A number of quants are at dinner, and start discussing compensation. They want to calculate the average compensation among themselves, but are too embarrassed to disclose their own salaries. How can they determine the average compensation of their group? They do not have pens or paper or any other way of writing down their salaries. (Thanks to Arroway.)

Einstein's brainteaser

There are five houses of five different colours. In each house lives a person of a different nationality. Those five people drink different drinks, smoke cigarettes of a different brand and have a different pet. None of them has the same pet, smokes the same cigarette or drinks the same drink.

We know:

• The Englishman lives in the red house.

• The Swede has a dog as a pet.

• The Dane drinks tea.

• The green house is on the left of the white one.

• The person who lives in the green house drinks coffee.

• The person who smokes Pall Mall raises birds.

• The owner of the yellow house smokes Dunhill.

• The man who lives in the house that is in the middle drinks milk.

• The Norwegian lives in the first house.

• The man who smokes Blends lives next to the one who has cats.

• The man who raises horses lives next to the one who smokes Dunhill.

• The man who smokes Bluemaster drinks beer.

• The German smokes Prince.

• The Norwegian lives next to the blue house.

• The man who smokes Blends is neighbour of the one who drinks water.

Question: Who has the fish?

(Thanks to NoDoubts.)

Gender ratio

A country is preparing for a possible future war. The country's tradition is to send only males into battle and so they want to increase the proportion of males to females in the population through regulating births. A law is passed that requires every married couple to have children and they must continue to have children until they have a male.

What effect do you expect this law to have on the makeup of the population?

(Thanks to Wilbur.)

Covering a chessboard with dominoes

You have a traditional chessboard, eight by eight square. From a single diagonal, any diagonal, you remove two squares. The board now has just 62 squares. You also have 31 domino tiles, each of which is conveniently the same size as two of the chessboard squares. Is it possible to cover the board with these dominoes?

(Thanks to alphaquantum.)

Aircraft armour

Where should you reinforce the armour on bombers? You can t put it everywhere because it will make the aircraft too heavy. Suppose you have data for every hit on planes returning from their missions, how should you use this information in deciding where to place the armour reinforcement?

(Thanks to Aaron.)

Hanging a picture

You have a framed picture with a string attached to it in the usual manner. You have two nails on the wall. The problem is to try to hang the picture on the wall such that if you remove either one of the nails then the frame falls down.

(Thanks to wannabequantie.)

Ages of three children

A census taker goes to a house, a woman answers the door and says she has three children. The census taker asks their ages and she says that if you multiply their ages, the result is 36. He says he needs more info so she tells him that the total of their ages is the address of the building next door. He goes and looks, then comes back and says he still needs more information. She tells him that she won t answer any more questions because her eldest child is sleeping upstairs and she doesn't want to wake him.

What are the children's ages? (Thanks to tristanreid.)

The Monty Hall problem

You are a contestant on a gameshow, and you have to choose one of three doors. Behind one door is a car, behind the others, goats. You pick a door, number 2, say, and the host, who knows what is behind each door, opens one of the other two doors, number 3, say, and reveals a goat. He then says to you, 'Do you want to change your mind, and pick door number 1?' Should you?

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