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It's really easy, place the bottom of your cup in the palm of your hand, then forcefully smack it against the ear of your victim. This will rupture the eardrum and cause immense pain, the victim will be as disabled as if you had shot or stabbed him.
Quick someone call the TSA!
I never liked styrofoam cups anyway. Time to get rid of them.
Next up, how to snap a man's neck with rolled up magazine...