In one day, I solved the problem because I systematically listed out all the assumptions they made by stating the problem the way they did. Here's how I did it.
1) chemical energy is used
2) two surfaces are involved
3) contact is crucial to the act of adhering
Negate the assumptions and explore alternatives to each, such as:
1) magnetic energy
2) three surfaces
3) contact is NOT crucial to the act of adhering
The result is the Teflon Sandwich.
In sum, listing out your assumptions in a systematic manner can quickly get you unstuck by uncovering possible features of the solution that you are overlooking.