Riddlewords

Paradox Analysis

Paradox Analysis Difficulty 6 7 questions by Marco DeLuca

Situations that seem logically impossible or produce counter-intuitive results. Your job is to identify the hidden assumption, resolve the contradiction, or explain why intuition fails.

Instructions Each problem presents a paradox or counter-intuitive situation. Explain what's really going on — identify the flaw in reasoning, the hidden assumption, or why the surprising answer is correct. Show your work for full credit.
Question 1 of 7
A barber shaves all and only the men in town who do not shave themselves. Who shaves the barber?
Sign up to answer
Question 2 of 7
A train leaves a station traveling east at 60 km/h. A fly starts at the front of the train and flies to the back wall and forth continuously at 120 km/h until the train reaches the next station 60 km away. How far does the fly travel in total?
Sign up to answer
Question 3 of 7
If a plane flies from Toronto to Vancouver with a strong tailwind and returns with an equally strong headwind, is the average speed for the round trip simply the average of the two speeds? Explain why or why not.
Sign up to answer
Question 4 of 7
A game show offers three doors. Behind one door is a car; behind the other two are goats. You pick a door. The host, who knows where the car is, opens a different door showing a goat. He then offers you the choice to switch doors. Should you switch? Why?
Sign up to answer
Question 5 of 7
In a room of just 23 people, what is the approximate probability that at least two share the same birthday? Explain why the answer is surprising.
Sign up to answer
Question 6 of 7
Two envelopes each contain money. One envelope contains twice as much as the other. You choose one envelope but do not open it. You reason: "The other envelope has either half or double my amount, so the expected value of switching is (0.5x + 2x)/2 = 1.25x — I should always switch!" What is wrong with this reasoning?
Sign up to answer
Question 7 of 7
A teacher announces: "There will be a surprise exam next week, and you will not be able to predict the day in advance." The students reason: the exam can't be Friday (they'd know by Thursday evening). So Friday is eliminated. But then it can't be Thursday either (they'd know by Wednesday). Continuing this logic, they eliminate every day and conclude no surprise exam is possible. Yet the teacher gives the exam on Wednesday and the students are indeed surprised. Where does the students' reasoning go wrong?
Sign up to answer

Want to solve this puzzle?

Sign up free and get AI-powered feedback on every answer.

Get started free Browse more puzzles