## Three Cannibals

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### Three Cannibals

Three cannibals and three anthropologists have to cross a river.

The boat they have is only big enough for two people. The cannibals will do as requested, even if they are on the other side of the river, with one exception. If at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them.

What plan can the anthropologists use for crossing the river so they don't get eaten?

Note: One anthropologist can not control two cannibals on land, nor can one anthropologist on land control two cannibals on the boat if they are all on the same side of the river. This means an anthropologist will not survive being rowed across the river by a cannibal if there is one cannibal on the other side.
Don L. Sargent

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### Re: Three Cannibals

The easiest plan would be to shoot all three cannibals from across the river, then have two anthropologists cross in the boat, leave one safely with the now-dead cannibals (perhaps starting to bury them), have the other anthropologist come back with the boat across the river to pick up the last one so both anthropologists can now cross the river to join their comrade and help in the burial detail.

But I'm guessing that's not the solution you're looking for.
RonWessels

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### Re: Three Cannibals

Spoiler:
C = cannibal
A = Anthropologist
B = boat
Code: Select all
`CCCAAAB......CCAA......BCACCAAAB......CAAA......BCCCCAAAB......CCCA......BCCAACCAAB......CACC......BCAAACCCB......AAAC......BCCAAACCB......CAAA......BCCCAAA`
Why put off till today what you could just as easily get done tomorrow?

I can mathematically prove that 1 equals 0!.

Parts a-x in my plan weren't that important anyways.

Ansain

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Location: Here

### Re: Three Cannibals

Try to find a solution for n cannibals and n anthropologists.

Some observations:

Spoiler:
• It suffices to keep track of the "other side". My notation for a state: a/c, where a is the number of anthropologists, a the number of cannibals on the other side. You start with 0/0 and want to get to n/n. There are n-a anthropologists and n-c cannibals on "our side" in each state.
• The only valid states are k/k, 0/k and n/k, where 0 <= k <= n
• The states can be seen as nodes of an directed graph, an edge pointing from state a/c to a'/c' when former can lead to latter with one move from our side to the other side (this is the case when a <= a' and c <= c' and a+c < a'+c' <= a+c+2.
• A solution is a path from 0/0 to n/n, with alternating directions
blinry

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### Re: Three Cannibals

I reject your dehumanizing categorization of cannibals as unable to suppress their socially-unaccepted urges.

What?

Okay okay. If you have more than 3 but the same number N of each A and C then,

Spoiler:
The only valid non-degerenerate first two moves result in one C ending up across the river, and the boat back where it started.

The only valid non-degerenate next move is to move two C’s across the river, so you have 3 C’s on the other side. Then one brings the boat back, so 2 C’s are across.

It is valid to continue moving C’s across, but if more C’s are on the other side than the total that can fit in the boat, no A’s can cross. The only time it might be worth having more temporarily is to have one to bring the boat back. But we just did that.

Since moving more C’s is unproductive, and moving an A and a C together is not valid, we must move 2 A’s across. There are now 2 of each type on the other side, and the boat is there.

The only valid moves are to have the 2 A’s that just arrived turn around and come back, or to have an A and a C together come back. But in the latter case the only valid next move would be to send them both right back across.

So there are no solutions with a 2-person boat with more than 3 of both A and C.
Small Government Liberal

Qaanol

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### Re: Three Cannibals

What about if you vary the boat size so instead of a fixed capacity of 2 passengers, the boat can carry X passengers. What value of X is required for N anthropologists and N cannibals to cross the river?

(NB: I'm not entirely convinced Don L. Sargent isn't a spambot - he seems to be doing nothing but posting numerous relatively well known logic puzzles - most of which are repeats - and not replying to any of his threads, and his nickname fits with previous spambots I've seen. Perhaps I'm maligning him, though.)

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### Re: Three Cannibals

Spoiler:
Wait, there's a wording error: You should say more or equal cannibals to anthropologists. Otherwise just take a cannibal and an anthropologist each trip.
Ghostly, she stood in front of him and looked into his eyes. "I am here," she said. "I am here. I want to touch you." She pleaded: "Look at me!" But he would not see her; he only knew how to look at the outside of things.

math

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### Re: Three Cannibals

math wrote:
Spoiler:
Wait, there's a wording error: You should say more or equal cannibals to anthropologists. Otherwise just take a cannibal and an anthropologist each trip.

How do you get the boat back?
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

skeptical scientist
closed-minded spiritualist

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### Re: Three Cannibals

I suppose they will both taste the same to a cannibal...

streetto

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### Re: Three Cannibals

streetto wrote:I already knew this puzzle, but with missionaries instead of anthropologists.
I suppose they will both taste the same to a cannibal...

i knew it as foxes and chickens... slightly less exotic

AvatarIII

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