9 days? No sweat, man! I've made over a dozen games in one week each, with a 48-hour limit a few times.
So, here's what you've got to know.
First off, you need an idea. Now, you might think that the best way to get an idea is to not restrict yourself. Oddly, you'd be wrong. Humans seem to be better off exploring ideas within the confines of a stricter concept.
That means we need some concepts. Luckily, there are tons of concepts available for easy pickings. Here, for example, are a ton of historical concepts from the Experimental Gameplay Project (which I highly recommend taking on, by the way.)
Pick one. I recommend picking the most recent one. Tada, you're making a game about economy. What does that mean? I dunno! That's where it's up to you. Maybe that's a business sim. Maybe it's about recycling. Maybe it's about making careful use of resources. You've got a word - "economy" - and now it's up to you to make a game.
Write down a bunch of ideas. Throw out the bad ones. Pick the idea you're most interested in. Start writing code.
Now, keep in mind this is going to be a bit of a crapshoot. It's possible you'll pick a brilliant idea. It's possible you'll get seven days in and say "well, that idea was pretty crummy actually". If the latter happens, finish the game anyway and chalk it off as a learning experience.
Now, how do you make a game in nine days?
First: ruthless cutting of features. You don't need a title screen. You don't need an escape menu. You don't need good art or good music. If you get in five days and your game is done, yeah, sure, go back and flesh things out, but for now your goal is to get your gameplay working. Sit down and work until your basic gameplay exists. Then work until it's done. Don't waste time on finicky details, don't worry about making things look perfect. If you find a bug, think about whether it's worth fixing or not. If your character has a graphics glitch when he fires a gun, congratulations, you've just invented a weird kind of muzzle flash. If you're designing a clock and the face looks wrong, awesome, you've got a weird art deco clock. KEEP WORKING ON THE IMPORTANT THINGS.
Second: get rid of distractions. Yeah, I know you want to read Reddit. Don't do that. Stop reading Reddit. I've found that streaming my development as a video keeps me on-track - if I get distracted, everyone will know - but you probably don't want to set that up right now, you've got a game to write.
Third: Keep a list of goals. Again, cull it ruthlessly. Anytime you find yourself unsure of what to do next, that means you need to consult your list. If your list doesn't tell you, that means you need to improve your list.
Fourth: Make sure everything is worth the time. Yeah, you could download a good sound design package and spend five days learning how to make good sound effects. NOPE. You'll have time for that once the competition is done! Grab SFXR. You have five minutes per sound effect. GO. Are you an awesome artist? Can you make a great character sprite in a day? NOPE. Your main character is a square, your enemies are triangles. GO.
Good luck! This kind of a challenge is very difficult but it's also incredibly rewarding. If you really want to get into the games industry, I can promise you that releasing twelve games, one every month, looks miles better on a resume than a four-year college diploma.
As an example, here are a bunch of games I made under similar constraints. Yours probably won't be that developed - you just don't have the time or the experience - but it's certainly doable.
Are you playing those games?
STOP. GET TO WORK. YOU DON'T HAVE TIME TO PLAY GAMES. GO GO GO