So for those of you that have been following this channel, and you all know that I’m obsessed about cubes I like Klein bottles, but I like cubes even better and Recently I just really watched all of The Simpsons and I spotted this cube very well hidden in one of the episodes I’m sure nobody among all those millions of people who’ve watched the simpsons Particularly episode you’re gone Maggie gone have noticed this cube well if you have let me know, but otherwise I’ll show it to you anyway. Oh That’s not candy, sweetheart. What is it with kids and candy colored poison? Huh? You stupid dog. That’s Maggie’s bunny not in front of the poison man. How am I gonna get us all across this river? Oh, a boat! We’re too heavy Let’s see I need to get the baby the dog and the poison across the river But I can only take one thing at a time I can’t leave the baby alone with the poison and I can’t leave the dog alone with the baby Can’t someone help me with this puzzle me I can help Okay, so let’s just this is help homer with the puzzle first and then see whether we can find this very very special cube Okay, so what’s the problem? well we’ve got three characters to get across the river now plus plus Homer of course and You can’t take all three in fact. I mean you can only take one. It’s kind of implied here You can only can take one so homer can only take one of the characters across, okay? so There’s a problem here in terms of who we leave on the shore as we take one of those characters across so [Meggie] can’t be left alone with the poison and Mega can also not be left alone with Santa’s helper, right? so Okay, so just take them to this sort of set up here So the only thing we can really do here since we can’t take the poison since you can’t take the dog we have to take Maggie really choice you if it’s going to work. We have to take Maggie So let’s just do this okay. Take it across Okay, well, then what can we do but we can take Maggie back, but that’s not a good choice. So let’s just leave it there Homer goes back now He can either take the dog across so you can take the poison across let’s just go for the poison see what happens, right? so poison goes across Okay, now we can’t leave those alone and just go back and get the dog so the only thing we can really do here [that] gets us somewhere is take Maggie back, so we take my get back Okay now obviously the only thing you can do now is take the dog and take it across and then we’re all okay again in terms of Those two you know can stay together so we have to go back get Maggie and That’s it. You know very very nice Okay, now did you see the Cube? No!
You didn’t see the Cube? I’m sure nobody else saw the cube, alright I’ll show you the cube now all right, let’s just go back to those three guys here being on the left side, okay, and so if I actually wanted to solve this kind of mathematically In a very special way, which is actually very useful in many many situations. I would somehow encode this So I wouldn’t call dog and Maggie and the poison being on the left side of the river to say where we are instead left left left, right so that stands for the dog second L stands for Maggie and Then the purple one stands for for poison. It is color-coded right, okay now We could also be in this state here which just means that the dogs on the left the poisons on the left and Maggie’s on the right and So that state we write as left right left okay, and this state here we write as well right right left and Maybe everybody over on that side. We write as right right right and There’s a couple more distributions affected us for more my two days for two choices here Two choices here two choices here two times two [times] two is eight eight eight different ways of distributing those three characters You know and so there? They are so eight getting closer to the cube because when you think of eight eight eight cube eight Corners All right well That’s already kind of starting to materialize But it’s not quite there yet, right so we’ve got corners, but we need something else like cubes not only got corners but also has edges and faces and stuff like this. Okay, so let’s just see what happens of we’re in one of those states like for example starting configuration is left left left What can we do? Right, Homer can take three different things you can either Take a dog across make it across pr poison across right okay? So for example a dog goes across so we can actually Now say where we can get from the beginning state? To that state he about taking the dog across and that’s why we kind of make a make a line there We can also go back right? So that line also stands for kind of moving from the right to the left so it’s that connection here between those two states Stands for we can kind of move left to right or right to left okay? Now. We can also take Maggie a cross and That gives [us] [a] second edge or back let’s dance for kind of both Movements, and then we’ve got a third one going here, okay, [and] Where we can do this for any single one of the states and to kind of just figure out? What can we do well? We can move three different things that will give us three different edges and if you put all those edges in what do we get? Wha there’s the Cube? Okay, so there’s the cube and so basically when we solved the puzzle we kind of move across the Cube except Some of the edges. We can actually not move across right. They’re prohibited. Let’s just see where they are or which ones they are okay. So what shouldn’t we do well? We shouldn’t move the dog right? it doesn’t matter whether we go from here to there or there to there shouldn’t move the dog because if We did that, Maggie and the poison would be left, right so that particular edge We should never move across okay, so we take it out now. There’s the second edge We’d have to take out just looking at is well. We should also not just take the poison that’s if you take the poison And again making the dog left with Maggie shouldn’t be done. So that edge has to be taken out Yeah
And there’s actually two more edges that we need to take out and their basic symmetric to those it’s just you know imagine that you’re on this side of the river and they’re kind of going back then You know using the poison that’s out and a dog That one’s out and actually turns out that all the other connections that are still visible now They are okay, okay, and so now you can actually kind of see at a glance. You know what’s possible What’s not possible how to solve this problem, [so] let’s just go from the beginning, okay? So we’re down here and now you can see only one connection is possible so only one move is possible So let’s just do that. So we’ve done that Now what comes next we actually have a choice here. I think got a choice either. We do the dog or we do the poison okay, and actually we’ve done the poison the first time around so let’s just do the dog this time and And I mean if you just look at it you also already know how it’s going to continue right on You can kind of go from here that that Go there Or if you take the second part you kind of go there Obviously, there’s lots more ways of getting over you could kind of go up here and [in] disease and then eventually do something But it’s I mean in terms of shortest solutions, that’s it there’s two and they’re completely symmetrical and It just depends on what choice you make now you bring your poison across or the dog So we’ll do the dog this time so that gets us here, and then you can just read off We need to do Maggie right that’s the yellow connection, so we do yellow and now it tells us poison so we do the poison and then there’s one more we need to do Maggie a cross so hohmeister shuttle back and Take Maggie a cross, and it’s done. You know so very nice Cube in there So I’m really happy okay Hope you’re happy, too Alright Giuseppe: So how would the cube look like if you could actually carry two each time? Good point. Good point. I mean, so, it’s actually not clear from the clip but kind of implied that Homer can only take one of those guys across Right, but you kind of think about it right the poison doesn’t weigh much and you know either of those Maybe maybe dog. I don’t know who’s lighter maybe it would be actually be possible to kind of fit two of those guys in and take them across then things would change a little bit, right so Basically the restriction of only being able to take one across corresponds to just filling in the edges here of the Cube if you could take two across That would mean that we also have to fill in diagonals and then actually you can kind of see at a glance again that We get a much shorter solution, right? So we could just kind of go across here So what does that Correspond to? Giuseppe: That means bringing both the dog and the poison over That’s right. So dog and poison go over alright dog and poison go over you just leave them there just Bring Maggie over and then there, so that’s three times across instead of what we did before was I think seven yeah so it’s a lot better and actually if the board could carry more critters to All three in one go which was that? Correspond to so all three in one go would then correspond to these long diagonal of the cube right so we kind of go from Here to there, and be done with it. That’s you know. It’s very nice Now actually it turns out that Homer does not our help at all he actually figures it out right and then so he describes it to the dog and Maggie and even talks to the poison! And then he implements his strategy so he’s actually doing the right thing. He’s taking Maggie across. This is have a look at this So here we go. It’s got Maggie in the the boat so he does the right thing so he starts pedaling Mm-Hmm Are you listening at all? very funny But actually when you think about it When you think about it, I mean You know if if if we maybe change the puzzle to saying well the dog can swim across, what should we do that? What should we do them? Well maybe then you bring the poison? Poison and dog are going at the same time, then it is like that case when you can carry two You can actually make it in what two or three?
Three modes again, so it’s actually exactly right, right? So we would just instead of taking Maggie will put poison in the boat and then Homer rows across and the dog swims alongside. And poison and dog stay on the other side and homer comes back to get Maggie Done, that’s all Good to go, so yeah, it’s very funny But actually it’s not over yet, right it’s not over yet. So here comes another Twist in the story, I’d be obliged to you if you’d help me puzzle out my fox duck and corn situation Well the puzzle done puzzled itself out very funny So this is actually exactly the same problem that Homer has right So there’s three different things and you know This one wants to eat that and that one wants to eat that but those two are okay together on it So it’s exactly the same it’s exactly the same and then Well, there’s a different sort of solution because the problem there now still remains because the solution was that the fox ate the duck which eat the corn and it weighs too much And so you still can’t bring it.
Exactly because I mean now everybody’s kind of together Bundled together and that means that it’s still too heavy obviously right so it’s actually not a solution actually I mean, this is just a second way of phrasing the same problem They’re original well there is an original which actually dates a couple of hundred years back is a really really old old puzzle is about a Wolf and a Sheep, I think and some cabbage right and then you know it’s the same thing again the wolf wants two sheep and sheep wants To eat cabbage and well the wolf and the cabbage together are okay. I want to get across the river Okay, so that’s that and there’s even a whole book about just believe it on I have it somewhere. I couldn’t find it today It’s not a very Good book But it had to and we had to have at the collection all right now This is actually there’s lots of variations to this puzzle you know this kind of replacing objects, but there’s also other river crossing puzzles which are very similar and Which actually get a lot harder so one which is harder than the one we just looked at is like this and I’ve just used some simpsons characters here To talk about them quickly. So here. We’ve got three couples All right, and you all know them from the simpsons and the husbands are all very jealous, okay? and they’ve got a boat and the boat can carry two people at the same time and Because the husbands are very jealous the restriction here is well, not that somebody will eat somebody else but the restriction is that None of the women can be together with another man either on this side or on that side or in the boat unless her husband is also present okay, and so you can try and figure out how how that one works right and I’m actually going to show a quick solution of this as part of the credits But maybe you want to give this a try first itself and maybe if you’re really ambitious You could try and see kind of what sort of geometrical shape is kind of hiding in the back of all this. It’s not going to be a cube. It’s going to be something pretty complicated, but there’s something there so you can actually do it again You know mathematically which gives it kind of a complete overview of what can happen anyway? So that’s it for today So here’s one solution. There’s a few so what I’ll do is. I take two of the women across… Done!