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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:
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.
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?
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.