# Unsolvable Riddles

There is something about mysteries and riddles that attract the brightest minds. Sherlock, with his intelligence, could have become anybody but he chooses to be a detective.

There is a detective in each one of us. All of us love the thrill and excitement of solving a complicated mystery.

Here are some interesting riddles that would give your brain some serious exercise.

When problem-solving, our brain tends to overcomplicate things. More often than not, stepping back and approaching a problem from a different perspective is the best thing we can do! Here are some riddles you can attempt to solve, with answers so simple that even a child can get them right. But don’t be surprised when you’re staring blankly as you attempt to wrap your mind around them. Try them out, then share with family and friends and see how long it takes them to find the answers!

**Beginner**

### A Fox, A Sheep, And A Stack Of Hay

A farmer is traveling with a fox, a sheep and a small sack of hay. He comes to a river with a small boat in it. The boat can only support the farmer and one other animal/item. If the farmer leaves the fox alone with the sheep, the fox will eat the sheep. And if the farmer leaves the sheep alone with the hay, the sheep will eat the hay.

*How can the farmer get all three as well as himself safely across the river?*

- The farmer takes the sheep across the river, then returns back.
- The farmer takes the fox across the river.
- The farmer takes the sheep back to the first side of the river.
- The farmer leaves the sheep back on the first side of the river, and takes the hay to the other side.
- The farmer returns to the first side of the river.
- The farmer brings the sheep back to the second side.

### Horse Race

Two men ride their horses to the town blacksmith to ask for his daughter’s hand in marriage. To help decide who will get to marry her, the blacksmith proposes a very strange race:

“You will race your horses down the mile-long road from here to to the center of town, and the man whose horse passes through city hall’s gates LAST will get to marry my daughter.”

The men have no idea how to proceed, but after a few minutes of thinking, they come up with a great idea to abide by the blacksmith’s rules.

30 minutes later, one of the men is gloating, having won the daughter’s hand in marriage.

*What was the idea the men had?*

**horse**crosses last would win, so the man who wins the race would have his horse finish last.

### Two Coins

You have two normal U.S. coins that add up to 35 cents. One of the coins is not a quarter.

*What are the two coins?*

The coins are a quarter and a dime. The question notes that “**one** of the coins is not a quarter.” But the other coin is a quarter.

**Intermediate**

### Three Light Switches

There are 3 switches outside of a room, all in the ‘off’ setting. One of them controls a light bulb inside the room, the other two do nothing.

You cannot see into the room, and once you open the door to the room, you cannot flip any of the switches anymore.

*Before going into the room, how would you flip the switches in order to be able to tell which switch controls the light bulb?*

Flip the first switch and keep it flipped for five minutes. Then unflip it, and flip the second switch. Go into the room. If the light bulb is off but warm, the first switch controls it. If the light is on, the second switch controls it. If the light is off and cool, the third switch controls it.

### Two Ropes Burning

You have two lengths of rope. Each rope has the property that if you light it on fire at one end, it will take exactly 60 minutes to burn to the other end.

Note that the ropes will not burn at a consistent speed the entire time (for example, it’s possible that the first 90% of a rope will burn in 1 minute, and the last 10% will take the additional 59 minutes to burn).

*Given these two ropes and a matchbook, can you find a way to measure out exactly 45 minutes?*

The key observation here is that if you light a rope from both ends at the same time, it will burn in 1/2 the time it would have burned in if you had lit it on just one end.

Using this insight, you would light both ends of one rope, and one end of the other rope, all at the same time. The rope you lit at both ends will finish burning in 30 minutes. Once this happens, light the second end of the second rope. It will burn for another 15 minutes (since it would have burned for 30 more minutes without lighting the second end), completing the 45 minutes.

### Twin Brothers

You are in a room with nothing but two doors. Opening one of the doors will lead you to a life of prosperity and happiness, while opening the other door will lead to a life of misery and sorrow. You don’t know which door leads to which life.

In front of the doors are two twin brothers who know which door leads where. One of the brothers always lies, and the other always tells the truth. You don’t know which brother is the liar and which is the truth-teller.

You are allowed to ask one single question to one of the brothers (not both) to figure out which door to open.

*What question should you ask?*

Ask “If I asked your brother what the good door is, what would he say?”

If you ask the truth-telling brother, he will point to the bad door, because this is what the lying brother would point to.

Alternatively, if you ask the lying brother, he will also point to the bad door, because this is NOT what the truth-telling brother would point to.

So whichever door is pointed to, you should go through the other one.

**Advanced**

### Prisoners and a Light Bulb

There is a prison with 100 prisoners, each in separate cells, which are sealed off, soundproof and windowless. There is a lobby in the prison with a lightbulb in it. Each day, the warden will pick one of the prisoners at random (even if they have been picked before) and take them out to the lobby. The prisoner will have the choice to flip the lightbulb switch if they want. The lightbulb starts in the “off” position.

When a prisoner is brought out to the lobby, he also has the option of saying “Every other prisoner has been brought out to the lobby.” If a prisoner chooses to say this and it is true, all the prisoners will go free.

However, if a prisoner chooses to say this and it’s wrong, all the prisoners will be executed. So a prisoner should only say this if he knows it is true for sure.

Before the first day of this process begins, all the prisoners are allowed to get together to discuss a strategy to eventually save themselves.

*What strategy could they use to ensure their eventual salvation?*

Make one of the prisoners the “lead” prisoner. This prisoner is the ONLY one who is allowed to turn the light off.

Each time any of the other prisoners goes into the lobby, if the light is off, they will turn the light on, but only if they’ve never turned it on before. This means that each prisoner will only ever turn the light on once.

Meanwhile, every time the lead prisoner goes into the lobby, he will turn the light off if it’s on. He will keep track of the number of times he has turned the light off.

Once the lead prisoner turns off the light for the 99th time, he knows that every other prisoner has turned the light on once (and thus has been in the lobby). At this point, he may say that all the prisoners have been to the lobby, and they will all go free.

### Airplane Seats

People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random.

After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.

*The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?*

There is a 1/2 chance that you’ll get to sit in your assigned seat.

A common way to try to solve this riddle is to try to mathematically determine the chance that each person sits in your seat as they get on the plane. However, this math gets complicated quickly, and we can solve this riddle with a more analytical approach.

We first make two observations:

**If any of the first 99 people sit in your seat, you WILL NOT get to sit in your own seat.****If any of the first 99 people sit in Steve’s seat, you WILL get to sit in your seat.**To see why, let’s say, for the sake of example, that Steve sat in A’s seat, then A sat in B’s seat, then B sat in C’s seat, and finally, C was the person who sat in Steve’s seat. We can see that this forms a sort of loop in which every person who didn’t sit in their own seat is actually sitting in the seat of the next person in the loop. This loop will always be formed when a person finally sits in Steve’s seat (and if Steve sits in his own seat, we would consider this to be a loop of length 1), and so after that point, everybody gets to sit in their own seat.

Based on these observations, we know that the instant that a passenger sits in either Steve’s seat or your seat, the game for you is “over”, and it is fully decided if you will be sitting in your seat or not.

Our final observation is that for each of the first 99 people, it is EQUALLY LIKELY that they will sit in Steve’s seat or your seat. For example, consider Steve himself. There is a 1/100 chance that he will sit in his own seat, and a 1/100 chance that he’ll sit in your seat. Consider any other person who has been displaced from their own seat and thus must choose a seat at random…if there are N seats left, then there is a 1/N chance that they’ll sit in Steve’s seat, and a 1/N chance that they’ll sit in your seat.

So because there is always an equal chance of a person sitting in your seat or Steve’s seat (and one of these situations is guaranteed to happen within the first 99 people), then there is an equal chance that you will or will not get your seat. So the chance you get to sit in your seat is 50%.

**Bonus Riddles**

Think you could answer all 8 of these riddles correctly? Take our quiz and challenge your friends!

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