The Perilous Rope Bridge Dilemma | Solution

No doubt you worked this one out carefully with a diagram, either on paper or in your head. Let’s compare notes and see if we both agree on a plan to get them to safety. They only have one shot to get this right!

To make this easy, let’s use a letter for each person:

A = person who takes 1 minute

B = person who takes 2 minutes

C = person who takes 5 minutes

D = person who takes 10 minutes

We can put this together in our head:

A and B both go together. B will take 2 minutes, so he will be halfway across by the time A gets to the other side. This means B must carry the flashlight.

At the 2-minute mark, when A and B are both at the other side, A takes the flashlight from B, then goes back to the other side. This takes him 1 minute.

At the three-minute mark, A arrives back on the starting side, gives the flashlight to D, and gets C and D to cross together. C takes 5 minutes and gets to the other side when D is halfway across, shining the flashlight ahead so he can see. 8 minutes have elapsed at this point when C arrives.

At the 13-minute mark, D arrives on the other side and hands the flashlight to B, who will cross back to where A is waiting. It takes 2 minutes. The total time now is 15 minutes, when B arrives back on the starting side.

Now A and B will go together, A arriving first, at the 16-minute mark, then B arriving right at the 17-minute mark.

They are all on the other side now. They have just enough time to cut the bridge and escape. They can see the bear bounding through the trees on the other side.

In the dark, with the flashlight now burned out, they escape, glad they knew how to wield the most useful tool called logic.

There is another way to do this problem, which might have been your answer. (When your survival depends on it, you’ll take any solution that works.)

Suppose instead that B comes back instead of A:

At the 2-minute mark, B keeps the flashlight, then heads back.

At the 4-minute mark, B gives the flashlight to D so D and C can cross.

At the 14-minute mark, D arrives and hands the flashlight to A.

A arrives back at the starting side at the 15-minute mark to help B, hands him the flashlight, then they both cross, and right at 17 minutes, they both are on the other side. Just enough time to cut the bridge and not become bear food!

 

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