163453

The two slowest and the two fastest people should always cross together to spend the least amount of time and the returning person should be quicker. On either side of the bridge there should be a quicker person because one will have to return. Let the people to take 1 min and 2 min be 1 and 2 and 10 min and 7 min 10 and 7. 2 and 1 will cross the bridge first with the torch and 1 will take the torch back to 7 and 10. This takes 3 mins. Crossing the bridge with 1 and 10 will take longer since they will travel at 10 mins together and then 1 will come back and take 7 which will take 7 mins. Instead, 7 and 10 will cross the bridge with the torch. This is when it is important to have a quick person on the other side. 2 will return with the torch and 1 and 2 will cross finally. This will take 17 mins which is the shortest time possible.