Three surgeons and a clumsy cook go camping in the remote wilderness. The clumsy cook stumbles over the campfire as he is serving the surgeons, injuring himself and dumping hot stew on the hands of the surgeons.
The cook's injuries need surgical treatment. The surgeons' injuries are minor but open. It turns out they brought the equipment necessary for the cook's surgery with them, and they can use the campfire to sterilize the tools. But there are only two rubber gloves. Because of the different surgeons' skills, all three of the surgeons are needed to operate on the cook, in sequence.
How can this be done without any of them being exposed to the blood of any of the others?
First off, it doesn't say that the surgeons each have one injured hand, so the solution must work with the surgeons having open wounds on both hands.
If Dr. Moe must operate on Curley the cook first, followed by Dr. Larry, and finally by Dr. Shemp, here is a possible solution.
They're surgeons, so why can't they operate on each other? Dr. Shemp puts on the rubber gloves and closes Dr. Moe's wounds, leaving Dr. Moe free to operate on Dr. Larry (after having sterlilized the instruments). Then after re-sterilizing the instruments, Dr. Moe then begins the operation on Curley while Dr. Larry closes the wounds on Dr. Shemp's hands. Of course I am assuming that with the wounds closed, they are no longer in danger of being exposed to the blood of any of the others.