3 outside the box problems from China

[@essemque]

Oh that triangle flip on #3 is clever!!

[@roginutah]

I like the out-of-the-box solution on #2. Good job on #3, too.

[@mindlessmeat4055]

I was only interesting in problem one, but your comment made me watch problem 2 as well. That is extremely clever.

[@Omsip123]

Guys, look up the word “stacking” before commenting there could be holes inside!!1

[@nathanharrison2]

stacked never means there are holes. its one object placed on another. stack of rocks, stack of boxes, stack of paper. at any point would those have a spot missing in the middle? if there are missing blocks they have to stipulate the middle is covered by a block attached off the side in whatever way they want to word it. logic puzzles are alays careful with wording

[@to_loww]

Subtleties like this are often lost in translation or added inadvertently.

[@MakotoIchinose]

Silence! You think glues and thin planks don't exist, huh?

[@pierrecurie]

@@MakotoIchinose To be even more pedantic, what's the volume of the glue/planks?

[@fluffyfox3481]

@@pierrecurie to be even more pedantic, what if the cubes themselves are from some sticky material?

[@kavyagupta_3232]

The last solution of the puzzle 3 got me 💀 truly a genius soln. No required complications.

[@LLlap]

You can also do it backwards which seems easier. -12 on the above, -4 on the side and -1 on the front.

[@samuelbruyneel]

That's how I solved it.

[@naveenyadav1809]

-2 using side view

[@SahilYadav-pb6lc]

Nah dude you are overcounting, As corners get overlaped 😢

[@daryengreye6573]

I started with top view. 5 + 5 + 2. Easy

[@mathmannix]

For those who are saying the first puzzle can have only 10 or 11, I would have thought that, except that the instructions specified it was SOLID, i.e. not hollow.

[@EaglePicking]

And that they are "stacked", implying that gravity holds them together.

[@verkuilb]

Solid-as in the cubes are fused to each other, and therefore gravity doesn’t act on them independently. So yes, either/both of those cubes can be missing without violating what is stated.

[@xicufwm]

You know that that's NOT what the word "solid" means in Math, right? 😂

[@rls5907]

“The figure below shows a solid object MADE BY STACKING…” Stacking an object on level 3 requires levels 1 and 2 to be filled. The answer is therefore unambiguous.

[@user-ss7zq9lc3k]

@@xicufwm what are you yapping about

[@ryokubudo]

Puzzle no 1 was easy, puzzle no 2 especially second method thinking out of the box blow my mind! Thank you very much for this joyful puzzle!

[@heqitao]

What a great set of puzzles. I love the simple solutions in #2 and #3. Thank you for sharing.

[@themelancholyofgay3543]

how about #1

[@heqitao]

@@themelancholyofgay3543 I am not very educated so I enjoy simple solutions I can work out without a mathematics background (I am trying to remedy this deficiency). I was able to teach #2 and #3 to my 12 yr old. Also I have a decent spatial awareness, so I solved #1 in my head in just a few seconds. Have a great day.

[@WillRennar]

How I solved the 2nd puzzle: (x+5)(x+20)/2 = (x^2 + 25x + 100)/2 = area of triangle 5x/2 = 2.5x = area of upper triangle 20x/2 = 10x = area of lower triangle x^2 = area of square 2.5x + 10x + x^2 = x^2 + 12.5x = area of all 3 shapes combined = area of triangle 12.5x + x^2 = (x^2 + 25x + 100)/2 multiply both sides by 2 2x^2 + 25x = x^2 + 25x + 100 subtract (x^2 + 25x) from both sides x^2 = 100 = area of square

[@daveryanmacandog8029]

Or just use similar triangles. If you look closely, the hypotenuse of the triangle is a transversal cutting two parallel lines (the side of the square and the base of the triangle). Meaning that the angles of the small triangles are corresponding angles. Since we have proved that the two small triangles are similar using AAA, we can now use proportion. Let's name the two small triangles t2 and t3 b2/h2 = b3/h3 s/5 = 20/s Multiply by 5s s² = 100 Recall: A = s² A = 100

[@PhilipMurphy8]

Always with the great information content on this channel

[@xKovalskIx]

The 3d puzzle is so beautiful

[@_Loki__Odinson_]

What I don't understand is how on earth is it possible for a 10 year old to solve that last question

[@morbrakai8533]

Did you even watch the video? He literally showed an alternative solution.

[@ibrahimali3192]

@@morbrakai8533 how does someone find that solution tho, let alone a 10 year old

[@tomriddle2257]

Maybe the „creative“ out-of-the-box algorithms were hard drilled into them from age 1. You can’t compare Asian and Western children. No hate; Both cultures have advantages.

[@jasonphillips150]

Thank you for these excellent videos. I really enjoy trying to figure them out - and often surprised that I didn't see the easy solution. I love these videos and their content. Don't listen to the ignorant haters that have mean comments. You're fantastic!

[@razaele5495]

The first one is just descriptive geometry, I don't really get why it's it viral 🤔

[@jbinmd]

@@James_err Not really. I did it quickly on paper from the video thumbnail. I drew three tic-tac-toe boards for each layer in plan view (looking from the top), using X to mark occupied squares. Maybe it's all the old-school lego models I built in the 70s that helped me.

[@Fabelaz]

As someone who used to be an engineering student, that is just reading blueprints. Literally 3 orthogonal projections.

[@HotelPapa100]

@@Fabelaz Yep. And I am offended by the three projections not being aligned properly.

[@highpath4776]

@@Fabelaz but can we get a computer program to follow the logic and count each section etc to summate to the correct total ?

[@astronemir]

@@Fabelazorthogonal projections,for 6th graders.

[@shrijagadish]

Puzzle 3 can be generalized. For any angle b (that is ABD) less than 45 deg, angle BDC should be 45 - b and angle BCD should be 45 degrees. In the given problem b = 40 deg, so BDC = 45 - 40 = 5 deg. Another example b = 30 deg. So BDC = 45 - 30 = 15 deg. For all these cases the triangle flip can be done to get an isosceles right triangle with the same area.

[@tedwatson1743]

In the first puzzle, why are you assuming the unshown center bottom 2 spaces are filled with cubes? Unless they tell us that we cannot definitively say that they are there.

[@evansnyman6729]

Agreed... I was just about to post the same observation....

[@randomgamer-te8op]

well gravity ig? not realy defined, but given to assume, if you are "stacking individual blocks like that" then you can't reaaly just leave the center empty because they are just gonna fall

[@nutherefurlong]

@@evansnyman6729 They're obscured, yeah :) I guess the "stacking" means it's not free-floating, as someone else pointed out below

[@ensen89]

This is chinese 6 grade math so what I'm about to say might not apply but: In technical drawing / technical communication the rule is that material is there unless there is a (sectional) view that tells otherwise. If you gave this drawing to a machnist he would mill that "thing" and not carve out the 2 cubes that are invisible without questioning it.

[@ukaszm1137]

because the cubes are stacked on top of eachother, as stated in the beginning in the instruction

[@matthewleung2494]

The first puzzle should be wrong. The answer should be 12,or 11, or 10. Because there is two cube is invisible.

[@randomthings2270]

Good point - but gravity?

[@teddy-xdd]

Listen more carefully to the instructions what he says at 0:13

[@Ithaelk]

​​@@randomthings2270what he is saying is that, because of the front face, the minimum limit to the number of cubes at the bottom is 3 (arranged in a line). This has nothing to do with gravity. Unless there is a joke I'm not getting. 😅

[@verkuilb]

@@randomthings2270 It’s stated that it’s a solid object. Therefore the individual cubes are fused together, and gravity wont impact them independently.

[@ensen89]

This is chinese 6 grade math so what I'm about to say might not apply but: In technical drawing / technical communication the rule is that material is there unless there is a (sectional) view that tells otherwise. If you gave this drawing to a machnist he would mill that "thing" and not carve out the 2 cubes that are invisible without questioning it.

[@etaiah1225]

The puzzles are easy and fun ty for the video❤

[@Mr-__-Sy]

for the triangle problems we could also use the 30 degrees theorem and the height or catetes theorems to find the answers

[@maxinsano7376]

Problem #2 was very clever !

[@yellstr]

If 10 year olds did not learn any trigonometry, how would they know that the sum of triangle angles would be 180?

[@vishalahmad-ck6cu]

Strange cause u usually learn how to find missing angles in g5

[@shiinondogewalker2809]

that's basic geometry, trig refers to the sin & cos based math

[@Artseuss]

Now he got me thinking if triangles should be considered quadrilaterals. No rule in quadrilaterals explicitly states “no 180 degree angles” and the perimeter does work out just fine.

[@adarshgupta8215]

It's quite good to know that Chinese educators focus on developing insight at early age!

[@dhwyll]

For 2 and 3, Ihave the Martin Gardner method: The only information you've given is 5 and 20 for the first and 6 for the second, so the answers must be related to those. You're asking for the area of a quadrilateral in the first, so I'm gonna presume it's 5 × 20. You're asking for the area of a triangle in the second, so I'm gonna presume it's 1/2 × 6².

[@indigoziona]

The triangle one I solved with algebra with essentially the same as your second method - if we give the side length of the square as x, then the area of the triangle can be expressed as ½(20 + x)(5 + x) or ½(100 + 20x + 5x + x²) Or you could express it as ½20x + ½5x + x² Multiply both by 2 and you get 100 + 20x + 5x + x² = 20x + 5x + 2x² 100 = x²

[@AndreuPinel]

For Puzzle 1 you could also remove the 2 centered mini cubes from bottom and mid layers

[@shiinondogewalker2809]

no because the question states that the cubes are stacked, so it's implied it's a shape you could build by stacking cubes on a table and the top center cube would fall if there was a hole under it

[@KelseyThornton]

Nice one for #3

[@Vienticus]

2:00 most interesting way to solve Rubik's Cube ever.

[@wesleydeng71]

#1, how do we know whether the center cube of the middle layer and the center cube of the bottom layer are there? We can't see them from font, side or above.

[@kurniawandelima]

You can't have missing cubes below the center cube because in the question it said the figure made by "stacking cubes", implying there are cubes in the bottom.

[@markbothum4338]

I did #2 the hard way. Area of Square = Entire Triangle -Bigger Triangle-Smaller Triangle. Then using Area of Triangle = 1/2bh you get there pretty fast with basic algebra. I'm wondering if that's how they were expected to do it, being unaware of the 'similar triangle' property at that age. But then again, I went to an American public school, so...

[@KiloOscarZulu]

I used similar triangles for the 2nd puzzle. Ratios of the inner triangles are the same. 20/s1 = s2/5, where s1 is the top side of the square and s2 is the right side of the square. s1 and s2 are the same, just used the number suffix to differentiate in the text description here. Cross multiply and you get s^2 = 100.

[@mh94291]

In #2, if we put 5/x=x/10=tany , it would be easier

[@jeanlemire2681]

Why all that complexity for puzzle 2? From the equation that you found, x/20 = 5/x you find that x^2 = 100 and x^2 is the surface of the square.

[@yurenchu]

It's a good alternative and insightful solution. Moreover, it sets up the shortcut solution for puzzle 3 .

[@helderehemel--]

i did it the same way

[@SharienGaming]

the "out of the box thinking" solution is essentially the reason why he could even do that x/20 = 5/x shortcut - its the geometric proof for why that formula works

[@helderehemel--]

@@SharienGaming no, you canprove it withou the rectangle

[@SharienGaming]

@@helderehemel-- i mean yeah, you can also prove it purely algebraically - its math, theres always more ways to prove something^^

[@KenCool57]

Very clever flipping the triangle to form an isosceles triangle but you miss-spoke in the first half when you used trigonometry to solve it. You stated the answer was 18 units squared when you should have said 18 square units like you did in the second method when you flipped the triangle.

[@gregoryknapen9133]

In the second puzzle, you have similar triangles. So if x is the side length of the square, x/5=20/x, so the area x^2 = 100.

[@texsetter]

I was wondering if the central cube and the one below it could be removed too...

[@shloksddmusic]

In my opinion, the another method to solve puzzle 2 is not outside-the-box. It was outside-the-triangle instead.

[@zexiao]

Puzzle 1: my 8 years old son just figured out the answer after he pondered for 5 seconds

[@KalijahAnderson]

You used the same solution I did for #3 as I realized the angles added up to 180° if you flipped the edge triangle.

[@qwerty3663]

The first cube problem is easier if you go right to left than your left to right. (2+5+2) + 2+3

[@murlirathiya4231]

Nice❤

[@zushyart]

I solved the 1st puzzle just from the thumbnail 😄 For the 2nd one, I used two ways of finding the total area and the quadratic formula, but the video’s solution is way more clever and easier.

[@divyanshbhatt5570]

Sir, Please tell how did you make the 3d animation of the final solid shape in puzzle 1

[@naitiksingla4954]

Damn 3rd was a really good one

[@uni-byte]

There is a far easier way to do the 2nd one. Note that triangles are similar and assign x to the side length of the square, so we can write x/20=5/x -> x*x=20*5, therefore x^2 (area of the square) = 100. You sure know how to complicate things sometimes.

[@cargoksrt]

isn’t that what he did?

[@uni-byte]

@@cargoksrt Yes, I guess he did. I must have jumped too far ahead.

[@trumpdonald652]

Well, far easier for you. I figured it out the other way first, since it was a lot easier for me to visualize the problem with a bunch of rectangles.

[@suspicious_door]

Me when I don’t pay attention to him

[@Skwertydogs]

What happened to the music at the end?

[@vcvartak7111]

Not all out of box solutions are quicker, in problem 2 in fact similar triangle side ratio is more easier ( In side box solution) . But yes problem 3 , second method is really good

[@JellyJonesey]

2:30, the cubes in the center of the first two layers can't be seen from any of those angles and could very well not be there, so the correct answer is {10,11,12} cm^2

[@devonyon4483]

It's stated it's a solid object composed of individual 1x1 cm blocks. There must be blocks there, or else the ones above it would simply fall!

[@wicromaev]

also the side picture told you that the bottom back cube is there

[@aldoorymahagoub3951]

you are right

[@tomriddle2257]

@@wicromaevThere are 2 hidden ones. Imagine it being hollow.

[@tomriddle2257]

I was thinking the same, but when actually starting the video instead of commenting directly you get the info „stacked cubes“, which is 100% unambiguous.

[@rizqiefajar]

Having a 3D model like that is very nice 👍

[@peterkallend5012]

Just have CAD solve it for you. Make your sketches in the given planes with the corresponding shapes and dimensions and extrude the solids. The perform a boolean operation for where they all intersect. Run an object analysis and it will tell you the volume. No math required.

[@borincod]

The 3d problem is a type of a problem that almost doesn't teach anything at all. The trick works only for this only special case and wouldn't really help you for others. The first and the 2nd are nice ones.

[@natashok4346]

Method of triangle's rotation is the best. 🤔

[@StarOfDavidWho]

I saw "Outside the box problems" and so my final answer for the first question was "10

[@thomasharding1838]

The real question regarding #1 is that because those cubes are three dimensional boxes, we should be calculating the volume of the universe "outside the box", (Their words, not mine!)

[@FieriaAreilielle]

People who says there's might be hollow inside the stacked cube in the first puzzle should stop playing Minecraft and touch real grass outside..

[@scottjenks5596]

Absolutely not, the answer is indeterminate and the questioners should have stop trying to be clever and write a proper question. There is also the issue of lack of foreshortening in the side view also makes the question invalid .

[@FieriaAreilielle]

@scottjenks5596 it's called common sense. You're thinking too much.

[@nottyseel949]

​@@scottjenks5596 Yeah, technically because there is always space between molecules there is no such thing as volume or solid. Also cups, bowls, and empty boxes would have zero volume. I'm not sure of the wording but I'm pretty sure volume is the space between the edges or "contained" not the sum of the molecules or mass. The hole in the center would not make a difference in volume. I could be wrong though, it's been a while since I was taught the specific definition. I just know the working definition.

[@stokmlnes-flame2025]

the first puzzle reminds me of a professor layton puzzle

[@alexmeijer2015]

The answer to puzzle 1 is incorrect! We do not have enough info to answer the question. The correct answer is 10, 11, OR 12 cubes based on the info given, as either of the 2 center bottom cubes can be absent and still giving the same projection as when they'd be present. QED.

[@angrytedtalks]

Puzzle 3: Chinese student (10): Flipping trig again...

[@jlhjlh]

Puzzle 1 is not entirely correct. We don't know whether the cube in the very center is missing, as we wouldn't see that in the three views. Also the one just below that (center bottom). So the volume might be 10, 11 or 12.

[@simonchen7207]

cubes are stacked

[@jlhjlh]

@@simonchen7207 Ah yes, you're right, I missed that. It's only said, but not on the video, so I missed it while pausing.

[@Necrozene]

I fell for it too!

[@Doeniz1]

@@simonchen7207 But that doesn't invalidate the argument. You can have only 1 or 2 cubes as the center pile and each cube, that isn't touching the ground, would still be stacked on another cube. This only ensures us that if the center pile consists of only 1 cube, it has to be in the bottom layer, and if it consists of two cubes, they have to be in the bottom and middle layer.

[@bartiii7617]

listen to the question again

[@burtenplays]

Oh man I just looked at the small side of the small triangle and was like, yep the side of the square seems twice as long and 15 for one side and 30 for the other side of the overall triangle seemed a little too perfect so assumed the answer was 100. Not a particularly great way to come up with a possible answer but took a couple seconds and turned out I was right 🤷‍♂️

[@Fabelaz]

Yeah puzzle one seems to prepare kids to be engineers. Pretty much used the skill of reading blueprints on that one.

[@MatttNguyen2]

Finally playing minecraft really paid off

[@HotelPapa100]

My mind is offended by the elevations of the first problem not put correctly in relation ot each other. The above view should be below the front view.

[@NorfolkCatKickers]

Puzzel 1) couldnt it be 12,11,10 cubes how do you know the middle one or the central bottom one is missing?

[@master_yugen7278]

the SOLID cubes were STACKED.

[@TheCrazyJoker96XD]

I think because he used the "shape" word, if he asked for how many cubes then I am with you, they are definitely 10, because you see 10 and you cannot count more than 10. but the shape occupies 12 of volume.

[@DashieDe]

I miss music at the end

[@deanjenkins3077]

did pyzzle 2 thru 5/x=x/20 since those are proportional triangles

[@Sphinx127sp]

Same

[@helderehemel--]

@Sphinx127spsame

[@helderehemel--]

in puzzle 2, cant you just make use of idk what it is called, triangles with the same shape, but not exact the shame form. so 5/x = x/20, 5 = (x^2)/20 , x^2 = 100 so the area is 100

[@nagyandras8857]

Before anyone thinks them chinees must be smart , kids figure things like this lightning fast.... The way chineese education works is that students practice the answers to problems. They don't figure out anything. They memorise gargantuan amounts of questions and answers. And when the test comes , they answer immerse amount of questions . But in reality they mostly don't understand why the solution is what it is. However , they memorise the answer to that question too. This works well for them , and for anyone who does not know the behind the scene stuff , looks impressive. However , give em any kind of question they have no memorised answer for , and they have not a slight hint about what to do whit it. Its very comic. Basicly every asian education follows this principle. Korean i have hands on experience whit. Its very comic to be honest. Had quite some very good laughs at em , they are verry cute when you present them even elementary level problems , that they have not yet encountered. They freeze instantly and come up whit excuses so bizarre , its very hard to not adore the efforth. Asians do exceptionally well in universities for the first year or so , but as soon as reasoning or ingenuity is required , or a problem has no pre-made solution to be memorised , they fail bigtime.

[@Myrslokstok]

12? I started with topview who gave us a lot of info, max 15. Then I removed the 3 that is missing. I didn't considered any holes, tough It might be some possible.

[@conrad5342]

Nice questions. Btw. Issue3: your labeling of the angles in the solution is wrong. Both labels do not follow the same logic. I assume you are talking about BDA and not ADB

[@abhinavanand9032]

They are same

[@GeorgeSmith-s8g]

6:32 Vsauce moment

[@yasin7271]

teşekkürler

[@musicxnr8876]

effortless puzzles

[@qekruxt5089]

What is your iq

[@adipy8912]

But, you've already made a video about the last one...

[@WesCiFur666]

the first one is actually 10cm^3-12cm^3

[@SotraEngine4]

At second puzzle I got stuck. This is how far I got: x(x^2-5^2) = 5 * 20^2 Where x^2 is the area

[@helderehemel--]

i used 5/x = x/20, 5 = (x^2)/20, x^2 = 100 so the area is 100

[@cyfur7858]

Solve for x and y in the following sequence: x, 10100, 202, 110, 40, 32, 26, 24, 22, y

[@tombullish3198]

Okay I literally don't understand trigonometry apparently, at 30 years old. I know Geometry, so I know a triangle has combined angles of 180°, but that's it. I don't understand SOHCAHTOA, don't think I ever have The 3rd puzzle is unsolvable for me. Even with the explanations I still didn't get it. It only makes me confused and frustrated for not understanding.

[@hakancetinkaya8154]

at the first question. the cube at the dead center and the one right under that are undecidable. any of them doesnt change the solution if they exist or not. So the question hae 3 answes. it can be 12 11 or 10. please reply me if I am wrong. I will start feeling that I am smart but it feels statistically hard. :)))))

[@PeerAdder]

First one: 12, easy by simple inspection. Second one: x=10, similar triangles. Third one: Flip the little triangle BCD to make a right isosceles triangle, side length 6. So the area = 18 square units.

[@maxhagenauer24]

In puzzle 1, the 2 inside cubes stacked vertically could or could not be there but there is no information that says its not, so there is not enough information.

[@bradfooks4485]

On the side view it shows that there are 3 bricks in the centre so for every other view there must be 3 bricks so if you go back to the side there are still 3 bricks

[@maxhagenauer24]

@bradfooks4485 No I am not talking about the bricks in the center on the side view, I am talking about the bricks in the center of all 3 views, meaning it's barriered around bricks everywhere except the bottom. We have no way of knowing if those blocks in the center exist or not. It has nothing to do with bricks on any of the views because it is not seen on any of the views.

[@igrim4777]

He says they're stacked. If there are no cubes in the middle space of layers 1 and 2 then layer 3's middle cube isn't stacked.

[@maxhagenauer24]

@igrim4777 I was thinking that as well but I don't know if by stacked, h me actually meant that every cube must he on top of another (besides the bottom layer of course). He may have meant that but I don't know for sure uf that's what he meant by stacked. He might have just meant that the cubes are stuck together. If he actually did mean stacked then you would be correct.

[@Omsip123]

Stacking clearly means there is always a cube on top of the other, absolutely no ambiguity here

[@saschahartung5448]

the 2nd solution of the 3rd problem was simply beautiful and genius

[@robertveith6383]

It's bad that a person would have to rely on what would not occur to him/her.

[@samuelbruyneel]

Puzzle 1 was not "out of the box" at all, but very straightforward. And quite easy for me as a mechanical engineer.

[@APprojection]

2nd was over complicated. just do x/5=20/x and you get 100 real fast

[@HambaTuhan-uf6po]

Damn, puzzle 3 is for 10 y.o kids? Genius

[@MDK2k]

You could make the argument that the first problem lacks enough information to solve. You could remove the center cube from the bottom and answer 11 cm3 and that would still be the correct answer based on the information given. If you removed the cube above that cube you would still get the same front, side and above images, but now it would no longer be single shape, but 4 separate pieces. So you need 1 of those 2 cubes for it to be a single shape. That still means that the answer could be 11 or 12.

[@MrNostril]

On Question 2 how do we know that 5/x=x/20? I figured it out without that assumption and it was much more complicated I labeled the hypotenuse of the the triangle with side lengths 5 and x "a" and the hypotenuse of the the triangle with side lengths 20 and x "b" So, 1 - 25+x^2=a^2 2 - 400+x^2=b^2 and 3 - (5+x)^2+(20+x)^2=(a+b)^2 25+10x+x^2+400+40x+x^2=a^2+b^2+2ab 2x^2+50x+425=25x^2+40x^2+2ab (inserting from 1 and 2) 50x=2ab 25x=ab 25x=[sqrt(25+x^2)] [sqrt(400+x^2)] 625x^2=(25+x^2)(400+x^2) 625x^2=x^4+425x^2+10000 x^4-200x^2+10000=0 (x^2-100)^2=0 for the product of two numbers to equal 0 one of the factors must equal 0. Therefore: x^2-100=0 x^2=100 x=10

[@MrNostril]

Disregard my question at the beginning. I figured it out. Would have have been a simpler solve if I realized that.

[@mfr2]

Pythagoras

[@JTtheking134]

​@@mfr2similar triangles actually

[@yurenchu]

Note to Puzzle 1: If the view-from-above had been a 3-by-3 red square, then the answer would have been: 20 cubes maximum (whether stacked cubes or floating cubes); 15 cubes minimum, in case of stacked cubes; 10 cubes minimum, in case of floating cubes.

[@KalijahAnderson]

#2 5 is to X as X is to 20. this results in x=10..

[@liesofgasandpilesofshoes]

these are not even maths. you should just glance at the shapes and know the answers

[@conmeuhungzu942]

12 cube ↓ (imagine this in 3D space) [] [] [] [] [] [] [] [] [] [] [] [] (i didn't wantch the video yet)

[@conmeuhungzu942]

its correct! lets go! (i just watched the video)

[@hvnterblack]

In middle column bottom and center cubes could be missing too, it will not affect 2d shadow.

[@daveryanmacandog8029]

It will on the side.

[@Nixelationz]

I used Minecraft for Puzzle 1…

[@yakovspivak962]

1. 12 = 8 + 4 2. 20/X = X/5 S = Х^2 = 100

[@umop_apisdn]

You can remove the center cube from the bottom layer and the center cube from the middle layer, giving a volume of 10 cm3.

[@EaglePicking]

Unless you have zero gravity, you can't.

[@verkuilb]

@@EaglePicking Sure you can. The problem states the design is solid-meaning the cubes are attached to each other, in which case gravity doesn’t act on them independently.

[@insidious6068]

​​@verkuilb The problem also states that the cubes are being stacked. Unless you're in a space with 0 gravity, cubes from the upper layers will fall. 12 is the one and only reasonable answer for 6th graders.

[@Omsip123]

⁠@@verkuilbit also says how it is assembled: “made by stacking cubes”, so… create this solid by stacking cubes… and there is only one answer

[@pablocristianecheverriaolh1691]

Yes that is The optimal Solucion

[@JetstreamSamReal]

Whole lotta smartasses not reading instructions and ignoring gravity in the comments.

[@nightfox6738]

Puzzle 1 could be 10, 11, or 12 cm3. You can't see the two bottom cubes on the inside of the shape and there's no guarantee they're there. Removing them results in the same silhouette.

[@Piasecznik72]

But it is described as a boxes, presumably on earth, with gravity. Without bottom two boxes, top one would fall to the ground.

[@peterkallend5012]

Nope, it says volume, not number of cubes. And you CAN see the cubes on the bottom. You're given cross section sketches from all 3 orthogonal planes, therefore you know the location of ALL the cubes. If you want, I can send you a 3d print of that object so you can inspect it from all sides to verify it fits the criteria.

[@nightfox6738]

@@peterkallend5012 you should probably recheck that 3d print yourself because there are in fact two cubes you can't see from the angles they give. And the question of volume vs cubes is moot. I gave cm3 so my answers are indeed in volume. Its just much easier to tell you which part could be missing without changing the silhouette by refering to the cubes. Tell me, from which of the three angles can you see the bottom two cubes in the center?

[@GourangaPL]

puzzle 1 was trivial, puzzle 2 i got the right answer but with the standard method, puzzle 3 i've already seen before

[@blookmaster1]

first one isn't that hard

[@masonharder709]

12.. ?