Duck, Duck, Goose!
Eighteen people are numbered from 1 to 18 and are standing in order in a line to play Duck-Duck-Goose. The first person starts out saying Duck, and the second person also says Duck. The third person says Goose, and has to sit down. The next two people both say Duck, and the third person says Goose and has to sit down. This procedure is repeated, with person number 1 speaking after person number 18.
The winner of the game is the last person standing, and he wins $1000. Odorf Sniggab wants to win this game badly, so he decides that he's going to position himself correctly. What number should Mr. Sniggab choose to guarantee that he will win the game?