SOCHI, Russia—The most carefully guarded sporting equipment in the Winter Olympics lies behind the door of a sealed-off corridor in a stadium near the upper reaches of the Caucasus Mountains. It is monitored at all hours by security guards who open the door only for its owners. And even then, they need personalized keys to retrieve it from their lockers. For biathletes, the security measures are just one more reminder: It isn't easy getting your equipment around the Olympics when your equipment includes a .22-caliber rifle.

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