2348: Boat Puzzle

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Boat Puzzle

Title text: 'No, my cabbage moths have already started laying eggs in them! Send the trolley into the river!' 'No, the sailing wolf will steal the boat to rescue them!'

Explanation

This comic is a twist on an old riddle. In the original riddle, a person has to cross a river in a boat that can only hold them and one other object. They have a wolf, a goat, and a cabbage that they need to bring across with them, similar to the first panel. If the wolf is left alone with the goat, however, the wolf will eat the goat; and if the goat and cabbage are alone, the goat will eat the cabbage. (The problem can be solved in seven trips.)

However, the comic quickly devolves into surrealism in the later panels as new characters show up, bringing deviations of the original "cabbage", "goat", and "wolf" that add extra layers of complexity to the riddle. White Hat brings extra wolves and cabbages. Black Hat, in his traditional classhole style, brings cabbage moths which will infest unsupervised cabbages with destructive larvae, and boat-destroying termites. How he intends to bring them across the river (or even if he wants to) is unknown, but it brings to mind the parable of The Scorpion and the Frog. Beret Guy arrives with a wolf who can operate a boat, who could perhaps serve as a second pilot to expedite the crossing, so long as he is not asked to ferry a goat, and also a goat who eats wolves, possibly in addition to the cabbages. This is unusual^{[citation needed]}, as one would expect from Beret Guy's associates.

The last panel is a reference to the Trolley Problem, a moral test that asks the participant whether they would passively let people in the way of an uncontrollable trolley die or actively divert the trolley to kill a single person standing on a branch of the tracks. The comic gives a twist here too: according to the title text, the characters must choose between stopping the trolley full of wolves with a cushion of cabbages (in which Black Hat's cabbage moths have laid eggs, which he implicitly argues are morally equivalent to "innocent children") or letting it crash into the river (at which point the wolf who can operate a boat will steal the boat to rescue the wolves from the trolley, which will delay the other characters from crossing the river).

The River Crossing puzzle was also mentioned in 1134: Logic Boat and referenced in 589: Designated Drivers and 2684: Road Space Comparison.

The Trolley Problem was also mentioned in 1455: Trolley Problem and referenced in 1938: Meltdown and Spectre.

Solving the problem

Unlike typical Logic Boat problems the presence of multiple humans makes finding a solution almost trivial, however trying to determine the solution with the least number of trips could still make the somewhat challenging. Because the set of constraints are both ambiguous and incomplete, it requires the reader to make assumptions that, in turn, will lead to different solutions.

Reasonable Assumptions

The following assumptions can be made based on the setup of the problem or are necessary to avoid an unsolvable puzzle.

• Cueball is an observer. He is set up as an observer there to solve the problem, not pilot the boat or "watch" the cargo.
• The boat can only hold two items. This is standard in logic boat problems. Groups of insects count as one item.
• Black Hat and Beret Guy both want to cross the river with their cargo. Neither states that they wish to cross the river like Ponytail and White Hat, but it can be inferred from the setup of the scenario.
• The termites will destroy the boat after crossing. Otherwise the problem is unsolvable. This is similar to the Poncelet–Steiner theorem, which shows that any compass-and-straightedge construction can be completed with a "rusty compass", so long as the compass works at least once.
• The wolf-eating goat also eats cabbage. The wolf-eating constraint adds to the goat's existing constraints.
• The sailing wolf follows the command of an adjacent human. The alternatives require more assumptions for a solvable puzzle.
• The sailing wolf returns the trolley wolves to the near shore. The trolley wolves show no indication of wanting to cross the river.
• Stopping the trolley destroys all the cabbages. Otherwise the event does not affect the logic puzzle.
• The pack of wolves from the trolley will eat a human or wolf-eating goat left by themselves. Aligns with the spirit of the constraints.
  • A wolf can protect a human from a pack of wolves. A human who is accompanied by one of the wolves who want to cross the river should not count as being "alone" for the purpose of getting eaten by the wolves from the trolley; otherwise, there is no way to get everyone across.

The Trolley

The trolley problem creates two versions of the puzzle, one where the cabbages are destroyed, the other where they are not and a wolf rescue takes place. The ethical issues associated with the trolley problem are independent from the logic of how to cross the river.

Solutions

• General

With four humans involved, the first trip across can bring an extra human who then can guard the cargo as it is brought across in arbitrary order with care being taken not to have predator and prey alone together at the end. The termites must be last cargo ferried across as they will destroy the boat.

• The Trolley is Stopped

The cabbages are destroyed. The second to last trip brings across the last human and the last trip brings across the termites.

• The Trolley is not Stopped

A pack of wolves is now on the near bank. The last human is brought across in the third to last trip, followed by the last wolf and lastly the termites.

Missing Information

No information is provided about whether or not the humans all get along with each other and this is left as a possible exercise for the reader given all of the characters' varying personality traits. However the sailing wolf would likely come in handy if certain humans (ex Black Hat, Beret Guy) cannot be left alone. It is also probable that certain characters might not serve in the capacity as a cargo guard.

It is also unclear if humans can leave with their cargo once all the cargo has been brought across. This could complicate matters if a far side "guard" leaves early.

Transcript

[Cueball and Ponytail are standing on the bank of a river. There is a boat in the river. A goat and wolf are also on the riverbank, and Ponytail is holding a cabbage.]

Ponytail: I need to cross the river. I have a wolf, a goat, and a cabbage.

Cueball: Hmm.

[White Hat appears, accompanied by two wolves and pulling a wagon full of cabbages.]

Cueball: OK, here's what-

White Hat: Hi, I also need to cross. I have two wolves and 100 cabbages.

[Black Hat arrives, surrounded by a cloud of flying creatures and carrying a jar of bugs under his arm. Beret Guy follows with another wolf and goat on leashes.]

Black Hat: I have 50 cabbage moths and 2,000 boat-destroying termites.

Beret Guy: I have a wolf that can operate a boat, and a goat that eats wolves.

[The fourth panel is a zoomed-out shot, where everything but the sky appears black.]

[A trolley speeds in, leaving a trail of dust in its wake. A person is standing on the front, and many ears are barely visible above the seats.]

Cueball: Hang on, I need to make a spreadsheet.

Trolley operator: Look out!

Trolley operator: My wolf-filled trolley is out of control and can only be stopped by a cushion of cabbages!

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Discussion

A link could be made to this wiki entry https://en.wikipedia.org/wiki/Wolf,_goat_and_cabbage_problem#Occurrence_and_variations . Also the last panel is seemingly a reference to the trolley problem https://en.wikipedia.org/wiki/Trolley_problem

Callback to strip 1134. https://xkcd.com/1134/ I don't know how to add a proper link. Pete 162.158.154.71 22:23, 19 August 2020 (UTC)

Oh boy someone out there is gonna get nerd-sniped real hard Fieldbox (talk) 23:48, 19 August 2020 (UTC)

Some thoughts I had:

- There's a hierarchy: Wolfeater -> Wolves -> Goats & Cabbage moths -> Cabbages

- Does Wolfeater also eat cabbage? Yes. It's a goat

- There are additional weapons for Rock paper scissors

- Black Hat's moths and termites could obviously be transported so far (Black Hat might lie, source needed), but in the spirit of the question: moths can't be left alone with cabbages, and termites will destroy the boat if a crossing with them is attempted

- Cabbages can cushion the trolley, and still function as cabbages afterwards. Use White Hat's, because he has 100/101 cabbages, Ponytail's 1 cabbage adds less than 1% to the cushion, and if it's a special kind (probably not in the spirit of the question), it would get jumbled with the rest of them in the cushioning

- 6 humans to keep an eye on things, instead of the normal 1

- Trolley doesn't get to cross. It can hold multiple wolves, let's say at least 3, and if the trolley could cross, then Cueball wouldn't hesitate to recommend Ponytail go across with her 3 items Coverbe (talk) 05:03, 20 August 2020 (UTC)

Relevant: "Rubicon" https://www.youtube.com/watch?v=f-ROdRgRRsY 162.158.159.14 07:28, 20 August 2020 (UTC)

Question: is the wolf-eating goat the same goat as the goat that Beret Guy won from Monty Hall? 172.69.63.247 15:53, 20 August 2020 (UTC)

On "Reasonable assumptions": "Stopping the trolley destroys all the cabbages. Otherwise the event does not affect the logic puzzle" - This could be a red herring. And: We can still see the cabbages as 2 groups: 1+100. Destroying White Hat's 100 still lets Ponytail's 1 survive intact

"The pack of wolves in the trolley, if rescued, will eat a human or wolf eating goat left alone" - This phrasing is strange. If part of it means "wolves will eat the wolf-eating-goat": I disagree. See rock-paper-scissors Coverbe (talk) 16:25, 20 August 2020 (UTC)

If you have (any) single wolf and (any) single goat alone on one side as you depart, upon your return you will probably discover either a wolf-eating-goat or a wolf eating goat. Which it is, will obviously depend upon the finer details, but it's a failure both ways... 162.158.159.14 18:29, 20 August 2020 (UTC)

That I agree with. I still wonder about "The pack of wolves […] will eat a human […]". I think it's a more reasonable assumption that any human can control any number of wolves Coverbe (talk) 19:03, 20 August 2020 (UTC)

That's a patently absurd suggestion in any other context, and arbitrary at best here. GreatWyrmGold (talk) 16:23, 24 August 2020 (UTC)

What if only Cueball of all the humans can row the boat? He could be the ferryman172.69.2.166 18:19, 20 August 2020 (UTC)

But no-one's allowed to use the boat if they haven't figured out their eye color yet. (Assume the people, goats, wolves, moths, and termites are all perfect logicians. Assume the water is unreflective, the trolley has no windows, and Cueball makes his spreadsheet without looking at a screen. Assume everyone is a very bad communicator outside of announcing their logical predicaments. Assume that Black Hat will strictly enforce these guidelines.) 108.162.219.18 19:31, 20 August 2020 (UTC)

"The pack of wolves in the trolley, if abandoned by the humans and rescued by the wolf who can operate a boat, will eat a human or wolf-eating goat left alone." - This seems really needlessly complex and doesn't really have a bearing on the problem in general.

Yeah, not sure that's better.Sturmovik (talk) 02:45, 21 August 2020 (UTC)

Given Beret Guy's surrealist nature, maybe the solution is to send him across in the boat alone, then he can return with one item: the opposite bank. 162.158.159.18 17:08, 21 August 2020 (UTC)

Certainly worth bringing up to him, I'd say. Also, thanks for the chuckle -- 162.158.186.196 19:27, 25 August 2020 (UTC)

And once the trolley hit the cabbages, a senior man from the Earth Kingdom is seen running and screaming. 172.71.11.149 00:14, 17 November 2024 (UTC)