Depending on how awesome your friend is, you can get away with it. The wort they give you is going to be riddled with wild yeast, bacteria, and mold spores (as others have noted), and that's what you're fighting. Here's what I would do in order of preference, and each step downward increases the likelihood of infection:
1. Have your friend boil the wort for 10 minutes, clean and sanitize the bucket and lid, seal the wort inside the bucket, and then put the whole thing in a chest freezer. If he does this for you, I would say you have almost 0 chance of an infection, and you'll be 100% good to go.
2. Do all of the same, but leave the bucket in a cold place outside. Looking at the forecast for Richmond, it doesn't like it's going to be as cold as one would like. If the daytime high was in the 20s or even low 30s, I'd say this is a perfectly viable option. Still, the boil and sanitizing will go a long way. Your friend could also put the bucket in a cooler packed with ice, which may just do the trick.
3. Stick the bucket in a chest freezer with no boil. Obviously, this isn't as desirable as having a boil first, but it's probably going to be perfectly fine this way. My chest freezer can drop the temp of 6 gallons of wort 10F/hr, which will get it at a safe temp pretty darn quickly.
4. Just set the bucket outside. Given the relatively high temps in Richmond, and the lack of a boil, this is the most risky option by far. But there are things that can be done to help... Packing in ice still may do the trick and you could also have your friend toss in 8+ IBUs of first wort hops. The hops won't kill everything, but it'll help.
The one thing I wouldn't do is not try it. $10 is not much to lose, and it sounds like a fun contest. If you're proactive, and do as much as you can to fight infection, then everything should turn out fine. Even if you do get a little souring, it may not be the end of the world. You could make a style where a little sour is suitable or maybe even cover it up. With a little luck, and a little effort, I think you'll open the wort Monday and make beer without issue.