How Many of These Tough Logic Puzzles Can You Solve?

Here at Popular Mechanics, we love riddles, brain-teasers, and logic puzzles so much that we decided to put together a collection of our favorites head-scratchers. These little games get increasingly more difficult as you click through, so try and make it to the end if you think you could handle it.

PLUS: The Amazing Math Inside the Rubik's Cube Puzzle

There is a lightbulb inside a closet. The door is closed, and you cannot see if the light is on or off through the door. However, you know the light is off to start. Outside of the closet, there are three light switches. One of the switches controls the lightbulb in the closet. You can flip the switches however you want, but once you open the door, you can no longer touch the switches. How do you figure out without a doubt which switch controls the light?

Flip those switches and check out the solution here.

Adam and Eve play rock-paper-scissors 10 times. You know that: Adam uses rock three times, scissors six times, and paper once. Eve uses rock twice, scissors four times, and paper four times. There are no ties in all 10 games.The order of games is unknown. Who wins? By how much

Hint

It can be tricky to figure out the solution just by looking at the list of information—grab a pad and pen.

Throw down your hand, don't eat that apple, and check the solution here.

A farmer lives on a small plot of land next to a river. One day, he travels across the river in a small boat and purchases a fox, a chicken, and a bag of corn from a feed and supply store. When the farmer returns to his boat to cross the river again and go home, he realizes he has a dilemma.The farmer can only take one item in his small boat at a time, otherwise he risks capsizing. He cannot leave the fox alone with the chicken, because the fox will eat the chicken. He cannot leave the chicken alone with the corn, because the chicken with eat the corn.How does the farmer successfully get all three items across the river?

Hint

For those who need a little help: The farmer cannot leave the chicken alone with anything—it will eat the corn or be eaten by the fox. So, how does the farmer get all three items across the river without ever leaving the chicken alone with the fox or the bag of corn?

You can see the answer to the riddle here, but wouldn't you rather solve it first?

You work in a factory that boxes apples and oranges to ship around the world. One day, the labeling machine goes haywire and incorrectly labels the crates of fruit.Your coworker decides to play a game. He pulls up three crates of fruit and tells you that one of them has apples in it, one has oranges in it, and the last one has both apples and oranges in it. You can see that one of the crates is labeled "A" for apples, another is labeled "O" for oranges, and the third is labeled "A+O" for both apples and oranges. Your coworker reminds you that all three crates are incorrectly labeled.You get to pick one crate, and your coworker will pull a fruit out of it and show you what it is. You get to do this only one time. How can you determine—without a doubt—which crate has apples, which one has oranges, and which one has both?

Hint

You don't need a hint, but here it is:If you have your coworker pull a fruit out of the crate that says "O" on it, and the fruit he pulls is an apple, then you don't know whether that crate has just apples or if it has both apples and oranges. But what would you know if he pulled an apple out of the crate labeled "A+O"?

Knock this one around in the ol' noggin for a while, and once you figure it out, feel free to check out the solution here.

NYPD officer John McClane and shop owner Zeus Carver are in quite the predicament. A psychopath who calls himself Simon is detonating bombs all over New York City. McClane and Zeus find another bomb in Central Park, and to disarm it they need to solve Simon's riddle.The bomb is in a briefcase with a precise electronic scale. McClane and Zeus have a 5-gallon jug and a 3-gallon jug. They are standing next to a fountain where they can take as much water as they want. They have 5 minutes to put one of the jugs on the scale with exactly 4 gallons of water in it, or the bomb will detonate. How do you get exactly 4 gallons of water into one of the jugs?

Hint

Just start filling up one of the jugs all the way and pouring it into the other one, and see where that gets you.

Once you have 4 gallons in one of the jugs, you can check the answer here.

Four people are trying to cross a sketchy rope bridge in the middle of the night. Only two can cross at a time. They only have one flashlight, and so one person must bring it back across the bridge to the starting side before anyone else can cross. One person takes 1 minute to cross, another takes 2 minutes to cross, another takes 5 minutes to cross, and the last person takes 10 minutes to cross. Hypothetically, if the 2-minute person and the 5-minute person crossed together, that would take a total of 5 minutes (but someone needs to bring the flashlight back, resulting in 7 minutes spent if the 2-minute person returns with the light). Everyone needs to get across in 17 minutes or less, otherwise they will be ripped apart and consumed by zombies.

Hint

Are you sure you want a hint? Here it is: The first assumption that many people make when attempting to solve this riddle is that the 1-minute person shuttles everybody across, returning with the flashlight every time. This is incorrect. There is a faster way.

After you have come up with an answer on your own, you can see the solution to the riddle here—we operate on the honor system.

You're a thief, and you've managed to break into the vault of an ancient bank filled with 100 sacks of coins. One of the sacks contains gold coins, while the other 99 are filled with counterfeit gold coins. You cannot tell the difference between the gold coins and the fakes by handling the coins, looking at them, biting them, or testing them.The fake coins weigh exactly 1 ounce each, while the real gold coins weigh 1.01 ounces. There is a large scale with enough room for all the sacks in the vault, but as soon as you weigh something it will trigger an alarm, so you can use the scale just once before you must flee the vault. How can you figure out which sack of coins contains the real gold by only weighing something on the scale once?

Note: The scale tells you the exact weight of whatever you put on it, it is not a balance scale.

Hint

You might want to consider labeling the sacks. And remember, you can take coins out of the sacks and weigh a combination of them. Once you come up with your strategy, you will need to make a calculation, and this equation will help you.

Once you have taken a crack at solving the riddle, you can see the answer here.

In a remote prison somewhere in South America, three prisoners are serving a life sentence. The guards decide to play a game with the inmates to pass the time.They have a trunk of hats, and they show the prisoners there are five hats in the trunk—three black hats and two white hats. The guards make the prisoners sit in chairs and line them up three in a row, such that the prisoner in the back of the line can see the two in front of him, the prisoner in the middle can see the one person in front of him, and the prisoner in the front can see nothing but the prison wall. The guards blindfold the prisoners, and place a hat on each of their heads. They then remove the blindfolds and tell the inmates that they can go free if they correctly name the color of the hat they have on—but if they guess wrong, they will be shot dead. Needless to say, the prisoners cannot see what color hat they have on their own head.The guards first ask the prisoner in the back of the line, "what color hat do you have on?" He says he doesn't know. They ask the man in the middle, and he also doesn't know. When the guards ask the prisoner in the front of the line what color hat he has on, he answers correctly, and goes free. What color hat did he have on, and how did he know?

Hint

Pretend that you are the prisoner in the back of the line. What do you see? Then pretend you are the prisoner in the middle of the line.

When you have your answer, you can look at the solution here.

After a long disagreement, Mr. Black, Mr. Gray and Mr. White agree to enter into a three-way duel, or a truel. They will stand in a triangle formation, each positioned at the vertices, each equidistant from the other two shooters.Mr. Black is the worst shot, he only hits 1/3 of the time, so he gets to shoot first. Mr. Gray is second-worst, hitting 2/3 of the time, so he get's to shoot second. Mr. White is an ace, and he hits 100 percent of the time, so he will have to wait and shoot third. The three men will take turns shooting in this order until only one man is left standing.

Mr. Black is up first. What should he do to secure his best odds of survival?

Hint

If you were Mr. Gray, who would you want to take out first? If you were Mr. White, who would you want to take out first?

Take a shot, then see the solution here.

You are sitting in a rowboat on a small lake. You have a brick in your boat. You toss the brick out of your boat into the lake, where it quickly sinks to the bottom.

Does the water level rise slightly, drop slightly, or stay the same?

Hint

Think about the density of the brick.

Toss that brick overboard, and then check the solution here.

You have two ropes coated in an oil to help them burn. Each rope will take exactly 1 hour to burn all the way through. However, the ropes do not burn at constant rates—there are spots where they burn a little faster and spots where they burn a little slower, but it always takes 1 hour to finish the job.With a lighter to ignite the ropes, how can you measure exactly 45 minutes?

Hint
You can light multiple ends and/or multiple ropes at the exact same time.

Think about clever ways to light these ropes on fire for a little bit, then see the solution here.

You sit at a sprawling table with hundreds of thousands of quarters in front of you, but you don't know exactly how many. You have a blindfold on, so you cannot see the quarters, but you do know that exactly 20 quarters are tails-side-up, and the rest are heads-up.You can move the quarters and flip them over as much as you want—but remember, you cannot see what you are doing. Though you can feel the quarters, you cannot determine which side is heads and which side is tails just by touch. How do you separate the quarters into two piles that have the same number of tails-side-up quarters in them?

Hint

The total number of quarters in each pile is irrelevant.

Once you have your piles separated, you can check the solution here.

There are five houses sitting next to each other on a neighborhood street, as depicted in the picture above. Each house's owner is of a different nationality. Each house has different colored walls. Each house's owner drinks their own specific beverage, smokes their own brand of cigar, and keeps a certain type of pet. None of the houses share any of these variables—nationality, wall color, beverage, cigar, and pet—they are all unique.

WHAT YOU KNOW--
The Englishman lives in the house with red walls.The Swede keeps dogs.
The Dane drinks tea.
The house with green walls is just to the left of the house with white walls.
The owner of the house with green walls drinks coffee.
The man who smokes Pall Mall keeps birds.
The owner of the house with yellow walls smokes Dunhills.
The man in the center house drinks milk.
The Norwegian lives in the first house.
The Blend smoker has a neighbor who keeps cats.
The man who smokes Blue Masters drinks beer.
The man who keeps horses lives next to the Dunhill smoker.
The German smokes Prince.
The Norwegian lives next to the house with blue walls.
The Blend smoker has a neighbor who drinks water.

THE QUESTION--
One of the house owners keeps fish, who is it?

Hint
If you would like a little help getting started, click here.

Once you know who keeps fish, you can confirm your answer here.

You've designed an incredibly advanced aircraft, a true marvel of aeronautics, the X-100. You want to fly all the way around the world in it without stopping. The only problem is that the plane can carry just enough fuel to make it halfway around the Earth.So you build a total of three planes, one for you to fly and two more for your assistants John and Jane. You equip these planes with some pretty incredible and futuristic features to help you along the way. For one, they can instantaneously transfer any amount of fuel to each other. One plane can even pass fuel to the other two simultaneously. Secondly, the aircraft can turn on a dime, literally reversing direction instantaneously, flying at the exact same velocity as soon as they about-face.

Now for the numbers: Each plane can carry 180 gallons of fuel. You plan to fly all the way around the world along the equator, where your plane can fly at the blistering speed of 1º of longitude per minute, meaning it'll take 360 minutes to make the whole 360-degree journey. (This is a speed of about Mach 5.4, for those who are curious). The three aircraft burn 1 gallon of fuel per 1º longitude traveled.

One more thing: There is only one airport along the equator route that you plan to take. You must start at this airport and finish there. John and Jane can return to the airport to refuel, filling their tanks to the full 180 gallons. The one airport is the only place that anyone can land.As you can see, with 180 gallons of fuel, one of the planes by itself would only make it 180º around the world, half of the required 360º. Fortunately, the planes have their nifty instantaneous refueling and about-facing features, and you have John and Jane to help you make the trip.How do you fly all the way around the world without stopping or turning around, and without any of the three pilots running out of fuel and crashing?

Hint

As mentioned, you are probably going to want pencil and paper for this. Draw out a circle representing the world and mark 90º, 180º, 270º and 360º. Imagine you are looking at the south pole and the equator runs along the circumference of the circle. It might help to make a table to keep track of all three planes' fuel levels as well. Where do the refuelings need to occur for you to make it all the way around in one continuous trip?

Note: If a plane hits 0 gallons of fuel, and at that exact moment another plane is there to refuel it, the plane does not crash. The fuel transfers instantaneously.

Before you check out the solution, you should have a piece of paper in front of you with circles and scribbles and cuss words and madness. Then check the answer here.

You are lost in the jungles of Brazil. After days of wandering, your food supplies dwindle, and you make a fatal mistake by eating a poisonous mushroom. You can feel the poison coursing through your veins, sure that you will collapse any second.But there is hope. The antidote to the poison is secreted by a certain species of frog found in this rainforest, and you can save yourself by licking one of these frogs. But, only the female frogs secret the antidote you need. The male and female frogs look identical, and they occur in equal numbers across the population. The only distinguishing feature is that the male frogs have a unique croak.

As your vision starts to blur, you look up and see one of these frogs sitting on a stump in front of you. You are about to make a mad dash to the frog, praying that it is female, when you hear the male frog's distinctive croak behind you. You turn around and see that there are two frogs on the grass in a clearing, just about as far away from you as the one on the stump. You do not know which one of the two frogs in the clearing croaked.

You only have time to reach the one frog on the stump, or the two frogs in the clearing (one of which croaked) before you pass out. Should you dash to the stump and lick the one frog, or into the clearing and lick the two?

Hint

Again, this is similar to the famously counterintuitive Monty Hall problem.

There is a lot to talk about here, and even then, certainly some will come to deny the answer as correct. When you are ready, you can see it here.