5 Paradoxes/Brain Teasers That Will Keep Your Brain Busy

Buridan's donkey is an easier to grasp around version of a paradox in philosophy on the conception of free will.

The paradox displays the hypothetical situation in which a donkey, that is equally hungry and thirsty, is put in front of a stack of hay and a pail of water at exactly the same distance from each of the two. Assuming that the animal will always go for whatever is the closest it will eventually die of both hunger and thirst, since it cannot make a rational decision on choosing one over the other.

Many thinkers had grasped around this concept (Aristotel, Abu Hamid al-Ghazali, Jean Buridan) either stating that the protagonist will die or that he must wait until circumstances change, thus leading to possible rational choice.

The Pinocchio paradox is a version of the liar paradox and it implies Pinocchio stating the following: "My nose grows now." If the nose isn't growing then it means that the statement was a lie which should have made his nose grow. On the other hand, if the nose is growing it means that it does it without Pinocchio lying, his statement being true. So how do we wrap our head around this?

The prisoner's dilemma is used in game theory as an example of a game analysis showing why two individuals might not cooperate, even if it might be in their interest to do so.

The problem statement goes as so. Two criminals from the same gang are caught and imprisoned. Both of them are locked in solitary confinement with no possibility of communicating to each other. After a while the police admits that they don't have enough evidence to convict both of them on the main charge so decide to try and at least keep them in prison for a year on a lesser charge. They offer each of them the chance of testifying against the other, thus going for betrayal, or remain silent. This leads to three possible scenarios:

1. Both Prisoner 1 and Prisoner 2 betray each other → both of them serve 2 years in prison;
2. Prisoner 1 betrays Prisoner 2 → Prisoner 1 is set free while Prisoner 2 serves 3 years in prison (or the other way around);
3. Both Prisoner 1 and Prisoner 2 remain silent → both of them serve 1 year in prison.

Given the fact that they are comrades, in a gang where respect is earned, but at the same time betrayal means freedom what do you think is the most probable outcome?

This paradox was named after the Monty Hall, the host of the American game show Let's Make a Deal, being originally proposed in 1975's American Statistician by Steve Selvin. The problem goes like so:

Let's say you are in a game show and you have to choose between three doors. Behind one of the doors is the grand prize, while behind the other two goats. If you now pick Door No.1 and before opening it the host, who knows what is behind every door, opens Door No.2 behind which is a goat. He than gives you the possibility of switching from Door No.1 to Door No.3. The big question is: Is it in your advantage to switch?

This is a short and easy to mess around paradox, great to start some laughs with your group of friends and is based on two statements considered as always true:

1. Buttered toast always lands butter-side down.
2. Cats always land on their feet.

If so:

What happens if we tie a piece of buttered toast with the buttered-side up on the back of a cat and drop the cat from a large height?

Do you know any other brain teasers or paradoxes? Feel free to share and comment.