Never hang out with cannibals - Part 2

Logic Level 3

4 anthropologists are trying to cross a river, and they have a boat that can only fit 2 people.

However, just as they are about to get into the boat, they are greeted by 4 cannibals. The cannibals will allow them to cross, but state that "If at any point in time, there are (strictly) more cannibals on one side of the river than anthropologists, then the cannibals will eat all of the anthropologists on that side."

What is the most number of anthropologists that can get across the river?

Note: We do not care about the number of cannibals that can get across.
Someone will need to row the boat back.
All 8 people are able to row the boat individually.
Include embarking/disembarking considerations. If you have 2 anthropologists rowing towards 3 cannibals, then no matter what the 2 anthropologists will be eaten.

All 4 anthropologists can get across At most 3 anthropologists can get across At most 1 anthropologists can get across At most 2 anthropologists can get across

1 solution

Ivan Koswara
Aug 10, 2015

We can bring 3 anthropologists across.

In the following, $x/y$ indicates $x$ cannibals and $y$ anthropologists on a side. The initial state is 4/4 vs 0/0 with boat on the left shore.

Bring 2 cannibals across. (2/4 vs 2/0, boat right)
Bring 1 cannibal back. (3/4 vs 1/0, boat left)
Bring 2 cannibals across. (1/4 vs 3/0, boat right)
Bring 1 cannibal back. (2/4 vs 2/0, boat left)
Bring 2 anthropologists across. (2/2 vs 2/2, boat right)
Bring 1 cannibal and 1 anthropologist back. (3/3 vs 1/1, boat left)
Bring 2 anthropologists across. The remaining one gets eaten. (3/0 vs 1/3, boat right)
Flee the scene. 3 anthropologists are safe.

However, this only states that 3 anthropologists can get across. I don't have any proof that all 4 across is impossible.

Why doesn't bringing one of each for each trip work, thus bringing all four across? I don't get the necessity of the back and forth. Am I misinterpreting the question?

Mike Sull - 5 years, 10 months ago

They only have 1 boat. How does the boat get back without someone rowing it?

Calvin Lin Staff - 5 years, 10 months ago

Lol. Oops.

Mike Sull - 5 years, 10 months ago

Are the cannibals prevented from being rowers?

Kevin Nolan - 5 years, 9 months ago

No. I have updated the phrasing of the problem accordingly.

Calvin Lin Staff - 5 years, 9 months ago

When the qtn says "at any point in time", does this include cases where the greater number of cannibals is only momentary? For eg if you have 3 cannibals on one side and two anthropologists are rowing toward them. Does this mean that during the moment when the two anthropologists hop off the boat for 2 cannibals to take the boat back, they will be eaten?

Nicole Tay - 5 years, 9 months ago

Yes. Let me add that "Include embarking/disembarking considerations. If you have 2 anthropologists rowing towards 3 cannibals, then no matter what the 2 anthropologists will be eaten."

Calvin Lin Staff - 5 years, 9 months ago

I see. Thank you!

Nicole Tay - 5 years, 9 months ago

Never hang out with cannibals - Part 2

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