Answer and explanation:
This is a puzzle question that needs logical reasoning to solve. From the question there are four items that must cross the bridge, the Santa, Rudolph, an elf and a snowman. To cross the bridge successfully, SANTA will have to act as a guide for each single cross. And the Rudolph is a threat to both the elf and snowman. Since this is so, the Santa will cross first with Rudolph to the other side of the bridge. Santa will return to the former side alone. This time around he will have to cross over with the elf to the other side where he left Rudolph. This leaves the snowman alone on the original side with Santa, Elf and Rudolph on the other side.
Now Santa is faced with the challenge of leaving the elf and Rudolph together (as the Elf is afraid Rudolph will bit him) to cross over snowman. The best thing he will have to do is to cross back to the original side with Rudolph, leaving the Elf alone. On reaching the original side, he will leave Rudolph to cross back to the other side with the snowman. The snowman and the Elf are safe being together, so he will have to cross alone to the original side to pick Rudolph back to the other side of the bridge. In this way they are all safe.