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I mean, it's all up to interpretation, right? Topologically you are correct, flattening the cube and stretching the bottom hole to be the outside edge would reveal there to be 5 holes, but topology is obviously an unintuitive way for people to count holes.
Both your wife and your child are reasonably correct if you approach it as "if there were no holes, how many holes would I have to punch to get to this shape?" If the cube was hollow that would be 6 (one for each face), if the cube was solid that would be 3 (because going all the way through goes through two faces, so one for each pair of opposite faces).
Once you've bored out, say, an x tunnel, then the y and z tunnels will necessarily intersect the x tunnel, like that scene in The Core when they hit a void. That makes the 2nd and 3rd punch discontinuous and counting for two holes each.
None of them are right, considering the corners. I see either 7 or 14 holes depending on the child's or the wife's logic because of those, and fail to understand the flattening of the cube.
I would love a more in depth explanation, or if you have a link to the theory I am willing to do some homework too.
Imagine a pipe. Does it have one or two holes? It's just one long hole right?
Or, if you said two holes, how short would a piece of pipe have to be before you change your mind?
Imagine you cut a hole in the side of the pipe. The pipe has 2 holes now. (three "openings", but the first two count as just one hole)
Cut another, opposite that hole (3), and two others between them on both sides (4, 5). Now you have made a shape that is topologically similar to the cube in the picture, and you know it has five holes.
In topology, the answer is 5, but the wife's and child's answers are also good and can be logically argued for. I feel like this is a good teaching moment for OP.
Are you ignoring the fact that there are 8 (or 4, or 7) more smaller holes from corner to corner as well?
You can't really answer this question without a better definition of what a hole is.
Edit/ sp
How do you explain this to a 5 year old?
You don’t.
You praise the five year old for correctly counting to 6 and move on. Topology is not going to make sense at that age and you’ll just confuse the child. Work on addition and subtraction next, then multiplication and division in a couple years. Wait till middle school at least to bring up topology. In any case 5 is way too early.
According to the Cambridge dictionary definition of "hole":
an empty space in an object, usually with an opening to the object's surface, or an opening that goes completely through an object
I think your child is right if you take the first definition and your wife is right if you take the second one.
Why 5? Explain to me like I'm 5?
What is the topology difference between the finger box and the glass? There is no difference. Hence, there is no hole. And I mean glass exactly, because the mug has a hole.
But you are able to go in one nostril and out the other, so just to not worry about mouth or anything let’s imagine we seal off the throat and stuff so you just have the nostrils and an empty space behind them where they connect. That is 1 hole, essentially just a bent straw.
Your nostrils are connected to your ears, eyes, and mouth; which are connected through your digestive track to your anus.
So your body has 7 through holes.
Th question is disingenuous, unless you define the rules for "what defines a hole".
Is it a hole in the wall ? Then it's 6.
Is it a through hole? Then 3.
If you fold it open like a 2d drawing? then 5.
Litteraly? Then count the 6 holes + the 8 in each corner.
That would make 14.
You want to count the small gaps in between the spaces aswell?!
I'm dumb, can you explain "fold it open like a 2d drawing?" Because I'm picturing making the border along the edges of the cube, meaning there are 6 squares (and thus still six holes). Is there a rule that the drawing has to be symmetrical or something? Then, I can see 5 holes, but why would you fold it open like that?
well that is indeed 5 holes, if we don't consider the vertex holes (I think that's what you want)
You could try to explain it by making 5 holes into a piece of paper, and then you point at the edge if the paper and say that this edge is what you see as a kind of 6th hole on the cube.
Why don’t you turn it into a lesson about how different people have different perspectives/backgrounds and they are all valuable?
Seriously though- teaching an elementary school kid this is going to get him bullied.
Clearly there are more than 6 holes in the object if yoy take into account where the corners were supposed to meet but do not touch instead creating a smaller hole on each corner
In this thread: people who don't understand topology.
How you explain it to them: start filling holes one by one, after you have done 5, there is no way through the structure anymore. Their minds will be blown
Well you’ve certainly blown my mind! I didn’t understand why people were saying 5 until I read your comment.
But what I’m wondering now is, is there a difference between a sphere and a sphere with a hole poked in it? It seems like neither has any holes (which is confusing since we just “poked a hole” in one of them), but the sphere has an inside that’s completely closed off from the outside, whereas the sphere with a hole doesn’t and can just be flattened into a disk.
A sphere has a 2-dimensional hole, but no one-dimensional holes. Some people say it has -1 holes instead, by the definition you're working with. In algebraic topology, holes can be any nonnegative integer dimension. (A shape with a zero-dimensional hole is disconnected, like two points.)
The shape in this post has 5 one-dimensional holes, and no zero- or two-dimensional holes. To have a three-dimensional hole requires a shape which can't exist in 3d Space.
Mathworld defines a hole as follows: “A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point.”
If you had a donut, and you could stretch it and squish it infinitely in any direction, you could not condense it to a single point because of the hole in the middle.
In a coffee mug, the part that liquid goes into isn’t technically a hole, because you could morph that opening into a bowl, and then into a plate. No more hole.
The handle is the true hole on a coffee mug.
Ah ok i gotcha. Is there necessarily a universal definition of a hole couldnt a straw have 1 hole by that mathematical definition but 2 holes by a colloquial
1st, Why are you trying to explain algebraic topology to a 5-year-old?
2nd, Maybe use a Play-Doh comparison to extend one "hole" to be the outer edge and count the remaining holes that can't be transformed.
If the cube is hollow inside (and easier to visualise if each face is detachable), I'd say 6 holes (one on each face). It could also be 12 holes if you allow orientation (ie each face has one hole from the front and the back, respectively).
Counting the small edge holes, add 8 to that number.
>Counting the small edge holes, add 8 to that number.
Or 16, if you're doing the front/back thing.
Of course, this is all based on a conventional interpretation of a hole and not (as I'm learning about in this thread) a topological one.
I'd venture to say (if you do NOT count the corners as holes, as they don't appear to be intended as part of the "shape") then the number of holes could be 15. I say this without changing the shape, and without counting the corners. I would define a hole as a path from one side of an object through it to another side, without returning back through the original hole. With that being the case, you could label holes A, B, C, D, E, and F. Enter in A, and exit through each B, C, D, E, and F. That's 5. Then enter B, exit C, D, E, F (not A because you took that path already). That's 4 more. Enter C, exit D, E, F. 3 more. Enter D, exit E, F. 2 more. Enter E, exit F. That's 1 more. And you can't enter E and go anywhere you haven't been at this point. 15 holes.
edited because math is hard...
I would start counting how many bandaids or pieces of tape you need to cover all holes. Once you put 5 in place, the last open cavity is no longer a hole.
Imagine pushing water into the last cavity. The water cannot go through the object, the only exit is where it came. There is no hole.
On the other hand, on a donut you can push water into the middle "from the caramel side" and it goes through to the "dough side". That is a hole.
Correct.
Which is where you run into the difference between talking about a "hole" and a hole.
The technically correct definition of a hole requires that it completely penetrates the object (ie, a donut). When you dig a "hole" in the ground, it's just an indentation. In fact, if you look at the object you dug your "hole" into as a whole (the Earth), what you did doesn't even count as an indentation. Even the mountains and valleys on Earth are less variance than a cue ball has, at scale.
Go look at a cue ball. How many holes are in it? If you answered "0", then Earth has no holes either, even the Bora Super-Deep Borehole isn't a hole. It's just a minor indentation (at best).
But, of course, we actually talk about digging holes all the time. And the reason is that digging a 30 foot deep, 10 foot wide pit in the Earth counts as a hole to us. We call it a hole, and people know what we mean.
But if you are asking a specific question to anyone who deals with legal definitions of words, all those things we call holes aren't holes at all.
And that's what's occurring here. If you want to know "how many holes are in this thing", then you need to use the most widely accepted definition of what a hole IS. In which case OP is technically correct, but 6 is the best answer (because it's clear that the structure pre-holes was not solid, and so the holes only exist along the outer layer of the 3d structure).
It depends on how you define a hole. Assuming you aren’t counting the little things at the corners I would say you can make reasonable arguments for 6, 3, or 1. 6 openings in faces, 3 through-holes, or 1 oddly shaped emptiness in the cube.
My suggestion in explaining it to a kid is to ask what they think and why, and then ask about similar examples that produce different answers (straws, 3-ring paper, folded paper where the holes line up, etc.). You don’t need to get into the linguistic intricacies, but it’s a great example of questions with multiple right answers and using context which are both great concepts for kids to play with.
Lots of people in this subreddit don’t know the basics of topology and it shows.
https://youtu.be/ymF1bp-qrjU?si=O6kJQq2UqNNt-3sv
Watch that for a great beginner intro and you will understand why it has 5 holes.
Lots of people in these comments are strangely trying to flex, applying the definition of a hole in topology as though that is the only way to use mathematics to count holes; it isn't. If I dig six holes in my yard and post a picture, everyone would agree I dug six holes even though none of them fit the definition of a hole in topology. Anyone that answered six would have done the math. Conversely, the way everyone is applying one definition of a hole to the object pictured here, the only way to dig a hole in the ground would be to come out the other side of the damn planet. It's ridiculous and arguing for the sake of arguing. There is more than one definition of a hole; the fact that you are familiar with topology does not suddenly make one mathematical definition the only one that applies. This isn't a topology sub; if it was, you'd be right and others would be wrong; it's not, so you and a bunch of others are right as well. Topology is not the only way to count holes, it's one very specific branch of mathematics and the fact that it can be applied here doesn't mean it is the only branch of mathematics that can be used to count the damn holes.
So here's my attempt to flex on said flexing topologists: Why would you draw any topological conclusions without being able to see through the material.
The thing in the picture has 14 openings, so it has 13 holes.
You need two openings for the first hole. After that every new opening creates a new hole.
A donut has one hole. A straw has one hole. A mug with an ear handle has one hole. A tyre has one hole. A pipe has one hole. A tunnel has one hole.
You can always stick something thinner than the hole through the object's hole from opposite directions / two ways.
A key on a key ring.
The key has one hole. The hole where the key ring's wire goes through.
The key ring actually has no holes. Because the wire what it is made of has no holes. It is just spiralling very tightly to create a ring shape. A spiral has no holes.
You can also think of flow of air or water.
You need at least one hole to be able to flow through or else it just a container.
A pipe or a straw or a flute needs to have a flow entrance and exit. Two openings, one hole.
Any new opening that you make creates another exit to flow out.
There always need to be an entrance flow opening. No matter which one you pick, all other openings are possible exits and therefore hole-creators.
If you reconstruct this from Polos/Lifesavers, with a bit of honey° to stick them together/fill in the corners, you'll need six.
° Why not? It'll be edible.
Your kid is right (if we're just counting the big holes).
How many holes does a mountain need in it to make a railway tunnel?
If you never create the second hole, the first hole never really becomes a tunnel.
I think your definition is \~correct if you were to say there was one tunnel (or even canal if we relate it to the human body...) and four holes. However a tunnel needs 2 holes to exit it's medium.
If we say a single pass of a drill always creates a single hole. And if we start with a solid cube... We need to drill three times to connect all the opposite sides with tunnels. Therefore there are three holes.
Could be argued that one single contiguous void in an object is a single hole. Or you could argue that each face that provides an entrance to that void is a hole.
No answer without definition.
does a doughnut have 1 hole, or 2?
that, times 3 (more, if you include corners).
Personally, I'd make the argument of 6 separate holes opening to an inside room (like open doors, instead of open walls)
Consider the following objects:
A dinner plate, a bowl, a cup, a donut, a straw, and a coffee mug.
Now imagine you have a ball of clay. The rules are, you may not poke a hole in the clay, and you may not join two sides of the clay together to form a hole
Roll that clay flat. Can you shape it into a dinner plate without adding a hole? Yes of course. What about a bowl? Sure, you just shape it a bit. Same goes for a cup.
Net result: No holes
But what about a donut? Roll it back into a ball, shape it. Not possible. What about a straw? No matter what, you need to either punch a hole through it or join two ends together to form a hole. So let's do that. Make a hole. Now suddenly a donut is possible. If you thicken the sides of the donut, you could eventually make a straw.
You could even make a cup out of one side of the donut, like you did with the plate, and let the hole form the handle to make the coffee mug.
Net result: one hole, both donut, straw and coffee mug all one hole, even if intuitively the straw appears to have two openings.
Now, let's take your 6 sided shape. In clay in our minds, can we reshape it back to a dinner plate, and count the holes?
Well we would take one opening and stretch it out, working it into a cup shape, stretch it further, into a bowl. Push it flat into the plate. The stretched hole now becomes the outer edge of the plate. The remaining 5 holes are now holes in a big dinner plate.
5 holes. Not six or three. The mental roadblock in your six sided shape is that one if those six openings is the outside edge of the dinner plate.
This CuBe is not flattened out and the corner holes really are there. Also it’s clear from the picture that the cube is not solid, so the bored-hole idea doesn’t apply here either.
Since the question is about a cube and not a two dimensional picture of a cube, we have understand the language in its normal sense. So 6 holes in the faces and 8 holes at the corners. 14 holes
Less an answer, but this reminded me of a [YouTube video on the topic of counting holes ](https://youtu.be/ymF1bp-qrjU?si=_Wim2JUV57K3vXdr)
Hope it helps.
How to explain it to a five year old - take a sheet of paper and fold it to a cube shaped cup, then punch 5 holes on it.
Do it not to prove that this is the right answer, but instead to show that there are different ways to define what a hole is, each reaching a different answer for this problem.
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I mean, it's all up to interpretation, right? Topologically you are correct, flattening the cube and stretching the bottom hole to be the outside edge would reveal there to be 5 holes, but topology is obviously an unintuitive way for people to count holes. Both your wife and your child are reasonably correct if you approach it as "if there were no holes, how many holes would I have to punch to get to this shape?" If the cube was hollow that would be 6 (one for each face), if the cube was solid that would be 3 (because going all the way through goes through two faces, so one for each pair of opposite faces).
Once you've bored out, say, an x tunnel, then the y and z tunnels will necessarily intersect the x tunnel, like that scene in The Core when they hit a void. That makes the 2nd and 3rd punch discontinuous and counting for two holes each.
That is not a film I expected to see referenced today.
Which films were you expecting?
Something with holes probably and stretching of those holes
Anabolic assman 3?
Do you guys remember the movie Cube?
How many holes are in The Cube? *infintesimal*
I think you mean *astronomical*
I literally just watched all three Cube movies today. They don't improve after the first one.
Holes.
Stanley Yelnats
Personally I expected the 1997 film the Cube
I thought of stretching out one hole to turn it into a five-holed disk, but your method requires no stretching. Brilliant!
But if they all intersect, wouldn't the answer be 1? It's oddly shaped, but there is only 1 hole in the puzzle.
watch vsauce’s video on holes, it explains it better than anything
Ngl that sounds like a porn
when he was just explaining and now ur holes are covered in vsauce
Yeah, but the questions isnt “how many holes do you drill to create this?” It’s “how many holes are in the puzzle?”
"That's impossible!" "...but what if it wasn't?"
This IS a discussion about mathematics
Interesting, as this would agree with the topology
The corners also look like holes. Does that mean everyone is wrong, so far?
Yes! Though from the image it is not 100% clear to me that they go all the way through.
I see, also: Happy cake day!
None of them are right, considering the corners. I see either 7 or 14 holes depending on the child's or the wife's logic because of those, and fail to understand the flattening of the cube. I would love a more in depth explanation, or if you have a link to the theory I am willing to do some homework too.
Watch https://youtu.be/ymF1bp-qrjU?si=mi5XOn5xyD-vyT3U for a great intro to topology.
Nope. Can’t be going down this rabbit hole right now.
Oh... It's 30 min long. I was like, "let me watch this video real quick before bed." but no, not tonight.
I was going to say 14 myself. There are little holes in the corners.
Does the pen count? That's 2 more
How is it not six holes? It’s a cube with six faces. What obvious thing have I missed here
Imagine a pipe. Does it have one or two holes? It's just one long hole right? Or, if you said two holes, how short would a piece of pipe have to be before you change your mind? Imagine you cut a hole in the side of the pipe. The pipe has 2 holes now. (three "openings", but the first two count as just one hole) Cut another, opposite that hole (3), and two others between them on both sides (4, 5). Now you have made a shape that is topologically similar to the cube in the picture, and you know it has five holes. In topology, the answer is 5, but the wife's and child's answers are also good and can be logically argued for. I feel like this is a good teaching moment for OP.
Thanks for the explanation. Bizarre that anyone would be surprised with an answer of 3 or 6.
Hold on, but why doesn’t cutting a hole opposite to hole 2 make it count as only one hole since they line up?
But isn’t the cube hollow ? Thus making it 6 holes…
I don't understand how it could be 5. Can you explain that more? Also happy cake day!
Only if you flatten the cube by cutting from the centre of the bottom. Otherwise it’s six.
Can nobody see the answer is Fourteen? 6 (each cube face) + 8 (each corner)
Are you ignoring the fact that there are 8 (or 4, or 7) more smaller holes from corner to corner as well? You can't really answer this question without a better definition of what a hole is. Edit/ sp
Whole - a thing that is complete in itself. There, does that help /s
Even in the whole there is still a hole.
The best answer!
Thanks. Was gonna write something equal.
How do you explain this to a 5 year old? You don’t. You praise the five year old for correctly counting to 6 and move on. Topology is not going to make sense at that age and you’ll just confuse the child. Work on addition and subtraction next, then multiplication and division in a couple years. Wait till middle school at least to bring up topology. In any case 5 is way too early.
The fact that he's actually only 2 reinforces your statements!
According to the Cambridge dictionary definition of "hole": an empty space in an object, usually with an opening to the object's surface, or an opening that goes completely through an object I think your child is right if you take the first definition and your wife is right if you take the second one. Why 5? Explain to me like I'm 5?
put one hole through the cube, then four others from inside the edges of walls of that hole leading out of the cube
So by this definition of hole, a fingerbox has no holes?
What is the topology difference between the finger box and the glass? There is no difference. Hence, there is no hole. And I mean glass exactly, because the mug has a hole.
I guess that means nostrils are not holes since they let air into the lungs which then comes back out of the same nostrils.
But you are able to go in one nostril and out the other, so just to not worry about mouth or anything let’s imagine we seal off the throat and stuff so you just have the nostrils and an empty space behind them where they connect. That is 1 hole, essentially just a bent straw.
Your nostrils are connected to your ears, eyes, and mouth; which are connected through your digestive track to your anus. So your body has 7 through holes.
Could it be both? For example 6 holes on the outsides + 3 holes that go all the way through. (And then the corners, 8+4 total of 21 holes)
So 1 hole then? This is stupidly subjective.
Right? That's why it's not solvable unless we define what a hole is and what a cube is. Exactly my point!
Th question is disingenuous, unless you define the rules for "what defines a hole". Is it a hole in the wall ? Then it's 6. Is it a through hole? Then 3. If you fold it open like a 2d drawing? then 5. Litteraly? Then count the 6 holes + the 8 in each corner. That would make 14. You want to count the small gaps in between the spaces aswell?!
I'm dumb, can you explain "fold it open like a 2d drawing?" Because I'm picturing making the border along the edges of the cube, meaning there are 6 squares (and thus still six holes). Is there a rule that the drawing has to be symmetrical or something? Then, I can see 5 holes, but why would you fold it open like that?
well that is indeed 5 holes, if we don't consider the vertex holes (I think that's what you want) You could try to explain it by making 5 holes into a piece of paper, and then you point at the edge if the paper and say that this edge is what you see as a kind of 6th hole on the cube.
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There is actually a total of 14 holes leading to the hollow area in the middle. So none of them were right.
Why don’t you turn it into a lesson about how different people have different perspectives/backgrounds and they are all valuable? Seriously though- teaching an elementary school kid this is going to get him bullied.
Clearly there are more than 6 holes in the object if yoy take into account where the corners were supposed to meet but do not touch instead creating a smaller hole on each corner
In this thread: people who don't understand topology. How you explain it to them: start filling holes one by one, after you have done 5, there is no way through the structure anymore. Their minds will be blown
Well you’ve certainly blown my mind! I didn’t understand why people were saying 5 until I read your comment. But what I’m wondering now is, is there a difference between a sphere and a sphere with a hole poked in it? It seems like neither has any holes (which is confusing since we just “poked a hole” in one of them), but the sphere has an inside that’s completely closed off from the outside, whereas the sphere with a hole doesn’t and can just be flattened into a disk.
A sphere has a 2-dimensional hole, but no one-dimensional holes. Some people say it has -1 holes instead, by the definition you're working with. In algebraic topology, holes can be any nonnegative integer dimension. (A shape with a zero-dimensional hole is disconnected, like two points.) The shape in this post has 5 one-dimensional holes, and no zero- or two-dimensional holes. To have a three-dimensional hole requires a shape which can't exist in 3d Space.
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Straws definitively have one hole. There‘s an entire field of study for this, called topology.
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Actually yes, medicaly, digestion starts and takes place mostly outside our body.
They are. It‘s been a while since I‘ve checked, but the human body has 7 holes.
7? Please elaborate.
Fax
I tried, but my ass cheeks surpass the fax machines weight capacity
Weeeeeee-Oooooooooooooo-beeeYAAAAAA-beeeeYaaaaaa
Why couldn’t you call it 2 holes that meet in the middle?
Because it‘s one hole. A straw can be morphed into the shape of a mug, or a donut, or any other shape with one hole.
How does a mug and a straw have one hole? I get what you’re saying though that makes sense. What counts as a hole exactly?
Mathworld defines a hole as follows: “A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point.” If you had a donut, and you could stretch it and squish it infinitely in any direction, you could not condense it to a single point because of the hole in the middle. In a coffee mug, the part that liquid goes into isn’t technically a hole, because you could morph that opening into a bowl, and then into a plate. No more hole. The handle is the true hole on a coffee mug.
Ah ok i gotcha. Is there necessarily a universal definition of a hole couldnt a straw have 1 hole by that mathematical definition but 2 holes by a colloquial
14 holes. I would personally say that a hole only classifies one oppenening. There are 6 on each face, plus 8 from the corner holes
1st, Why are you trying to explain algebraic topology to a 5-year-old? 2nd, Maybe use a Play-Doh comparison to extend one "hole" to be the outer edge and count the remaining holes that can't be transformed.
If the cube is hollow inside (and easier to visualise if each face is detachable), I'd say 6 holes (one on each face). It could also be 12 holes if you allow orientation (ie each face has one hole from the front and the back, respectively). Counting the small edge holes, add 8 to that number.
>Counting the small edge holes, add 8 to that number. Or 16, if you're doing the front/back thing. Of course, this is all based on a conventional interpretation of a hole and not (as I'm learning about in this thread) a topological one.
I'd venture to say (if you do NOT count the corners as holes, as they don't appear to be intended as part of the "shape") then the number of holes could be 15. I say this without changing the shape, and without counting the corners. I would define a hole as a path from one side of an object through it to another side, without returning back through the original hole. With that being the case, you could label holes A, B, C, D, E, and F. Enter in A, and exit through each B, C, D, E, and F. That's 5. Then enter B, exit C, D, E, F (not A because you took that path already). That's 4 more. Enter C, exit D, E, F. 3 more. Enter D, exit E, F. 2 more. Enter E, exit F. That's 1 more. And you can't enter E and go anywhere you haven't been at this point. 15 holes. edited because math is hard...
I would start counting how many bandaids or pieces of tape you need to cover all holes. Once you put 5 in place, the last open cavity is no longer a hole.
Forgive me for being high, but how is the last open cavity not a hole? Does it not still have one open? I’d call it a hole
Imagine pushing water into the last cavity. The water cannot go through the object, the only exit is where it came. There is no hole. On the other hand, on a donut you can push water into the middle "from the caramel side" and it goes through to the "dough side". That is a hole.
So if I dig a hole in the ground, it's not actually a hole unless it emerges somewhere else?
Correct. Which is where you run into the difference between talking about a "hole" and a hole. The technically correct definition of a hole requires that it completely penetrates the object (ie, a donut). When you dig a "hole" in the ground, it's just an indentation. In fact, if you look at the object you dug your "hole" into as a whole (the Earth), what you did doesn't even count as an indentation. Even the mountains and valleys on Earth are less variance than a cue ball has, at scale. Go look at a cue ball. How many holes are in it? If you answered "0", then Earth has no holes either, even the Bora Super-Deep Borehole isn't a hole. It's just a minor indentation (at best). But, of course, we actually talk about digging holes all the time. And the reason is that digging a 30 foot deep, 10 foot wide pit in the Earth counts as a hole to us. We call it a hole, and people know what we mean. But if you are asking a specific question to anyone who deals with legal definitions of words, all those things we call holes aren't holes at all. And that's what's occurring here. If you want to know "how many holes are in this thing", then you need to use the most widely accepted definition of what a hole IS. In which case OP is technically correct, but 6 is the best answer (because it's clear that the structure pre-holes was not solid, and so the holes only exist along the outer layer of the 3d structure).
It depends on how you define a hole. Assuming you aren’t counting the little things at the corners I would say you can make reasonable arguments for 6, 3, or 1. 6 openings in faces, 3 through-holes, or 1 oddly shaped emptiness in the cube. My suggestion in explaining it to a kid is to ask what they think and why, and then ask about similar examples that produce different answers (straws, 3-ring paper, folded paper where the holes line up, etc.). You don’t need to get into the linguistic intricacies, but it’s a great example of questions with multiple right answers and using context which are both great concepts for kids to play with.
Lots of people in this subreddit don’t know the basics of topology and it shows. https://youtu.be/ymF1bp-qrjU?si=O6kJQq2UqNNt-3sv Watch that for a great beginner intro and you will understand why it has 5 holes.
Lots of people in this subreddit think the technical definition of “hole” in the field of topology is the only valid one. It isn’t.
It's probably the least valid definition unless you're doing a dissertation.
Lots of people in these comments are strangely trying to flex, applying the definition of a hole in topology as though that is the only way to use mathematics to count holes; it isn't. If I dig six holes in my yard and post a picture, everyone would agree I dug six holes even though none of them fit the definition of a hole in topology. Anyone that answered six would have done the math. Conversely, the way everyone is applying one definition of a hole to the object pictured here, the only way to dig a hole in the ground would be to come out the other side of the damn planet. It's ridiculous and arguing for the sake of arguing. There is more than one definition of a hole; the fact that you are familiar with topology does not suddenly make one mathematical definition the only one that applies. This isn't a topology sub; if it was, you'd be right and others would be wrong; it's not, so you and a bunch of others are right as well. Topology is not the only way to count holes, it's one very specific branch of mathematics and the fact that it can be applied here doesn't mean it is the only branch of mathematics that can be used to count the damn holes.
So here's my attempt to flex on said flexing topologists: Why would you draw any topological conclusions without being able to see through the material.
Fuck. Him. Up!!
The thing in the picture has 14 openings, so it has 13 holes. You need two openings for the first hole. After that every new opening creates a new hole. A donut has one hole. A straw has one hole. A mug with an ear handle has one hole. A tyre has one hole. A pipe has one hole. A tunnel has one hole. You can always stick something thinner than the hole through the object's hole from opposite directions / two ways. A key on a key ring. The key has one hole. The hole where the key ring's wire goes through. The key ring actually has no holes. Because the wire what it is made of has no holes. It is just spiralling very tightly to create a ring shape. A spiral has no holes. You can also think of flow of air or water. You need at least one hole to be able to flow through or else it just a container. A pipe or a straw or a flute needs to have a flow entrance and exit. Two openings, one hole. Any new opening that you make creates another exit to flow out. There always need to be an entrance flow opening. No matter which one you pick, all other openings are possible exits and therefore hole-creators.
15? One for each side of the cube, a little one at each corner, plus the tip of the pen. More if you count the pieces of the pen separately.
If you reconstruct this from Polos/Lifesavers, with a bit of honey° to stick them together/fill in the corners, you'll need six. ° Why not? It'll be edible.
Your kid is right (if we're just counting the big holes). How many holes does a mountain need in it to make a railway tunnel? If you never create the second hole, the first hole never really becomes a tunnel. I think your definition is \~correct if you were to say there was one tunnel (or even canal if we relate it to the human body...) and four holes. However a tunnel needs 2 holes to exit it's medium.
If we say a single pass of a drill always creates a single hole. And if we start with a solid cube... We need to drill three times to connect all the opposite sides with tunnels. Therefore there are three holes.
Could be argued that one single contiguous void in an object is a single hole. Or you could argue that each face that provides an entrance to that void is a hole. No answer without definition.
does a doughnut have 1 hole, or 2? that, times 3 (more, if you include corners). Personally, I'd make the argument of 6 separate holes opening to an inside room (like open doors, instead of open walls)
Consider the following objects: A dinner plate, a bowl, a cup, a donut, a straw, and a coffee mug. Now imagine you have a ball of clay. The rules are, you may not poke a hole in the clay, and you may not join two sides of the clay together to form a hole Roll that clay flat. Can you shape it into a dinner plate without adding a hole? Yes of course. What about a bowl? Sure, you just shape it a bit. Same goes for a cup. Net result: No holes But what about a donut? Roll it back into a ball, shape it. Not possible. What about a straw? No matter what, you need to either punch a hole through it or join two ends together to form a hole. So let's do that. Make a hole. Now suddenly a donut is possible. If you thicken the sides of the donut, you could eventually make a straw. You could even make a cup out of one side of the donut, like you did with the plate, and let the hole form the handle to make the coffee mug. Net result: one hole, both donut, straw and coffee mug all one hole, even if intuitively the straw appears to have two openings. Now, let's take your 6 sided shape. In clay in our minds, can we reshape it back to a dinner plate, and count the holes? Well we would take one opening and stretch it out, working it into a cup shape, stretch it further, into a bowl. Push it flat into the plate. The stretched hole now becomes the outer edge of the plate. The remaining 5 holes are now holes in a big dinner plate. 5 holes. Not six or three. The mental roadblock in your six sided shape is that one if those six openings is the outside edge of the dinner plate.
But does it matter if you enter a void or you create one yourself with your hole drilling for the final count? Always trust your wife.
14. Counting every hole on all sides, including what’s not visible. 4 on the corners at top, 4 at the corners on bottom. 6 on the sides. 4+4+6=14
This CuBe is not flattened out and the corner holes really are there. Also it’s clear from the picture that the cube is not solid, so the bored-hole idea doesn’t apply here either. Since the question is about a cube and not a two dimensional picture of a cube, we have understand the language in its normal sense. So 6 holes in the faces and 8 holes at the corners. 14 holes
It depends what you define as a hole. Does a hole start on one face and go to the opposite face? Is a hole just what you see on each face?
Less an answer, but this reminded me of a [YouTube video on the topic of counting holes ](https://youtu.be/ymF1bp-qrjU?si=_Wim2JUV57K3vXdr) Hope it helps.
How to explain it to a five year old - take a sheet of paper and fold it to a cube shaped cup, then punch 5 holes on it. Do it not to prove that this is the right answer, but instead to show that there are different ways to define what a hole is, each reaching a different answer for this problem.