River Crossing Problems: An Algebraic Approach

We consider two well-known river crossing problems, one concerning jealous husbands and the other missionaries and cannibals. We show that a symmetry group action on the state set of the jealous husbands problem allow us to simplify it to the missionaries and cannibals problem. Then category theory is used to describe the relationship between the two problems. It is also noted that the missionaries and cannibals problem arose (more than a thousand years after the jealous husbands problem) precisely when the group approach began to be widely spread and popularized.