Tora finally got to the top of the stairs only to be confronted with that blasted door knocker again. Ugh. She really hated this door knocker. She tapped it and waited for the expectedly annoying question.

You are given a mystery ball and are told that it has a whole-number weight between 1 and 40 lbs (inclusive).
You are then given a balance scale are are allowed to pick four weights, each weighing any whole-number amount. You much choose these weights so that no matter what the mystery ball weighs, you will be able to determine its weight using just the balance scale and these four weights.
What weights should you choose?

Oh why could she not just enter the common room? She sat down at the top of the stairs and tried to puzzle it out but couldn't come up with anything. As she was sitting, she realized that she was sitting in yet another pile of dust and dirt. Astronomy homework time! Maybe she could figure out the answer after she sucked up some of this dirt. (Maybe she could suck the door knocker up too if she was lucky)
"Vacavus!" She said tapping the blue vacuum that she carried with her practically everywhere now. After a couple minutes she had finished sucking up any dust and dirt she could conceivably reach. The vacuum died out and she sat down comfortably leaning against the wall.
OOC: Just so you know, Professor, the homework part of this post is done

She got out her notebook and continued to attempt to figure out the ridiculous riddle. First she figured that she would need a 1 weight, so she could measure the least amount it could be, then she tried 1 and 2, but that would only get her to weights 1-3. So she tried 1 and 3 which would give her weights up to four but that seemed too little still. She continued to think for several more minutes, very glad that she had decided to use a pencil so she could erase the combinations that didn't work. Finally she came up with the numbers 1, 3, 9, and 27. She tapped the door knocker again and said irritably "One, three, nine, and twenty-seven. Now please just let me in already!" It was really frustrating that she couldn't ever seem to just get in the common room when she wanted. And now on top of that she had to go pay at the turnstiles!