Talk:River crossing puzzle

Suggest change to logic problem

Hey,

I'm a new user and I just noticed that the puzzle could be edited a little. I changed the word goose to chicken because that was the way my logic teacher had explained at my University. However, it was deleted. I was just thinking we should provide both versions of the puzzle - fox, goose, and beans as well as fox, chicken, and grains.

Thanks!

--Kwells1989 (talk) 20:12, 24 May 2011 (UTC)

It's not actually a different puzzle, so I don't think it merits being listed as a separate entry in the list of puzzles. Our Fox, goose and bag of beans puzzle article mentions your variation, but "we should change it to match the way my local instructor presented it" seems to me a pretty unconvincing reason: lots of people are likely to have seen the puzzle presented in lots of different ways (to me, the wolf/goat/cabbage variation is more familiar). But maybe we can at least state here, in a single entry, that other variations are known. —David Eppstein (talk) 21:35, 24 May 2011 (UTC)

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forced solutions

I suppose more complex types of these puzzles could benefit from graph-theoretic methods, dynamic programming, or integer programming, as you say. But such versions as the fox, goose and bag of beans as stated have a forced solution, that is, once you start to outline a solution, you have no options other than to solve it. There are simply no other moves allowed by the rules…you literally cannot fail.

For example, the rules tell us that if two things are left together, it must be the fox and the beans. So there is no other first step but to take the goose across. Then what? If you next take the fox across, you must bring the goose back…or if you take the beans across, you must also bring the goose back. Either way, the goose comes back…there is no other way to do it. And the rest of the solution follows in like manner.

And what is like manner? Well, suppose you take the fox over as the second step…you have no choice but to take the goose back. Then what? You just brought the goose back, it makes no sense to bring it over again, so you bring the beans over. The beans can safely stay with the fox, so you can now bring the goose back over and you’re done. True, the second step had two options, but both had the same result, bringing the goose back. At each step, you couldn’t not solve it if you tried!

The true key is the realization that you must temporarily undo something that you previously did. This is a tactic also used in solving square 15 puzzles. 71.162.113.226 (talk) 00:16, 31 January 2021 (UTC)