# A river crossing puzzle

Here is a puzzle I came up with.

Ali and Billie are approaching a river from one side, and Casey and Devin from the other side.
Ali shouts: "Do you two also want to cross?"
Casey shouts back: "Yes! This should be no problem, there is plenty of boats on each side, and it takes just one minute to cross."
Devin shouts: "I don't know, the boats seem rather difficult to steer. I will only go if either Ali or Billie are in the boat."
Billie shouts: "They're also pretty small. I will only go with Devin alone."
Ali shouts: "I'm OK as long as I'm not alone with Casey in the boat!"

What is the fastest way for everyone to cross the river?

I'd also be interested in ideas on how to improve the story (the constraints seem a bit arbitrary...)

• Your sentence Billie shouts: "They're also pretty small. I will only go with Devin alone." can have multiple correct interpretations: 1. Billie will only go when Devin is left alone. 2. Billie will go with nobody ecxept Devin, and will also go alone. 3. Billie will only go if Devin is with him. 4. Billie will not go in a group that includes Devin unless it is just the two of them. Oct 25, 2020 at 15:45
• I tried to clarify this. Oct 25, 2020 at 18:06
• Please avoid making edits that invalidates answers. Oct 25, 2020 at 18:46
• Swim, perhaps?? Nov 1, 2020 at 18:04
• Billie will only go with Devin—not alone or with more than two people, correct? Ali will go alone, or with Devin, or with Devin and Casey, correct? Nov 1, 2020 at 22:21

Assume that

• one person alone can steer a boat (otherwise there is no possible move at beginning);
• a boat can accomodate at least two people;
• multiple boats can travel on the river at the same time.

Let's call the two sides "left" (where A, B originally stay) and "right" (where C, D originally stay).

Five minutes:

First minute: [A] -> right;
Third minute: [BD] -> right, [A] -> right;
Fifth minute: [A] -> right.
[C] -> left can happen any time.

Explanation:

There must be a moment when [BD]->right.
Before that, D must get to the left side, and this can only happen with A on the right side.

Thus the following must happen in order: [A] -> right; [AD] -> left; [BD] -> right.

After that, we must get D back to left, and this can only happen with [AD] -> left, since we don't want to bother B again...
And finally A should be back to right again.

• The assumptions are correct, and this is the fastest way! I'll wait a little to accept this answer in case someone has some great new ideas for a story :-) Oct 24, 2020 at 20:29
• I don't have any great idea for a story, but I think it might be interesting to consider more complicated versions, where we have more people on each side and everyone has a set of possible partners. Oct 25, 2020 at 1:27

Looking at these two sentences:

Devin shouts: "I don't know, the boats seem rather difficult to steer. I will only go if either Ali or Billie are in the boat."

Billie shouts: "They're also pretty small. I will only go with Devin alone."

Devin is making it clear that he will not go alone, as he will only go if either Ali or Billie are in the boat. Billie, however, merely stated that he will only go with Devin, as in, no other person. But he did not say that he won't go alone.

Assuming my assumption is correct, I'd say it would take a minimal of

3 minutes to cross.

Procedure:

Let me call the side of the river that Ali and Billie are on side1, and the other side side2.

1. Casey goes to side1 while Billie and Ali goes to side2 (three boats were in use).

2. Billie and Devin goes to side1 (one boat was in use).

3. Billie goes to side2 (one boat was in use).

EDIT: Here is a post that justifies my argument.

• Billie will only cross with Devin, so he wouldn't cross alone in step 1 or 3 Oct 24, 2020 at 20:35
• @AnthonyIngram-Westover wait, i'll edit Oct 24, 2020 at 20:37
• The intention was to not allow Billie alone in a boat. Oct 24, 2020 at 20:43
• @FalkHüffner I see. Still, your way of putting it does not make my answer wrong. Oct 24, 2020 at 21:10
• @AnthonyIngram-Westover - The OP's comment confirmed the intention, but the wording of the sentence in the question has more than one possible interpretation. The puzzle's wording needs to be tightened up. Oct 24, 2020 at 23:50