With practice, it isn't all that difficult to remove the head of a screw by drilling. Start with a 1/8"drill to make a 1/4"-deep pilot hole. Follow this with a drill of the same diameter as the shank of the screw, and the ringlike remains of the head will suddenly be clinging to the bit. After the head has been removed this way, it's often possible to remove the hardware or plank it was holding, and then turn out the remaining threaded portion of the screw with a pair of Vise-Grip pliers or with a dedicated screw-removal tool.
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