Impossible Riddles With Answers
Updated · Best Riddles With Answers editorial team
Quick answer: Impossible riddles describe a situation that cannot be true, or ask for something nobody can do, and then show how it works after all. This page has 42 of them with answers. Some have clever solutions, and a few of the toughest are proofs that the thing really is impossible, with the reason explained.
Warm-Up Impossible Riddles
How can a person go eight days without sleep?
By sleeping at night. The question only says he did not sleep during the day.
How can you carry water in a sieve?
Freeze it first, so that it is solid ice.
A girl fell from a fifty foot ladder and was not hurt. How?
She fell off the bottom rung.
How can you throw a ball as hard as you can and have it come back to you, with nothing attached to it and nothing in the way?
Throw it straight up into the air.
A man stood in heavy rain with no hat or umbrella, yet not a hair on his head got wet. How?
He was bald.
Make this sum true by adding a single straight line: 5 + 5 + 5 = 550.
Add a short stroke to the first plus sign to make a 4, giving 545 + 5 = 550.
Using exactly eight 8s and only addition, can you make 1000?
Yes: 888 + 88 + 8 + 8 + 8 = 1000.
How can you cut 13 in half and get 8?
Write 13 in Roman numerals, XIII, and cut it horizontally. The top half reads VIII, which is 8.
A hunter walks one mile south, one mile east and one mile north, and ends up exactly where he started. How?
He started at the North Pole, where walking east keeps you the same distance from the pole.
A man marries twenty women in a single town in one year, breaks no law and is never divorced. How?
He is a minister who conducts weddings for other people.
A man pushes his car up to a hotel and tells the owner he is bankrupt. What is going on?
He is playing the board game Monopoly and landed on a hotel.
How can one plus one equal one?
Join one puddle to another puddle and you have one bigger puddle.
Main Set Impossible Riddles
A prisoner may leave through one of two exits: one leads into a room of fire and the other into a room with a lion that has not eaten for three years. Which should he choose?
The lion room. A lion that has not eaten for three years is dead.
Two men fall down a chimney, one with a clean face and one with a dirty face. Which one washes?
The clean one. He sees the other's dirty face and assumes his own is dirty too, while the dirty one sees a clean face and thinks nothing.
How can you take 1 from 19 and get 20?
In Roman numerals 19 is XIX. Remove the I and you are left with XX, which is 20.
Add one letter to IX to make it 6.
Put an S in front to make SIX.
I am an odd number. Take away a letter and I become even. What number am I?
Seven. Remove the S and you have even.
Four cards lie on a table showing E, K, 4 and 7. Each has a number on one side and a letter on the other. To test the rule 'if a card shows a vowel on one side, it has an even number on the other', which cards must you turn over?
The E and the 7. The E could hide an odd number, and the 7 could hide a vowel. The K and the 4 cannot break the rule.
A hotel with infinitely many rooms is full, yet a new guest arrives. How can she be given a room?
Ask every guest to move one room along, from room n to room n + 1. Room 1 is then free.
Is 0.999 with the nines going on forever really equal to 1?
Yes. One third is 0.333 repeating, and three thirds is 1, which is also 0.999 repeating.
In a village, the barber shaves every man who does not shave himself, and no one else. Who shaves the barber?
No one can. If he shaves himself he must not, and if he does not he must. Such a barber cannot exist.
A chessboard has two opposite corners removed. Can 31 dominoes, each covering two squares, cover the other 62 squares?
No. Opposite corners are the same colour, leaving 32 squares of one colour and 30 of the other, but each domino covers one of each.
A town has seven bridges linking two banks and two islands. Can you take a walk crossing each bridge exactly once?
No. All four land areas have an odd number of bridges, and such a walk would allow at most two.
You walk to a wall, each step covering half the distance still to go. Will you ever reach it?
Yes. The steps get smaller, but half plus a quarter plus an eighth and so on adds up to the full distance.
Toughest Impossible Riddles
Let a = b. Then a squared = ab, so a squared minus b squared = ab minus b squared. Factor: (a + b)(a - b) = b(a - b). Divide both sides by (a - b): a + b = b, so 2b = b, so 2 = 1. Where is the mistake?
Dividing by (a - b). Since a = b, that is dividing by zero, which is not allowed.
A sentence reads: 'This sentence is false.' Is it true or false?
Neither can hold. If it is true then it is false, and if it is false then it is true. It is a paradox, not a statement with a value.
One hundred prisoners must each find their own number among one hundred shut boxes, opening at most fifty. If any prisoner fails, all lose. Is there a strategy better than hopeless odds?
Yes. Open the box with your own number, then the box numbered by what you find, and so on. This succeeds about 31 percent of the time, whenever no loop is longer than 50.
Can you connect three houses to three wells with paths that never cross on a flat plane?
No. Each house links to all three wells, and that network cannot be drawn on a plane without a crossing.
A city has 1,000,000 people and no one has more than 500,000 hairs. Must two people have exactly the same number of hairs?
Yes. There are only 500,001 possible counts from 0 to 500,000, so with a million people at least two must share one.
Among any six people, must there always be three who all know each other or three who are all strangers?
Yes. Pick Ann. Three of the other five are all her friends or all strangers to her. If any two of those three share that same bond, they and Ann form a trio. If not, those three form one.
Is there a largest prime number?
No. Multiply the primes on any list and add 1. That number has a prime factor that is not on the list.
Can the square root of 2 be written as a fraction of whole numbers?
No. If p/q were in lowest terms, p and q would both have to be even, which contradicts lowest terms.
A hotel with infinitely many rooms is full, and now infinitely many new guests arrive. How can everyone have a room?
Move the guest in room n to room 2n. All the odd numbered rooms are then free for the new guests.
A sheet of paper is 0.1 millimetre thick. How many times must it be folded in half for its thickness to pass the distance to the Moon, about 384,000 kilometres?
42 folds. Each fold doubles the thickness, and after 42 folds it reaches about 440,000 kilometres.
Quick-Fire Impossible Riddles
What number can you never divide by?
Zero.
What can you put in an empty bucket to make it lighter?
A hole.
How many sides does a circle have?
Two, an inside and an outside.
Which long English word has no a, e, i, o or u in it?
Rhythm.
What time is it when a clock strikes thirteen?
Time to get the clock fixed.
Which is heavier, a ton of bricks or a ton of feathers?
Neither. They both weigh a ton.
What can you never hold with your right hand?
Your right elbow.
What kind of cup can never hold water?
A cupcake.
How to Think About Impossible Riddles
An impossible riddle depends on an assumption you did not know you were making. When a scene seems to break the rules, look for the word that hides a second meaning, such as bald, bottom or hotel, or ask what extra detail would make the story ordinary. The answer usually removes the contradiction.
The harder ones on this page are different. They ask whether something can be done, and the answer is a proof that it cannot, or a surprising proof that it can. To check one, ask what a counterexample would have to look like, and read the explanation slowly.
Frequently Asked Questions
Are impossible riddles really impossible?
Most are not. They look impossible because of an assumption in the wording, and the answer shows how the situation can happen. A few are real proofs that something cannot be done.
What is an example of a famous impossible puzzle?
The seven bridges of Konigsberg is a classic. It asks for a walk crossing each bridge once, and there is a proof that no such walk exists. The mutilated chessboard is another.
How do I solve a how-can-that-be riddle?
Reread the question and check each word for a second meaning. Then imagine a normal situation that would match every clue, such as a person who is bald or a ship that rises with the tide.
Are impossible riddles good for kids?
The first two sets suit teenagers and families. The toughest ten involve ideas like infinity and proofs, so they suit older teens and adults who enjoy mathematical puzzles.
