Riddle: I own a hotel. It's not a large hotel, mind. Just a little place for passing people to drop by and spend the night if need be. After all, I do only have nine rooms available. Considering how humble my little hotel was, I thought nine was all I would need. Boy, was I wrong.
My hotel was completely empty for a while, but one night, ten people barged in, all at once. Ten! Ten is a fine number to have in a day, but could you imagine they all came at once! And what's more, none of the ten were together - they were ten individuals wanting a room each! As you can tell, fitting ten people into a nine room hotel was a slight problem.
But by thinking on my feet, I solved the problem without delay.
I put the first two people in room 1. I know I said they wanted a room each, but bear with me for a moment. I then put the third person in room 2, the fourth in room 3, the fifth in room 4, the sixth in room 5, the seventh in room 6, the eighth in room 7, and then ninth in room 8. Now I still have room 9 left over, and guess what? I still had the pair in room 1. So I took out one person and put him in room 9, thus fitting the tenth person in the ninth room.
Would you make a good hotel owner - do you have any idea how my little magic worked here?
Answer: It's quite simple, really. I threw you off scent by saying that I stuck the tenth person in the ninth room. However, pay close attention, and you'll see I did no such thing - I placed the SECOND person in there. And what about the tenth? He had to find a different place. Can't expect me to go and add a new room in a second, can you?