Get yourself set up with two possible wins. Your opponent can only defend one of them, so you win.

But then we have to think of how to get yourself in that position. There is definitely more than one way to get there. One way might be more efficient in certain circumstances, but as long as the end goal is achieved, all methods are valid.

This type of thinking will (hopefully) get kids to think about intermediate steps on the way to the end of the proof, but always keeping the end in mind. And help them to see that you must start with some sort of plan of how you could get to "win".

Hmm, maybe I could even present the discussion with an #anyqs following a heated competition...

*I got this idea from a grad class discussion of what another grad student did in collaboration with a geometry teacher. Bottom line, it's not my own idea, but I can't be sure of where it originated either!*