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Visualisation of the fox, goose and bag of beans puzzle by CMG Lee. Uppercase denotes an object at the destination and lowercase denotes it at the origin. Movement of each object is represented by a coordinate axis. All the 8 valid and invalid placements are shown as vertices of a cube, and all 12 movements as its edges. Invalid moves are crossed out, leaving the 2 solutions shown in blue and purple. This was placed on Wikicommons under a Creative Commons Attribution-Share Alike 4.0 International license here: https://commons.wikimedia.org/wiki/File:Fox_goose_beans_puzzle_visualisation.svg

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Visualisation of the fox, goose and bag of beans puzzle by CMG Lee. Uppercase denotes an object at the destination and lowercase denotes it at the origin. Movement of each object is represented by a coordinate axis. All the 8 valid and invalid placements are shown as vertices of a cube, and all 12 movements as its edges. Invalid moves are crossed out, leaving the 2 solutions shown in blue and purple. This was placed on Wikicommons under a Creative Commons Attribution-Share Alike 4.0 International license here: https://commons.wikimedia.org/wiki/File:Fox_goose_beans_puzzle_visualisation.svg
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Sunday, 22-Dec-2024 04:55:37 JST John Carlos Baez
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The wolf, goat and cabbage problem comes in many versions - like fox, goose and beans.
It's also a graph theory problem! You can make a cube where fgb means all three are on the near shore of the river, FGB means they're all on the far shore, and so on for all 8 possibilities. Certain edges are forbidden - because then the farmer would be on a boat while the fox and goose are on the same shore, or the goose and the beans. This makes getting from fgb to FGB a bit tricky.
(2/n)

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