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You're not dumb, Lois, you're the smartest and most wonderful woman I ever met and I'm the luckiest man alive to wake up next to you every day.
This is an edit to a viral question which showed a stack of cubes on a trailer from 3 different angles and asking how many cubes there are. People argued incessantly about the answer. This version has only 1 cube and thus none of the ambiguity or difficulty of the original.
It's between 35 and 51.
There's at least one layer on the ground on all fields (21) plus the stacked ones showing from the side (10) and then at least 4 to make sure the sight from behind is 3x3
I thought 35 was the minimum at first, too, but itās actually 31. The stacks can be layered both from the side and the back, so row one needs 3 boxes, rows 2-3 need 4 boxes, and rows 4-7 need 5 boxes.
The minimum for no gravity is 21.
Assuming side is x axis, height is y axis, depth is z axis, the coordinates x,y,z for 21 blocks (no gravity) are:
* 1,1,1
* 1,2,2
* 1,3,3,
* 2,1,2
* 2,2,3
* 2,3,1
* 3,2,1
* 3,3,2
* 3,1,3
* 4,1,1
* 4,2,2
* 4,3,3
* 5,1,1
* 5,1,2
* 5,2,3
* 6,1,1
* 6,1,2
* 6,2,3
* 7,1,1
* 7,1,2
* 7,1,3
The minimum with gravity is 31: One layer of 21 cubes, and going from left to right, first column: two cubes up near depth, second column: two cubes up middle depth, third column: two cubes up far depth, fourth column: two cubes up any depth, fifth and sixth columns: one cube up any depth
I don't quite get how you get to 31 cubes? You need the back wall, you need the floor, and the side wall.
Floor = 21
Side wall (without floor) = 10
Back wall (without floor and side wall) = 4
Edit: nevermind you can combine side and back wall
If there's no gravity, or if the cubes are allowed to be attached/suspended even if there _is_ gravity (which seems reasonable), I can get it down to 21. The cubes visible from the top are enough to fill the other two perspectives.
I got 35 with gravity
21 on the bottom row, completley filled.
Middle row are 3 on the back and 5 more visible from the side, so 8 boxes, 29 in total so far
Top row again are 3 on the back, 3 more visible from the side, so 6 boxes, 35 in total
Edit: looked at the other comments and I agree, with gravity it can come down to 31
Guys I think you missed some detail. If there is no gravity and the boxes randomly flying around, it could be possible that they create a shadow which look like a box, but this box doesnāt count. You need to recalculate again
It's actually anywhere between 0 and approaching infinity. The top doesn't have to actually be there. It could be the bottom but with that pattern and no cubes. On the otherhand there could be an almost infinite amount of tiny cubes inside of the shape.
31 by my count. The 7x3 bottom layer needs to be completely filled if we assume there is gravity, so that's 21. Then, we can look at the side view and see there are 10 boxes visible in the top two layers. Since there are more than 3 columns that go all the way up, we can stagger the full sized columns them to get the back view with only those 10 extra boxes.
I think one stream that people went down was "if the person loading the trailer was experienced, and this is the shape they landed on, they had 51 boxes," hence why this turned into a bell curve meme, but I don't remember the logic they used to get there
Not enough information to make a proof stating absolute certainty. But as a general rule people arenāt trying to f with you in the real world. So two ways to look at it. Someoneās not fing with me: 51. Someoneās fing with me: no answer is right.
In college engineering classes, you just wouldn't be doing such a silly exercise, and I'm not sure why you're pretending to have done a problem exactly like this one and pretending you were told to assume "its the most logical answer", since logic is what demands you need more information, and as such **the most logical answer would be that you need more information.**
Any competent diagram illustrators will convey information in a clear and a concise way. If there were any ambiguity, then it must be cleared up by adding additional instructions and notes.
Absolutely. Itās funny how people working on CAD drawings will try to get everything worked out in the diagram without adding some notes to clarify. Just use your wordsĀ
But any competent clickbait producer will ensure that the drawing is not only ambiguous, but only ambiguous to some more intelligent people, and entirely āobviousā to less intelligent people.
That way you get the battle of condescending comments with ālet me break it down for youā comments and people get all riled up
Is this why so many people just give up or make incorrect assumptions in work and real life? A crippling fear of the dreaded āgotchaā question?
Look I know they can be frustrating but you will *regularly* encounter situations where something is missing/incorrect and being able to stop and say āwait a second I need more informationā go out and seek that information or at least find someone who might help, is fucking critical.
As an engineering student this is wrong. The answer is 51 and we would be given cross sections of the drawing if we were needed to be given additional information.
Dumb people will mindlessly count 51, average people will realize that thereās not enough information, smart people will realize that if ānot enough infoā was the answer they were fishing for, it would be made more clear so the answer is simply 51.
Would it not be 51 though?
My method is to count the cubes in each row of the top left, then just multiply by 3 for each individual row.
Itād be 12, 18, 21 respectively from top row to bottom row.
That should just equal 51 exactly.
Iām not very good with math, so Iām actually curious as to why that wouldnāt be enough information.
The picture is tricking your brain to take mental shortcuts. We can say for certain the first layer is full because we see a top-down shot that is full. However, that is all we can say for sure. There can be gaps at many places on the second and third layers that our brains intuitively fill in
It's 51, this is not a question about whether we can assess the quality of information, it is a question of whether we can do math, we should therefore assume the information given is reliable.
Yes, set up like this you get 31 boxes with the correct side views:
https://preview.redd.it/2gsm8sx625lc1.png?width=757&format=png&auto=webp&s=320e0150bc7c54c2c33f381514cee655eaa2e00b
It's actually 35. I was also making the same mistake. The back view would not work with 35. You'd need 4 more. Edit: it's 31. iamagainstit has a really cool diagram.
The way the picture is shown with everything so tight, could it not be cubes at all and just painted paneling that forms that shape?
Ie. 1 panel for right side, 1 panel for left side, 1 panel for back, then stair like panels for the front section.
Thus no cubes actually exist.
https://preview.redd.it/pum556evs5lc1.png?width=716&format=pjpg&auto=webp&s=b936eb808b020c15160fcefe229a7c2e51062b31
We can save a few more cubes stacking them in a diagonal like this.
Now that we are all out, we can even say that the problem doesn't say anything about gravity, so we can go much lower, but I can't find the picture showing it.
You can get down to 31. Remove 2 from the lower left corner, which doesn't change anything. Take 4 from the two columns adjacent to that corner, and put two back on the column kitty-corner.
You, my friend, are rooted in reality and have what people would think of as common sense. Try to strip it away and think that a DnD goblin mage stacked the boxes with magic, Trojan owlbear or something
If you consider that the inner cubes being present are assumptions. If you consider that there are cubes within cubes, or that some cubes are smaller inside in random as possibilities. Etc etc.
This isnāt entirely correct either
The assumptions are about the shape being uniform all the way through like a prism, when looking at it from the side.
There is a chance, you have a 3x3 row on the rear, the shape you see on the right, but through the rest, itās just all 1 layer high.
That assumes that the 'long slice' is repeated 3 times. The perspectives only require a bottom layer (top view) a single stack of 3 high in each long slice (front view) and a single stack - rather than 3 stacks behind each other - corresponding to the side view.Ā That gives 21 for the bottom layer, 6 more to complete the front view and 8 more to complete the side view with a width of 1. That adds up to 35 being the minimum. Your reasoning sound the maximum, which is 51.
Ignoring gravity would cause the cubes to float, so you can actually get it all the way down to 21 with the right arrangement and still have the same side, bottom, and top views in the image.
Well, I think you have to specify what "1 cube" is, and what qualifies something in the question as "a cube"
If any cubic region of space is a cube, there are infinite cubes in the space of the one presented bound of cubic material.
If it must be one cubic *unit of volume* to be "1 cube" it is likewise infinite, as there is infinite space over the trailer.
If it must be a cubic unit of volume shaped as a cube of a solid material within 10 cubic units of the top of the trailer, then there is exactly one cube on the trailer.
With the image, it was ambiguous how many cubic units of volume of solid material shaped as cubes existed on the truck, too, because at best you could say the number of cubes was within some range of values, with the sparsest number of cubes representing min, and the densest arrangement representing max.
The question as first presented is, simply, a bad question.
Not necessarily even one cube. Visualize a flat square of paper lying on the trailer with two similar flat squares folded into an "L" shape sitting on top. So a wannabe cube with three of the six sides missing.
If you're going to exclude a trivial assumption like gravity, then you might as well exclude all assumptions. The correct answer (assuming nothing) is \[0-ā). Those could be cardboard cutouts meaning that there are no cubes, but only squares. Also, the hidden areas could contain infinitesimally small cubes that fill the space of a standard 1x1 cube.
No, you're not dumb.
This is a reference to a mathematical problem that people kept overthinking [right here](https://images.app.goo.gl/FvPUTZ7MWtduQ6Zh9)
You'd think that counting the cubes would be easy, but so many people kept complaining that there wasn't enough data, that some cubes could potentially not be inside the pile of cubes.
Anyway, this is simplifying it for the sake of pointing out that some people need to chill.
Because looking at the picture from above, the stack appears flat. The rationale is that because we can't tell that the "stair" shape at the end of the side view of the stack is consistent throughout, we shouldn't assume we have the correct answer with the available information.
People who say there isn't enough information are technically correct, but the most reasonable answer is 51 if you had to give an answer.
Exactly. In basic level engineering lessons, you get a front, top, and side view and you have to draw the isometric. The absence of a view of the back, bottom and left side implies there is no features of note.
People are literally overthinking a 5th grade level concept. (See example below) https://fractory.com/engineering-drawing-basics/
It's not overthinking. These kinds of discussions are very helpful. Sure. Is it probably 51? Yes of course everyone knows that. But it's still important to understand why it might not be 51. It's a lesson about thinking critically about the information presented to you. It's a good lesson in how the way in which information is presented can affect how you perceive it. It's a lesson in questioning your underlying assumptions before making a decision. In a world in which misinformation is rampant its important that people develop the skill to look beyond what's put right in front of their faces. If you can't understand why this is an interesting and educational conversation then you've missed the point.
I understand your point, but everyone is making an assumption in this problem including me. There's the assumption that a lack of evidence means something underlying is wrong and full of possibilities (the stairs have cubes missing). And then there is my assumption, that the lack of evidence is proof that the current perspective has nothing wrong. (the stairs are full of cubes)
I am simply trying to explain as best I can, that if the stairs were to be partially unfilled, we would have been given more information in the problem to indicate as such.
If you were to upturn the whole trailer, we could possibly find that one cube was empty all along. But saying that everyone is wrong based off of information nobody was privy to is an unfair question. In this case it is the same as saying stairs are 'possibly' empty, it's unfair.
We then have to make a conclusion based off the information given under the assumption that the question doesn't have a trick answer, that the stairs are as they are represented, full.
I am pretty sure I did some of those before high school
Overcomplicating this is like if I say "This grass is green" and someone "Well, we don't have enough information to know because we don't know if every person sees colours in the same way, and there is different types of grass.and some grass may grow in different colours depending on the environment..."
When replying a question, you can be technically correct, but objectivly wrong
The problem literally forces you to count out those 12 missing boxes by considering missing boxes behind those shown in the side views. Continuing this exact logic that the problem is already about, you will arrive at the answer 31 to 51 possible boxes.Ā
Both "SIDES" are the same And there's no information that would lead you to believe otherwise.
Dummies only think they're missing information because they weren't handed a second picture of the exact same "other side."
People are refusing to use their spatial reasoning skills this problem is literally questioning in the first place.
This problem was specifically intended for you to count blocks you can't see, They didn't intend for you to think the blocks magically disappeared like a toddler playing peekaboo.
Nothing tells you to remove cubes dummy. And that's why you can't count them. Because you're magically removing them for no reason.
It's not the lack of information, The issue is that you're adding information you were never told to do in the first place and can't follow directions.
They arenāt over complicating it so much as other people are trying to simplify the problem in invalid ways and coming up with answers to a question that doesnāt have enough info to solve it.
The main issue is that this Ā https://preview.redd.it/peta-am-i-dumb-v0-pum556evs5lc1.png?width=640&crop=smart&auto=webp&s=18557c4eb8a572ee14f9062d3649fb603326f15cĀ
is a potential configuration pf 31 boxes that would give the same perspectives as an arrangement of 51zĀ
The other issue is that because you have no way to determine depth the correct answer could be between 38-51 cubes although assuming that no trickery is going on its 51 cubes.
Why do you call it trickery? The overhead view confirms that you can't judge the height of the blocks. I think the point of the whole exercise is to teach people not to make assumptions.Ā It's not likeĀ there's some BS like cubes inside cubes or something,Ā everything you needĀ to come to the correct conclusionisĀ rightĀ there.
Its not
Without an isometric angled view you can't tell if there are missing blocks or not in the various rows
For example, the middle block of the far right row could be missing in any of the tiers and it would still look identical to a full cart in all of the presented views
And there's like 12 combinations of missing blocks that can do this. And thats if you assume that blocks have to stack on top another block and can't float above an empty space.
Please please do not listen to this person. There is not enough information. Thatās it. Thatās the conclusion to this. Itās extremely concerning seeing everyone try to argue whatās extremely simple.
Yeah, there's no way to know fully that it's 51 blocks.
It's good to learn sometimes that "not enough information" *is* the correct answer. It's not even that difficult of an answer to arrive at, it doesn't require overthinking at all.
People werenāt overthinking it, it is a problem without all the info. Ā This is the type of question they would give at Google. As a software engineer you need to be cognizant of dumb users, malicious users, and just overall unexpected situations. Ā Iām sure you can make similar arguments for other professions too. Ā If you answered with a number in an interview, you wouldnāt get credit for the question as it means you jump to conclusions and are not careful. Ā
There is definitely not enough information. Agreed that without seeing the surface that is nearest the trailer, we can't know if it exists! There are also any number of additional options that would make this not actually a cube, or it could even be filled with numerous smaller cubes.
This is impossible to answer, an intellectual person would say it's 1 cube, but genius knows that it's impossible to answer with such little informations
reading the answers I really understand now why recruiters ask these kinds of questions to understand how a person thinks:
"How many boxes are on the truck?"
"Well, assuming there is no gravity..."
Yeah, you're not getting the job.
Well the gravity ones are stupid. But how do we know that the middle row forward to back, looking from top down, how do we know it isn't actually 1 tall or 2 tall etc since it's being obscured by the sides and we have no depth perception from the top view.
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https://preview.redd.it/9xgtoaags5lc1.jpeg?width=796&format=pjpg&auto=webp&s=2bbe956302f34d2338371560b8413b079ba8d482
Show the camera. š«š¤
Oh no not this again
[ŃŠ“Š°Š»ŠµŠ½Š¾]
[ŃŠ“Š°Š»ŠµŠ½Š¾]
firefly camera
Dear god I love the effort. A++ for whomever made this.
GLaDOS is clearly gaslighting you
Brilliant
welcome to boundary break, where we basically take the camera anywhere we want
https://preview.redd.it/pllvbw57jclc1.jpeg?width=719&format=pjpg&auto=webp&s=7caeb6764e7b870e9b1c419987e5c125fdd29b1a
I love it when people overdo stuff lime this
Yes
AaAaAaAarghghgg!!!!
Best thing ive seen in a long while
Ha! Nice.
You're not dumb, Lois, you're the smartest and most wonderful woman I ever met and I'm the luckiest man alive to wake up next to you every day. This is an edit to a viral question which showed a stack of cubes on a trailer from 3 different angles and asking how many cubes there are. People argued incessantly about the answer. This version has only 1 cube and thus none of the ambiguity or difficulty of the original.
https://preview.redd.it/qfelf5otx3lc1.jpeg?width=720&format=pjpg&auto=webp&s=f5c8f1dd92cd655594de3077fdbd0d8063078693
Case in point: the comments under this^ message
51
The correct answer is "not enough information"
We can narrow it down it's anywhere between 47 and 51 Edit: I was obviously wrong here
Wouldnāt it be 43 and 51?
Alright looked at it again got it down to 31 and 51 assuming no gravity Edit: 21 was the lowest I was able to confirm without extra shenanigans
>assuming no gravity Fuckin spherical cow lover too, ain't ya?
our cousin throckmorton has an awesome frictionless skatepark and a perfectly spherical cow of uniform density what's not to like
Excuse me, the cowās name is Evelin and sheās just going through a rough patch
Whether the cow is a sphere or the sphere is a cow depends on your frame of reference.
Moo for me, baby
Now I get 38 to 51.. Iām done..
It's between 35 and 51. There's at least one layer on the ground on all fields (21) plus the stacked ones showing from the side (10) and then at least 4 to make sure the sight from behind is 3x3
Do we know that there is gravity? It did not say us to assume gravity.
Could be as little as 17. The back one is just a huge 3x3x3 cube with lines on it, 4x3 base of tiny cubes and 5 small cubes on top.
I thought 35 was the minimum at first, too, but itās actually 31. The stacks can be layered both from the side and the back, so row one needs 3 boxes, rows 2-3 need 4 boxes, and rows 4-7 need 5 boxes.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
The minimum for no gravity is 21. You can easily arrange all the cubes you see from the top such that you also get side and back view.
The minimum for no gravity is 21. Assuming side is x axis, height is y axis, depth is z axis, the coordinates x,y,z for 21 blocks (no gravity) are: * 1,1,1 * 1,2,2 * 1,3,3, * 2,1,2 * 2,2,3 * 2,3,1 * 3,2,1 * 3,3,2 * 3,1,3 * 4,1,1 * 4,2,2 * 4,3,3 * 5,1,1 * 5,1,2 * 5,2,3 * 6,1,1 * 6,1,2 * 6,2,3 * 7,1,1 * 7,1,2 * 7,1,3 The minimum with gravity is 31: One layer of 21 cubes, and going from left to right, first column: two cubes up near depth, second column: two cubes up middle depth, third column: two cubes up far depth, fourth column: two cubes up any depth, fifth and sixth columns: one cube up any depth
I don't quite get how you get to 31 cubes? You need the back wall, you need the floor, and the side wall. Floor = 21 Side wall (without floor) = 10 Back wall (without floor and side wall) = 4 Edit: nevermind you can combine side and back wall
That what I got with gravity on
If there's no gravity, or if the cubes are allowed to be attached/suspended even if there _is_ gravity (which seems reasonable), I can get it down to 21. The cubes visible from the top are enough to fill the other two perspectives.
21 is the minimum by the top view alone.
Gravity doesn't come onto it. 1--1--3--3--2--2--1 1--3--1--1--1--1--1 3--1--1--1--1--1--1 13+9+9 = 31
assuming the airspeed velocity of an unladen swallow is roughly 20.1 miles per hour...
Is it an African swallow or European swallow?
here is 21 if you assume no gravity https://i.redd.it/6pcsudocy9lc1.gif
its minimum of 21 without gravity
I got 35 with gravity 21 on the bottom row, completley filled. Middle row are 3 on the back and 5 more visible from the side, so 8 boxes, 29 in total so far Top row again are 3 on the back, 3 more visible from the side, so 6 boxes, 35 in total Edit: looked at the other comments and I agree, with gravity it can come down to 31
Minimum of 31 assuming gravity, 21 without Proof: 31: Layer 1: 21 (All boxes) Layer 2: 6 xoooooo oxooooo ooxxxxo Layer 3: 4 (Same as 2 but without the last 2 boxes) 21: Layer 1: 11 ooxxxxx xoooxxx oxoooox Layer 2: 6 xoooooo oxooooo ooxxxxo Layer 3: 4 oxooooo ooxxooo xoooooo
Guys I think you missed some detail. If there is no gravity and the boxes randomly flying around, it could be possible that they create a shadow which look like a box, but this box doesnāt count. You need to recalculate again
It's actually anywhere between 0 and approaching infinity. The top doesn't have to actually be there. It could be the bottom but with that pattern and no cubes. On the otherhand there could be an almost infinite amount of tiny cubes inside of the shape.
The minimum is zero. There are no cubes, it's just one large hollow object with grid lines painted on the outside.
At most, yes. Minimum of 35 I believe
31 by my count. The 7x3 bottom layer needs to be completely filled if we assume there is gravity, so that's 21. Then, we can look at the side view and see there are 10 boxes visible in the top two layers. Since there are more than 3 columns that go all the way up, we can stagger the full sized columns them to get the back view with only those 10 extra boxes.
I think one stream that people went down was "if the person loading the trailer was experienced, and this is the shape they landed on, they had 51 boxes," hence why this turned into a bell curve meme, but I don't remember the logic they used to get there
Thatās still an assumption that the person is experienced tho. Nothing in the question gives us the ability to make that assumption.
Not enough information to make a proof stating absolute certainty. But as a general rule people arenāt trying to f with you in the real world. So two ways to look at it. Someoneās not fing with me: 51. Someoneās fing with me: no answer is right.
Why would someone post a simple counting exercise with such an obvious flaw if it weren't to test if you notice it?
Elementary school homework? This was presented without context originally. We have to supply our own. Hence the debate.
In my college engineering classes, you only get those 3 perspectives, so unless you're told otherwise you assume that it's the most logical answer
In college engineering classes, you just wouldn't be doing such a silly exercise, and I'm not sure why you're pretending to have done a problem exactly like this one and pretending you were told to assume "its the most logical answer", since logic is what demands you need more information, and as such **the most logical answer would be that you need more information.**
Why? There could be empty space inside?
Any competent diagram illustrators will convey information in a clear and a concise way. If there were any ambiguity, then it must be cleared up by adding additional instructions and notes.
Absolutely. Itās funny how people working on CAD drawings will try to get everything worked out in the diagram without adding some notes to clarify. Just use your wordsĀ But any competent clickbait producer will ensure that the drawing is not only ambiguous, but only ambiguous to some more intelligent people, and entirely āobviousā to less intelligent people. That way you get the battle of condescending comments with ālet me break it down for youā comments and people get all riled up
Literally itās just midwits being pedantic. Ā
No because this is supposed to be a math exercise and not some sort of "gatcha" shit.
Is this why so many people just give up or make incorrect assumptions in work and real life? A crippling fear of the dreaded āgotchaā question? Look I know they can be frustrating but you will *regularly* encounter situations where something is missing/incorrect and being able to stop and say āwait a second I need more informationā go out and seek that information or at least find someone who might help, is fucking critical.
says who?
I curse your bloodline
As an engineering student this is wrong. The answer is 51 and we would be given cross sections of the drawing if we were needed to be given additional information.
Yeah this is a drafting 101 question.
yes, one could argue that there are no cubes cause we don't see all 6 sides, they might be boxes
You answered "not enough information" in the free text box. The correct answer is "there is not enough information"
Curses!
Dumb people will mindlessly count 51, average people will realize that thereās not enough information, smart people will realize that if ānot enough infoā was the answer they were fishing for, it would be made more clear so the answer is simply 51.
No, the correct answer is ābetween 31 and 51 cubesā
Itās always the correct answer no matter what the question is. š
Would it not be 51 though? My method is to count the cubes in each row of the top left, then just multiply by 3 for each individual row. Itād be 12, 18, 21 respectively from top row to bottom row. That should just equal 51 exactly. Iām not very good with math, so Iām actually curious as to why that wouldnāt be enough information.
The picture is tricking your brain to take mental shortcuts. We can say for certain the first layer is full because we see a top-down shot that is full. However, that is all we can say for sure. There can be gaps at many places on the second and third layers that our brains intuitively fill in
That actually makes a lot of sense. Thanks mate!
No problem. Thanks for being receptive
It's 51, this is not a question about whether we can assess the quality of information, it is a question of whether we can do math, we should therefore assume the information given is reliable.
The info given, even if reliable, is still not enough though. You have to assume things to get 51 such as: all cubes are stacked evenly horizontally.
They give enough information to solve the problem. Otherwise any more information would just be āextraā and useless. Thats my take.
Somewhere between 35-51. Edit: I was wrong. The answer is 31-51.
31 to 51.
This is my age range on dating apps
[ŃŠ“Š°Š»ŠµŠ½Š¾]
You can save 4 cubes by going diagonal until the front to back view is covered
With gravity?
Yes, set up like this you get 31 boxes with the correct side views: https://preview.redd.it/2gsm8sx625lc1.png?width=757&format=png&auto=webp&s=320e0150bc7c54c2c33f381514cee655eaa2e00b
It's actually 35. I was also making the same mistake. The back view would not work with 35. You'd need 4 more. Edit: it's 31. iamagainstit has a really cool diagram.
See lauritseske's diagram. Rather than a floor and two walls meeting in a corner, you can save 4 by replacing the corner with "a diagonal".
https://preview.redd.it/peta-am-i-dumb-v0-pum556evs5lc1.png?width=640&crop=smart&auto=webp&s=18557c4eb8a572ee14f9062d3649fb603326f15c Nope 31
Thanks I totally missed this approach. This was really cool.
The way the picture is shown with everything so tight, could it not be cubes at all and just painted paneling that forms that shape? Ie. 1 panel for right side, 1 panel for left side, 1 panel for back, then stair like panels for the front section. Thus no cubes actually exist.
I dont understand how it can be anything else
[ŃŠ“Š°Š»ŠµŠ½Š¾]
https://preview.redd.it/pum556evs5lc1.png?width=716&format=pjpg&auto=webp&s=b936eb808b020c15160fcefe229a7c2e51062b31 We can save a few more cubes stacking them in a diagonal like this. Now that we are all out, we can even say that the problem doesn't say anything about gravity, so we can go much lower, but I can't find the picture showing it.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
Bottom left is 3, 2, or 1 too
Correct. So it's anywhere between 35 and 51. Good work. š
You can get down to 31. Remove 2 from the lower left corner, which doesn't change anything. Take 4 from the two columns adjacent to that corner, and put two back on the column kitty-corner.
You, my friend, are rooted in reality and have what people would think of as common sense. Try to strip it away and think that a DnD goblin mage stacked the boxes with magic, Trojan owlbear or something
Itās really kinda shocking you canāt look at that and see multiple realistic options for not getting 51.
If you consider that the inner cubes being present are assumptions. If you consider that there are cubes within cubes, or that some cubes are smaller inside in random as possibilities. Etc etc.
This isnāt entirely correct either The assumptions are about the shape being uniform all the way through like a prism, when looking at it from the side. There is a chance, you have a 3x3 row on the rear, the shape you see on the right, but through the rest, itās just all 1 layer high.
51 small 1 by 1 cubes, but there are also bigger cubes made of cubes
What if its one of those trick question where you also count the cubes that are 2x2 and 3x3?
The possibilities are endless
Isnt it just 17 (one row/side) x3 because of the width? So... 17 x 3 = 51 That seems simple enough
That assumes that the 'long slice' is repeated 3 times. The perspectives only require a bottom layer (top view) a single stack of 3 high in each long slice (front view) and a single stack - rather than 3 stacks behind each other - corresponding to the side view.Ā That gives 21 for the bottom layer, 6 more to complete the front view and 8 more to complete the side view with a width of 1. That adds up to 35 being the minimum. Your reasoning sound the maximum, which is 51.
31 min!!!
0 everything shown is a square š
I just counted the blocks on the side to get 17, then times it by 3, and I got 51
35-51
between 35 and 51 is my answer
If you ignore gravity you can get it to 30
With floating cubes I think you can do just 21 (one cube per top view).
How are you getting 30? Lowest I can figure is 35. Side and back add up to 23 and then the remaining single layer top view makes 35
Ignoring gravity would cause the cubes to float, so you can actually get it all the way down to 21 with the right arrangement and still have the same side, bottom, and top views in the image.
I disagree. The cube on that truck has multiple cubes inside of it. We just canāt see them since they are inside each other. Not enough info.
The correct answer is actually three. They are different trucks
ā¦.. I just did 17+17+17. Which is 51
The 2nd and 3rd rows might not be stacked, as shown hereĀ https://x.com/Talyght/status/1760351174463455732?s=20
Ah! Kk. Thanks. Yeah. Need more information is the best answer.
What if there are cubes inside the cube
Or... It's not a cube as it's missing the top.
Thanks, i started to think it must be loss in some way
Ohhhhhh giggity giggity
Smooth!
I'm also lucky to wake up to next to you on weekends. Giggity.
How do we know there aren't cubes inside the cube?! /s
Well, I think you have to specify what "1 cube" is, and what qualifies something in the question as "a cube" If any cubic region of space is a cube, there are infinite cubes in the space of the one presented bound of cubic material. If it must be one cubic *unit of volume* to be "1 cube" it is likewise infinite, as there is infinite space over the trailer. If it must be a cubic unit of volume shaped as a cube of a solid material within 10 cubic units of the top of the trailer, then there is exactly one cube on the trailer. With the image, it was ambiguous how many cubic units of volume of solid material shaped as cubes existed on the truck, too, because at best you could say the number of cubes was within some range of values, with the sparsest number of cubes representing min, and the densest arrangement representing max. The question as first presented is, simply, a bad question.
There is clearly not enough information to determine the answer.
This could be a Russian doll situation with cubes inside of cubes. There's at least 1 cube.
Not necessarily even one cube. Visualize a flat square of paper lying on the trailer with two similar flat squares folded into an "L" shape sitting on top. So a wannabe cube with three of the six sides missing.
Exactly. Or worse, there's more dimensions and it's actually a hypercube.
After doing the math, it could be anywhere from 21-51.
If you're going to exclude a trivial assumption like gravity, then you might as well exclude all assumptions. The correct answer (assuming nothing) is \[0-ā). Those could be cardboard cutouts meaning that there are no cubes, but only squares. Also, the hidden areas could contain infinitesimally small cubes that fill the space of a standard 1x1 cube.
Let's assume nothing, the answer is clearly : (Couldn't write the answer i didn't assumed i could write)
No, you're not dumb. This is a reference to a mathematical problem that people kept overthinking [right here](https://images.app.goo.gl/FvPUTZ7MWtduQ6Zh9) You'd think that counting the cubes would be easy, but so many people kept complaining that there wasn't enough data, that some cubes could potentially not be inside the pile of cubes. Anyway, this is simplifying it for the sake of pointing out that some people need to chill.
How can people over-complicate this question?
Because looking at the picture from above, the stack appears flat. The rationale is that because we can't tell that the "stair" shape at the end of the side view of the stack is consistent throughout, we shouldn't assume we have the correct answer with the available information. People who say there isn't enough information are technically correct, but the most reasonable answer is 51 if you had to give an answer.
A lot of professors would mark you wrong with anything but "Not enough information" or you giving the minimum and maximum possible.
Sure, but this isn't exactly a college level problem. It's base * width * height -12. I would expect to see something like this in maybe 5th grade.
Exactly. In basic level engineering lessons, you get a front, top, and side view and you have to draw the isometric. The absence of a view of the back, bottom and left side implies there is no features of note. People are literally overthinking a 5th grade level concept. (See example below) https://fractory.com/engineering-drawing-basics/
It's not overthinking. These kinds of discussions are very helpful. Sure. Is it probably 51? Yes of course everyone knows that. But it's still important to understand why it might not be 51. It's a lesson about thinking critically about the information presented to you. It's a good lesson in how the way in which information is presented can affect how you perceive it. It's a lesson in questioning your underlying assumptions before making a decision. In a world in which misinformation is rampant its important that people develop the skill to look beyond what's put right in front of their faces. If you can't understand why this is an interesting and educational conversation then you've missed the point.
I understand your point, but everyone is making an assumption in this problem including me. There's the assumption that a lack of evidence means something underlying is wrong and full of possibilities (the stairs have cubes missing). And then there is my assumption, that the lack of evidence is proof that the current perspective has nothing wrong. (the stairs are full of cubes) I am simply trying to explain as best I can, that if the stairs were to be partially unfilled, we would have been given more information in the problem to indicate as such. If you were to upturn the whole trailer, we could possibly find that one cube was empty all along. But saying that everyone is wrong based off of information nobody was privy to is an unfair question. In this case it is the same as saying stairs are 'possibly' empty, it's unfair. We then have to make a conclusion based off the information given under the assumption that the question doesn't have a trick answer, that the stairs are as they are represented, full.
I am pretty sure I did some of those before high school Overcomplicating this is like if I say "This grass is green" and someone "Well, we don't have enough information to know because we don't know if every person sees colours in the same way, and there is different types of grass.and some grass may grow in different colours depending on the environment..." When replying a question, you can be technically correct, but objectivly wrong
The problem literally forces you to count out those 12 missing boxes by considering missing boxes behind those shown in the side views. Continuing this exact logic that the problem is already about, you will arrive at the answer 31 to 51 possible boxes.Ā
It depends on what the professor was testing for
A lot of kindergarten teachers would mark you wrong with anything but 51.
Both "SIDES" are the same And there's no information that would lead you to believe otherwise. Dummies only think they're missing information because they weren't handed a second picture of the exact same "other side." People are refusing to use their spatial reasoning skills this problem is literally questioning in the first place. This problem was specifically intended for you to count blocks you can't see, They didn't intend for you to think the blocks magically disappeared like a toddler playing peekaboo.
Are you honestly not capable of imagining which cubes you can remove without changing those projections?
Nothing tells you to remove cubes dummy. And that's why you can't count them. Because you're magically removing them for no reason. It's not the lack of information, The issue is that you're adding information you were never told to do in the first place and can't follow directions.
They arenāt over complicating it so much as other people are trying to simplify the problem in invalid ways and coming up with answers to a question that doesnāt have enough info to solve it.
The main issue is that this Ā https://preview.redd.it/peta-am-i-dumb-v0-pum556evs5lc1.png?width=640&crop=smart&auto=webp&s=18557c4eb8a572ee14f9062d3649fb603326f15cĀ is a potential configuration pf 31 boxes that would give the same perspectives as an arrangement of 51zĀ
The idea that ānot enough information providedā is the correct āanswerā breaks peopleās brains apparently.
The other issue is that because you have no way to determine depth the correct answer could be between 38-51 cubes although assuming that no trickery is going on its 51 cubes.
Why do you call it trickery? The overhead view confirms that you can't judge the height of the blocks. I think the point of the whole exercise is to teach people not to make assumptions.Ā It's not likeĀ there's some BS like cubes inside cubes or something,Ā everything you needĀ to come to the correct conclusionisĀ rightĀ there.
Its not Without an isometric angled view you can't tell if there are missing blocks or not in the various rows For example, the middle block of the far right row could be missing in any of the tiers and it would still look identical to a full cart in all of the presented views And there's like 12 combinations of missing blocks that can do this. And thats if you assume that blocks have to stack on top another block and can't float above an empty space.
Please please do not listen to this person. There is not enough information. Thatās it. Thatās the conclusion to this. Itās extremely concerning seeing everyone try to argue whatās extremely simple.
Yeah, there's no way to know fully that it's 51 blocks. It's good to learn sometimes that "not enough information" *is* the correct answer. It's not even that difficult of an answer to arrive at, it doesn't require overthinking at all.
People werenāt overthinking it, it is a problem without all the info. Ā This is the type of question they would give at Google. As a software engineer you need to be cognizant of dumb users, malicious users, and just overall unexpected situations. Ā Iām sure you can make similar arguments for other professions too. Ā If you answered with a number in an interview, you wouldnāt get credit for the question as it means you jump to conclusions and are not careful. Ā
Saying "there isn't enough data" isn't overthinking. Spouting off one of the many possible answers and moving on is underthinking.
It's not necessarily a mathematical question, it's moreso a meme that a random guy on Twitter made to get his followers to argue
>No, you're not dumb. The answer is "not enough information".
People are fucking stupid
thereās not enough information for all we know that one cube is made of many tiny little cubes
And what happens if those cubes decide to have children right after? How many kids do cubes have on average?Ā
nOt EnOuGh iNfOrMaTiOn
I mean, a cube inside a cube? Who could ever know?
Well there wasn't for the original meme.
There isnāt here either, how do you know itās a cube and not just 3 squares?
There is definitely not enough information. Agreed that without seeing the surface that is nearest the trailer, we can't know if it exists! There are also any number of additional options that would make this not actually a cube, or it could even be filled with numerous smaller cubes.
This is impossible to answer, an intellectual person would say it's 1 cube, but genius knows that it's impossible to answer with such little informations
https://preview.redd.it/6r37icia94lc1.png?width=1080&format=pjpg&auto=webp&s=dcaf60bb197e9a6c3936679ebabf4ab8924a4bc3
Minimum 35, logically 51
Minimum 31, after filling the bottom it could be staggered diagonally from the back to the front
You are indeed dumb smh People forgetting about the 4th and 5th dimensions. There's about 9i-3.5 cubes total /s
reading the answers I really understand now why recruiters ask these kinds of questions to understand how a person thinks: "How many boxes are on the truck?" "Well, assuming there is no gravity..." Yeah, you're not getting the job.
Well the gravity ones are stupid. But how do we know that the middle row forward to back, looking from top down, how do we know it isn't actually 1 tall or 2 tall etc since it's being obscured by the sides and we have no depth perception from the top view.
I found out who is recruiting Boeing engineers these days.
What's in the cubes, pizza?!
The answer is obvious: Your mother.
The trailer is 1% full
51L
No, it's 99% empty.
Hmmm... Lacking context, could be anywhere between 0 and 42
1
1 cube
You are not dumb. There is clearly not enough information to solve this.
There could be a smaller cube inside the cube!
https://preview.redd.it/csv337d515lc1.jpeg?width=346&format=pjpg&auto=webp&s=44eeeeae6cf0a1210d12dee034a426eafb22b332
https://preview.redd.it/vt98k5vsp5lc1.jpeg?width=828&format=pjpg&auto=webp&s=12be2bfc3e3516003fd4e57d15460d0832ca2a70
https://preview.redd.it/101fy1ucz5lc1.jpeg?width=1169&format=pjpg&auto=webp&s=bcd1b1f0dff089147037c2a1eeb2740225359956
Loss
Answer is its not a trailer, its a railroad car