Ok… I admit to being very skeptical about the… “challenge”.
But depending on your definition of “game” you can indeed make one without using any actionscript code using button symbols as Nqkoi1 suggested.
Here is an example of this. It only took me about 5 days to build. The goal is to the find the hat that contains the rabbit!
You can download the source:
I briefly tried to see if you could setup additional “logic” by putting a second rollover button in the rollover state of the first button. If this was possible you could create something that would definitely be considered a game. However, I couldn’t get this work. So it appears that any “game” you want to build without actionscript is limited to single tier rollover effects.