Panthera posted...
How exactly do you actually defeat Q? "Out thinking him" is just how Picard (and occasionally others) impress him and make him decide to leave, he doesn't really lose anything and I don't recall there ever being indications on how to actually fight a Q successfully.
Q would still have his usual personality, so out-thinking him would be a legitimate way to beat him. Failing that, there is always the "more gun" approach: use powerful enough attacks or reality warping to take him out.
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