There's no way to predict stock movements especially not in the short term.
However I do have a strategy for you. You have no downside risk. You don't lose anything if you lose all your money but you win something if you win. So you want the most risky portfolio possible. Choose one stock that's the cheapest and has the highest volatility you can find and put all your money in it. Yes a penny stock is a good choice. The cheaper and more volatile the better since the cheaper it is the better chance of a large % increase.
There's really no sense in diversifying your portfolio with more than one stock (more on this later).
If you can, spend all your money buying call options on this stock since they give you even more potential upswing than just buying the stock.
If you can, also borrow money (probably not allowed) and buy the call options if you can or the stock since this gives you more potential upswing.
The real strategy comes into play if your stock shoots up before the 3 months is up. Then it's a little bit of game theory. The question would be what return do you think you'll need to win? Obviously this depends on a lot of factors like how the market is performing, how many people are playing the game, and what type of portfolios your peers invested in.
If you're just playing against a small class you may want to take on a less risky portfolio (by buying other stocks that are just as risky not by buying less risky stocks!!!).
And even better strategy if it's allowed might be to short some high beta stocks. Most of your peers are going to do well if the markets go up but very few students will do well if the market goes down since most won't think of this strategy. If you even take a moderate risk short position then if the markets go down then I think you would have a very high chance of winning.