When I hunted musk ox in Canada quite a while back, my guide was an older Inuit (as they call themselves in Canada) whose favorite polar bear rifle was a .22 Rimfire Magnum. And no, he didn't use sled dogs to surround bears and then head-shoot 'em. Instead he stalked close enough to put a bullet broadside in the heart. After a while the bears just "went to sleep." He'd taken a number that way, and preferred the .22 Mag-a-num (as he called it) because it didn't tear nearly as big a hole in the valuable hide as his .30-30.
A .22 mag might be cutting things a bit thin, but I'd be happy to hunt big bears with a 7 mag and some good bullets.
"The trouble ain't that there is too many fools, but that lightening ain't distributed right." - Mark Twain
