Generalizing the Wolf-Goat-Cabbage Problem

  • Erich Prisner
  • Published 2006 in Electronic Notes in Discrete Mathematics

Abstract

The wolf-goat-cabbage problem is a fairly well-known puzzle. Certain items (wolf, goat, and cabbage) have to be transferred from one bank of a river to the other. The rower uses a boat with a limited amount of space (besides the rower only one item fits) and has to be careful not to leave certain forbidden pairs (in this case, wolf and goat form such a forbidden pair, and goat and cabbage are the other) back on any bank. In this talk we investigate a generalized setting where we have a larger boat, having space for k items besides the rower, more items than wolf, goat, cabbage, and different forbidden pairs. If we define a graph G with the items to move as vertices and all forbidden pairs as edges, then each graph G and each natural number k defines such a problem. Natural questions are whether or not the transition is possible, and if it is, how many boat trips across the river are necessary to do so.

DOI: 10.1016/j.endm.2006.08.067

Cite this paper

@article{Prisner2006GeneralizingTW, title={Generalizing the Wolf-Goat-Cabbage Problem}, author={Erich Prisner}, journal={Electronic Notes in Discrete Mathematics}, year={2006}, volume={27}, pages={83} }