A goose, a fox and a bag of grain

So this is a logic problem which you are all probably pretty well acquainted with, considering it’s been around since the dark ages.

It goes like this (or some variation thereof): a farmer has a goose, a fox and a bag of grain that he has to transport across the river. The boat that he has can transport the farmer plus one item, whether it be goose, fox or grain. The constraints are that the fox will devour the goose if left alone with it and the goose will devour the grain if left alone with it. So you can never leave the fox with the goose or the goose with the grain as you ferry items across the river.

I’ll give you a second to work it out, if you haven’t already.

The answer is that the farmer crosses with the goose (leaving the fox and grain), returns and takes the fox across, brings the goose back over and picks up the grain (leaving the goose), takes the grain to the fox, and returns finally for the goose again. Rather than thinking of it as what you can’t do, think of it instead in terms of keeping the fox and grain together.

I know what the goal of the problem is – to stump someone or to develop some critical thinking skills – but I’ve long been bothered by it. It obviously has some assumptions built into it, otherwise it wouldn’t work. It is just a mental exercise, I tell myself, but I still can’t help but worry over it. I think the farmer’s problem isn’t that he’s got to manage himself and these items across a river in a small boat, I think that he needs to better plan his trips in general. Perhaps there is a scenario where he absolutely must travel with three items, two of which wish to eat two others. Ok – I suppose that could happen. There are other issues that he should address in order to not have to repeat the problems he faces trip after trip. First: contain these animals in some manner. Why are they not wandering off as it is? If the goose is sufficient incentive for the fox to stay with the farmer, wouldn’t the fox want to leave as soon as the goose is across the river? Same question regarding the goose and the grain. So I think he’d have more problems if he ferries the goose across the river and returns to find the fox has left – particularly if he needs the fox for some purpose. Meanwhile, he’s picking up his grain and returns to the goose to find IT has wandered off as well. Perhaps it has waddled to it’s natural habitat – the river – and floated away. So now the farmer has only one of his three items. Surely that would be a complete defeat of his purpose.

Second: get a bigger boat. Better yet, collaborate with other farmers in the area and build a sturdy bridge. Use the ferry or boat as a back-up in case of wash-out.

Third: this can’t be emphasized enough – plan better. A fox who is full won’t go after prey. That’s not how predators work. Something tells me a goose will eat itself to death if it could (maybe I don’t have much faith in geese – I was once attacked by a guard goose on a Scottish farm when I was little and these are not smart birds). If the farmer can’t plan a trip where he isn’t transporting these three particular items at once, perhaps he can plan on feeding the fox first (perhaps a different goose) so that he at least eliminates one restriction.

Speaking of logic problems, I was thinking about how many frozen peas it would take to fill a room the other day (something I was idly wondering about while driving, “who knows where thoughts come from, they just appear!”) and besides not having the room dimensions in mind, nor understanding how to determine the volume of the room (length x width x height?), nor the average size of a pea (something to do with diameter, I am sure), I was wondering how the filling would occur. If the room was going to be filled from the ceiling, you can fill the room with loose frozen peas, and you would get a very different answer than if you were filling via a door (or window, I guess). If you were filling by walking into the room, you’d probably need to have some kind of stacking happen, otherwise it just wouldn’t work, logistically. Try to imagine a firehose shooting frozen peas into a space you’re trying to fill. It really only works from the ceiling down, not floor-level up. So anyway, if you fill from the door, you will probably be using cases of frozen peas (those stack nicely, I’m sure) and then you have to figure out the volume of a case to determine how many cases fit in the room, and then the average amount of peas in each case to figure out the total number of peas. So that’s my question: firehose of peas from the ceiling, or cases of peas by the door?

Speaking of how nicely cases of peas fit into a (presumably) square room, at one point, scientist speculated that atoms were probably square, because it’s the best shape for packing a lot of stuff together without wasting any space.

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