How can these people cross the bridge? [duplicate]

Question

• There are 4 people that must cross an old dilapidated bridge at night, All four walk at different speeds:

  • There is a young teenager that can cross the bridge in 1 minute.

  • There is teenager's older brother can cross the bridge in 2 minutes.

  • Their father can cross the bridge in 5 minutes.

  • Their grandfather can cross the bridge in 10 minutes.

• Only two people can cross at a time otherwise the bridge will break.

• Also they have an oil lamp that will only last 17 minutes

• Any party that crosses the bridge (only one or two people) must have the oil lamp with them.

• If two people cross together, they have to walk at the speed of the slower person.

How can the entire group cross the bridge in 17 minutes?

The best answer I got was:

1. The teenager and the grandfather walk across the bridge with the oil lamp: 10 minutes

2. The teenager walks back with the oil lamp: 1 minute

3. The teenager and the father walk across the bridge with the oil lamp: 5 minutes

4. The teenager walks back with the oil lamp: 1 minute

5. The teenager and his older brother walk across the bridge with the oil lamp: 2 minutes

But that adds up to 19 minutes.

Answer 1

They can cross in a total of:

17 minutes

Like this:

(To simplify, let's name the people A, B, C, and D, in order from fastest to slowest.)

• A and B cross - 2 minutes, leaving CD|AB

• A comes back - 1 minute, leaving ACD|B

• C and D cross - 10 minutes, leaving A|BCD

• B comes back - 2 minutes, leaving AB|CD

• A and B cross - 2 minutes, leaving |ABCD