A completely free fixie built up from parts available to the general public? You could get a freecycled road bike, locktite the freewheel, remove the derailleurs and extra chainring, and go. But it wouldn't be pretty. And maybe someone with a few well placed dollars could make a much better bike, and still win the "Best for less than 50$" category or something! See, it would still be a challenge to hit each of the categories, or to make some surprisingly nice bikes with surprisingly cheap parts.

peace,
sam