Ms. Morris asked her students to each pick one or more of the following 4 numbers, all powers of 3:1,3,9,27and write the sum of the chosen numbers on a piece of paper. Students must not talk to each other about their choices. She then collected all papers, and wrote them down on the whiteboard, but no number would be written more than once. The class “won” the game if there were N numbers written down, where N was the greatest possible such numbers. What was the valueof N that Ms. Morris had in mind?