How Can Four Women Cross a Bridge in 17 Minutes?

[Inkcoder]

A question that was asked in a Microsoft Interview:

There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.

Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross

For example if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. What is the order required to get all women across in 17 minutes?

I'm still working it, and Google most likely holds the answer but try to figure it out on your own.
-Austin

 

[mattmns]

Not too bad.

Solution.
1,2 go across. 1 comes back. 5,10 go across. 2 comes back. 1,2 go across. (2 + 1 + 10 + 2 + 2 = 17)[/color]

 

[Tone.Tran]

This problem took me a while but once you figure it out, you'll kick yourself in the butt. Naturally, you think 19 minutes is the time you need for them to all go across but it's actually only 16.

What I thought was that if 10 and 5 go separate, it's 15 minutes which is obviously too much. So knowing this, you know that 5 and 10 must go together. How to do this is:

1,2 go across.
1 goes back.
3,4 go across.
2 goes back.
1 goes across.

This comes out to 2+1+10+2+1 = 16 minutes.[/color]

 

[d_leet]

This problem took me a while but once you figure it out, you'll kick yourself in the butt. Naturally, you think 19 minutes is the time you need for them to all go across but it's actually only 16.

What I thought was that if 10 and 5 go separate, it's 15 minutes which is obviously too much. So knowing this, you know that 5 and 10 must go together. How to do this is:

1,2 go across.
1 goes back.
3,4 go across.
2 goes back.
1 goes across.

This comes out to 2+1+10+2+1 = 16 minutes.[/color]

But 2 has to go with 1 back across, so their trip takes 2 minutes, hence the total time is 17.

 

[Tone.Tran]

Woops, my mistake there. 17 is correct.