Puzzle of the day

Prove that there are as many even numbers as natural numbers.

Prove that the repeating decimal 0.999999… is equal to 1.

Let’s say you’re on a game show where the host shows you three doors. Behind one of these doors is a brand new car. Behind the other two are goats. You get to pick a door. Then the host will open one of the doors you didn’t pick to reveal one of the goats.

General Gasslefield, accused of high treason, is sentenced to death by the court-martial. He is allowed to make a final statement, after which he will be shot if the statement is false or will be hung if the statement is true. Gasslefield makes his final statement and is released.

It was good to have the house full of people again; it had been far too quiet since the last of his seven daughters had left for college; seven daughters with seven different majors at seven different schools.

A, B, and C are three towns, each connected by a network of roads. There are 82 ways to get from A to B, including those routes that pass through C. There are 62 ways to get from B to C, including those routes that pass through A.

A sealed box contains two coins. One is a double-headed coin, and the other is an ordinary coin (heads on one side, and tails on the other). You take one of the coins out of the box and look at one of the sides.

Place the numbers 1 to 9 inclusive, once each, in these gaps to make the product correct. x 3 

What is the sum of all the positive integers in the universe? Zero? One? Minus one? Something else?

Stanford, Peter, Edward, and Arnold need to cross a bridge at night. At most two people can be on the bridge at once. Among the men is one flashlight which must be carried during any crossing. The flashlight may handed between men but may not be thrown.