Succesfully moving the Fox, Goat, and Cabbage across a river with a boat of size 1.
We are unable to move 2 Foxes, a Goat, and a piece Cabbage across a river with a boat of size 1.
ALCUIN NUMBERS
Thesis- Pure Mathematics and Graph Theory
The Alcuin number problem was introduced in the book " Propositiones ad Acuendos Juvenes" (Problems to sharpen the young) by Alcuin of York. It involves a goat, a piece of cabbage, and a fox, who all need to cross a river. Note the following:
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1. The boat has only one spot for an entity.
2. You cannot leave the goat and the cabbage alone on a either bank, as the goat will eat the cabbage.
3. You cannot leave the fox and the goat alone on either bank, as the fox will eat the goat.
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The problem is easy to solve (see the GIF on the left), but becomes unsolvable if we add a second fox to the mix (see the second GIF).
The Alcuin Number Problem is as follows: For any given collection of animals with any interactions between them, what is the smallest required boat size (called the "Alcuin Number") to move them across a river safely?
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My thesis, advised by Dr. David Lippel at Haverford, is about using graph theory and logic to find the smallest boat size for a given configuration of animals.