Three Brief Logic Riddles

The Problem: How can you throw a ball as hard as you can and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.

Answer: Throw the ball straight up in the air.

The Problem: Imagine there are 3 coins on the table: gold, silver, and copper. If you make a truthful statement, you will get one coin. If you make a false statement, you will get nothing.
What sentence can guarantee you getting the gold coin?

Answer: "You will give me neither copper nor silver coin." If it is true, then I have to get the gold coin. If it is a lie, then the negation must be true, so "you give me either copper or silver coin", would break the given conditions that you get no coin when lying. Therefore the sentence must be true and you must get the gold coin.

The Problem: Hotel Infinity has infinite rooms and infinite guests. If a traveler came by looking for a vacant room how could the hotel provide him with one without kicking out any guests?

Answer: Tell all the guests to move down one room, so room #1 is open.