Lucid Dreams Logo

A good puzzle, it's a fair thing. Nobody is lying. It's very clear, and the problem depends just on you.


Hempel's Ravens

Ship of Theseus

1=0 & 1=2

Logical Paradoxes

Optical Illusions

Hempel's Ravens: this is one of my favorites.

Ship of Theseus: so is this one!

1=0 & 1=2 proves that mathematics is necessarily false... or does it?

Logical Paradoxes contains just that.  Four logical conversations discovering paradoxes.

Optical Illusions: can you guess what is in here?  Graphics intense.

Below is a collection of worthwhile puzzles


On the Island of Knights and Knaves: On the island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights always tell the truth. Knaves never tell the truth any sentence uttered by a knave is false. A stranger came to the island and encountered three inhabitants, A, B, and C. He asked A, "Are you a knight, or a knave?" A mumbled an answer that the stranger could not understand. The stranger then asked B, "What did he say?" B replied, "A said that there is exactly one knight among us." Then C burst out, "Don't believe B, he is lying!" What are B and C?

One day I went to the island of knights and knaves and encountered an inhabitant who said, "Either I am a knave or else two plus two equals five." What should you conclude?
(Knights and Knaves puzzles by Raymond Smullyan)

The Surprise Test: One day the professor came into the class and announced, "Next week I will give you a surprise test. It will be a surprise, because you won't be able to figure out on which day it will occur until the class meets on the day of the test. It could happen on Monday, Tuesday, Wednesday, Thursday, or Friday, but I won't tell you which day."

The class were clever. They reasoned as follows: "She can't give the test on Friday, because then it wouldn't be a surprise; we'd know after class on Thursday that the test hadn't yet occurred, and hence we'd figure out that it would have to be on Friday. So we know the test can't be on Friday. But then it can't be on Thursday either, because if it were, we would know after class on Wednesday that it would have to be on Thursday, since it wouldn't have happened yet, and we have already shown that it can't be on Friday." Reasoning in this manner, the students concluded that the test could not occur on Wednesday either, nor on Tuesday, nor on Monday. Having concluded that a surprise test was impossible, the students didn't study. They were very disappointed and very surprised on Wednesday when they got a test. Where did the students' reasoning go wrong?

The Problem of the Light Switch: I have an ordinary light switch connected to a light. When the switch is closed, the light is on. When the switch is open, the light is off. At two minutes to noon, the light is on. At one minute to noon I flip the switch, turning the light off. At half a minute to noon I flip it again, turning the light on. At a quarter of a minute before noon I flip it again, turning the light off. I continue in this way, cutting the time between flippings of the switch in half each time. Now this will be an infinite series of flips. The switch flippings will occur closer and closer to noon, but will all be completed before noon. Will the switch be on or off at noon?

The Super Bullet:The Acme Arms Company has invented a Super Bullet: a Super Bullet penetrates anything it hits. But the Adamantine Armor company has invented a Super Strong Armor Plate: nothing that hits a Super Strong Armor Plate penetrates it. The army is planning to shoot a Super Bullet at a Super Strong Armor Plate. What will happen?


Epimenides' paradox
"This statement is false"
"Next statement is true. Preceded statement is false"
"Next statement is false. This statement is true"
"This statement is true"
"Liar's paradox"
"I am lying"
"I always tells a lie"


Sorites Paradox

1 grain of wheat does not make a heap.
If 1 grain of wheat does not make a heap then 2 grains of wheat do not.
If 2 grains of wheat do not make a heap then 3 grains do not.
If 9,999 grains of wheat do not make a heap then 10,000 do not.
10,000 grains of wheat do not make a heap.

Stanford Encyclopedia of Philosophy

© Copyright 2013. All Rights Reserved. Privacy Policy