bus driver." So based on what you know, what the actual professions of both people?

Since bus drivers don't lie, Shawn would not introduce himself as one. So Shawn is being truthful about his profession. But since truck drivers always lie about something, that means that Dylan is not a bus driver but is also a truck driver.

You're watching the 11 p.m. news and the meteorologist gives a forecast, saying that it's currently raining and will continue to rain for the next day. But in 48 hours, it'll be sunny and bright out. You know this is wrong, but why?

If you're being exact with what the meteorologist said, then 48 hours from 11 p.m. will be nighttime two days later. Typically, it can't be sunny and bright out.

The tortoise returned from a race where they competed with a hare, a snail and a snake. The tortoise tells you that the hare finished two places ahead of them, the snail was neither first nor last, and the hare was not second. Can you figure out which animals finished in which place?

In this animal race, unlike "The Tortoise and the Hare," the hare wins this race. Because the hare was two places ahead of the tortoise, the hare could never be last out of four animals, and the hare could not be second. The snail could neither be first nor last, so that puts it in second place, with the snake slithering into last place.

You, your brother, his son and his daughter are playing badminton. Your brother is directly across the net from his son. His daughter is diagonally across from the sibling of the best player. The worst player and the best player are on the same side of the net. So who is the worst player?

If your niece is diagonally across from the best player's sibling, and your nephew is directly across from your brother, then that makes you the best player. That's because your niece is diagonally across from your brother, who is then the worst player.

What is the closest familial relationship you can have with your mother's brother's brother-in-law?

It's true that your mother's brother's brother-in-law could be another uncle, if your mother and her brother have another sibling. But the closest relationship you could have would be your father.

You're at a football watching party and Michigan and Ohio State are playing. Your friend introduces you to one Michigan alum and one Ohio State alum. A man shakes your hand saying, "Hi, I went to Michigan." A woman waves and smiles saying, "Hi, I attended Ohio State." Your friend whispers in your ear that at least one of them is lying. Neither of them are wearing any school paraphernalia, so which one is the liar?

If only one of them is lying, then that means either both of them went to Michigan of Ohio State. But your friend tells you that one of them went to Michigan and one of them went to Ohio State. This means they're both lying.

The Davidsons are a musical family with several kids. Five kids play piano, four kids play guitar and three kids play the violin. Each child plays only two instruments. What is the least number of kids in the Davidson family?

The longer way of doing this is counting off the possible combinations (e.g., piano guitar, piano violin, violin piano, violin guitar, guitar piano, guitar violin). The shorter way is to multiply the number of instruments each child could play (two) by the number of instruments (three). Either will give you the answer of six.

Let's pretend you've never seen a parrot before. You're in a tropical rainforest with two friends. One shows you a hummingbird and tells you it's a parrot. The other friend shows you a toucan and tells you it's a parrot. Which friend is telling you the truth?

The only thing you don't know is what a parrot looks like. But we're not pretending that that you don't know what a hummingbird and toucan look like. You shouldn't trust either friend.

You've been prescribed this obnoxious prescription where you have to take two pills every 15 minutes for three hours. Within the first hour, how many pills will you have taken?

You may think this is six pills, but you would have taken the pills at the top of the hour, and then every 15 minutes after that. Two pills multiplied by the four times you would have taken it in the first hour is eight.

Zoe Abelson consistently has the worst grades in her algebra class. Everyone recently took a test, but when the grades were posted, Zoe's grades were at the top of the list. What's the reason?

Zoe's surname is Abelson, which means that she will have her name listed first no matter what. You can believe that she consistently got bad grades, and usually grades are not listed in reverse grade order.

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