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It's actually possible to win on impossible. Just spam egg catapults and cavemen to hold off the enemy until he gets machine guns, by which time you should be able to get multiple rocket launchers. Once the cavemen stack, the concentration of force should be able to easily take down even cannoneers.
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Fun game, but what's funny is I forgot that I could upgrade troops and stuff, so I was battling knights with cavemen for five minutes before I realized Club < Armor, LOL