Not knowing the correct solution to a problem doesn't make you dumb.

All that would need to change in the story is for the guys to ask Barbie what she's doing, and for her to explain it to them instead of them "helping her" (Bonus points if you make Brian and Steve offer incorrect solutions before Barbie educates them). Then she finishes the game on her own, realizing she didn't need…

The balloon isn't paper. The tether isn't paper. The computer and battery aren't paper. It has an arbitrary propulsion device. By the same logic, you could win simply by crumbling some scrap paper and tossing it across the ISS. 17 seconds and you've traveled further.

'Hi, I'm a photographer, I'm looking to buy a camera. I don't really care what the specs are, just give me the one with the loudest fucking shutter possible.'