River Crossing

A River Crossing puzzle is a type of optimization-based logic puzzle in which solvers must figure out how to get a series of items and/or people across a space (usually a river) in the fewest number of moves. The most common version of this puzzle is the Wolf/Sheep/Cabbage problem, where a farmer must ferry those three objects across a river one at a time, but knows that if left alone the wolf will eat the sheep and the sheep will eat the cabbage.

Background
The earliest known instance of a river-crossing-based puzzle comes from Propositiones ad Acuendos Juvenes, a 9th century Latin manuscript attributed to Alcuin of York. It details three different river crossings, two of which carry an amount of historical significance (due to their repeated use in puzzle books and culture).

The first is the "Wolf, Goat, and Cabbage" problem, wherein a farmer needs to transport one of each of the three things across a river one at a time, with the caveat that the wolf will eat the goat if left together, and the goat will eat the cabbage if left together. The goal is to get all three across in the fewest number of trips.

The second is the "Jealous Husbands" problem, wherein three married couples need to travel across a river via a boat that can only carry two people. However, the husbands will not allow their wives to be to be alone in the presence of another man without being present himself. As with the previous problem, the goal is to get all six across in the fewest number of trips.

Other river-crossing puzzles have been created since then, including the also-popular "Bridge and Torch" problem (first recorded in 1981 in the book Super Strategies For Puzzles and Games) where four people who walk at different paces need to cross a bridge with a weight limit of two people, while also making sure their one torch is present for every crossing.

Puzzle Application
At their core, river crossing puzzles are all about finding the best way to accomplish the goal of getting everything from Point A to Point B. Sometimes there's only one way to do it, and sometimes there's multiple ways where one is just faster than the others. Regardless of how it functions, this type of logic puzzle is a core piece of the Optimization genre.

River crossings are difficult to incorporate into hunt puzzles, as they require a significant amount of expansion in order to separate themselves from those that already have recorded solutions. As a result, authors wanting to apply the concept to their puzzles can focus on a few different aspects:


 * Constraints - What prevents certain moves from occuring? Is it based on who can do the transporting, or who is left alone?
 * Setting - A significant enough change in setting and language may prevent solvers from realizing they're working with a river crossing puzzle until they're already deep into it.
 * Extraction - How do solvers get their final answer? Is it based on the number of moves, the order that steps occur, or something else entirely?

Examples

 * - Themed after the TV show Futurama, this puzzles takes river crossing to an incredible new level. Not only does it require certain characters to pilot the ship that transports things and people, each item being transported has some amount of conflict with passengers, pilots, and other times. This gets even trickier to navigate when the puzzle introduces additional constraints based on the destinations themselves.