Tips

Overall:

Don't make this harder than it has to be. The more simple your "machine" is, the better it usually works. The requirements can easily be met with some junk and ingenuity. Don't spend a ton of money or time on this project.

Groups are a fun way to experience this project, but you can work alone if you'd like. Here are some ways to meet the requirements and use the simple machines:

Simple machines
Inclined plane
Most people use a ramp or a slope as part of their project. Anything tilty that something can roll down will count.
Lever
The teeter-totter is most commonly seen, but don't forget hidden levers. Lifting a ramp, using scizzors, attaching a stick to a wheel, a catapult, or any number of items can count as a lever.
Wedge
When I say wedge, many think of door-stops, but wedges can be more. Blades are wedges, like the cutting edge of scizzors. The tip of pins are wedges too.
Screw
It's hard to actually get the mechanical advantage of a screw to be used in a device such as these. I'll let you use a spiral as a screw for your project. Anything traveling downwards on a curved path is basically a screw.
Wheel and Axle
Your wheel and axle can be part of a larger item. For example, putting a model car in your project covers the wheel and axle requirements. You can build one if you'd like though. A pencil or dowel through an orange was one of my favorites.
Pulley
I know that only moveable pulleys have mechanical advantage, but I'll accept any type of pulley. Actually, I'll accept anything that has a string going over an object. For example, thread over a pencil will count as a pulley for this assignment.
20 Steps!!!

The 20 steps don't have to be big steps. Here's an example:

1. Drop marble into funnel2. Marble drops onto spiral ramp
3. Marble follows spiral4. Drops onto incline (ramp)
5. Rolls down incline6. Drops into cup
7. Cup pulls string8. Pulley changes string direction
9. String pulls up lever10. Other end of lever drops
11. Car on lever rolls12. Car topples dominoes
13. Dominoes hit mousetrap14. Mousetrap snaps shut
15. Mousetrap pulls rope16. Rope closes scizzors
17. Scizzors cuts thread18. Balloon attached to thread rises
19. Rising balloon tips lever20. Lever turns on stereo