Here’s my attempt at a design. I did not have a lot of time, so it’s not very big. I went for style over substance this time.
I put together a wind-up toy car. It will use an elastic to propel the car forward. It uses Ikea pencils (or probably any #2 pencil) as the wheel axles.
It stacks several layers of 1/4 in material.
It could be cut out of wood, with the “flames” engraved on the side. The different colors could be done by staining the different parts after they are cut (thus everything on one sheet).
Or it could be cut out of different colors of plastic (which would go against the rules of only using one sheet of material, since you would need to use different sheets for different colors).
You can see at the bottom, there is a hook for an elastic.
The elastic winds around the back axle, and hooks onto the hook. If you do it right, the elastic only catches on the pencil if you turn it in a specific direction. It’s loose when the pencil turns in the other direction (google “elastic powered toy car” to see how people do it). So theoretically, you should be able to wind the car back, and let it go so it moves forward.
I’ve never tried this, so I’m not sure if it will work or not.
It all EASILY fits on one sheet of material. I quickly calculated this (it’s missing the flames):
I still have LOTS of room, so either I could make the car bigger, or design another one (or two) to go with it so you can have races.
I’ve yet to cut it, so I have no clue how it will perform.