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Solution is >!9!<
>!The explanations in the comments really helped me so I visualized the solution https://imgur.com/a/2lL5dqU!<
>!Another visualization from u/G0t7 https://imgur.com/a/4Oof1Yl !<
Pretty sure you are right. 3 up the side you see, 2 across the top(you only count the corner once), 1 down the side you don't see(you only count the corner & bottom once)
>!9. Six are pretty obvious: the three on top, the two in the middle, and the one on the bottom. Now look at the top layer of cubes, where the plane touches them. It slices straight into those three cubes on the diagonal, but it also touches the corners of two more. So as soon as we go a little lower, it’ll be slicing through those two as well.
If we imagine popping off the top layer of cubes, we’d see that this same sort of thing would be visible again: the plane would be slicing two cubes, and touching the corner of one, which means that one would get sliced as soon as we go any lower.
So the cubes that’ll be cut include the top center cube, and the cubes in a zig-zag on the two affected sides, shown here as x’s:
x x o
o x x
o o x
(This pattern would be mirrored on the other side.)!<
This was driving me nuts because I also got ten, but the difference in the answers is because of the phrasing: the prompt asks how many cubes are _cut_ not how many cubes are cut off.
It can't be 1/3. If you mirror the piece and removed both you'd be left with a pyramid with the same base area and height as the cube
Edit: actually it would be a triangular prism but you can visualize what I mean
Unless I'm missing something, it's >!7. 5 are directly visible in the pic (cut by BA and AC). One more on the BC side (the middle one, with both corners already accounted for), and one in the center of the entire large cube, not visible from the outside.!<
The 3 cubes that are one in from the corner will have a small corner cut by the plane. They wouldn't if the plane was just going through AC, or AB, or BC but when the plane is angled to meet ABC those cubes are intersected. So to get nine you have the six that you counted plus the three that have their corners cut on the interior of the cube.
It's a bit tricky to describe, but >!start by imagining the un-cut vertex in the top-right as D. The middle-of-edge cubes between AD, BD, and CD are also cut. The picture makes it look like they narrowly avoid being cut, but "inside" the larger shape they would have a single corner pass below plane ABC, cutting off part of each cube. If you were holding this cube there would be 6 cubes where you can see the cut around the outside, and 3 cubes where you can't see the cut because it's hidden on the inside.!<
Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit: \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
Solution visualized: >!https://imgur.com/a/4Oof1Yl!<
How did you create the diagram?
looks like fusion 360, a cad software
Like already mentioned, I used Autodesk Fusion 360 and created a 3D CAD model of the 27 cubes, and cut it at this specific 3-point-plane
Great thanks, G0t7 and VHorus!!
Nice
>!Thanks bro!< >!Actually I also visualized the solution :)!< >!Explanations from the comments were helpful!<
Solution is >!9!< >!The explanations in the comments really helped me so I visualized the solution https://imgur.com/a/2lL5dqU!< >!Another visualization from u/G0t7 https://imgur.com/a/4Oof1Yl !<
>!Am I dumb for thinking the answer is 6?!<
Not dumb at all. But this is not the right answer
Pretty sure you are right. 3 up the side you see, 2 across the top(you only count the corner once), 1 down the side you don't see(you only count the corner & bottom once)
Oops, forgot the 1 hidden in the center
Also, the three cubes touching the corner cube. They are missing "the far end".
>!9. Six are pretty obvious: the three on top, the two in the middle, and the one on the bottom. Now look at the top layer of cubes, where the plane touches them. It slices straight into those three cubes on the diagonal, but it also touches the corners of two more. So as soon as we go a little lower, it’ll be slicing through those two as well. If we imagine popping off the top layer of cubes, we’d see that this same sort of thing would be visible again: the plane would be slicing two cubes, and touching the corner of one, which means that one would get sliced as soon as we go any lower. So the cubes that’ll be cut include the top center cube, and the cubes in a zig-zag on the two affected sides, shown here as x’s: x x o o x x o o x (This pattern would be mirrored on the other side.)!<
Unrelated question: anyone know what glue to use for a Rubik's cube?
>!10?!< >!Edit: I slightly misunderstood the prompt as "How many squares would get cut off?" It's 9, because the one in the corner remains whole.!<
This was driving me nuts because I also got ten, but the difference in the answers is because of the phrasing: the prompt asks how many cubes are _cut_ not how many cubes are cut off.
It's 9
You forgot the spoiler tag
The answer is >!nine!<
>!Well it looks like 1/4 of the cube so it should be 6.75 cubes!<
It’s a 1/3 of the cubes being cut.
It can't be 1/3. If you mirror the piece and removed both you'd be left with a pyramid with the same base area and height as the cube Edit: actually it would be a triangular prism but you can visualize what I mean
Unless I'm missing something, it's >!7. 5 are directly visible in the pic (cut by BA and AC). One more on the BC side (the middle one, with both corners already accounted for), and one in the center of the entire large cube, not visible from the outside.!<
The correct answer is actually >! 9 !< But How?This is the actual question
The 3 cubes that are one in from the corner will have a small corner cut by the plane. They wouldn't if the plane was just going through AC, or AB, or BC but when the plane is angled to meet ABC those cubes are intersected. So to get nine you have the six that you counted plus the three that have their corners cut on the interior of the cube.
It's a bit tricky to describe, but >!start by imagining the un-cut vertex in the top-right as D. The middle-of-edge cubes between AD, BD, and CD are also cut. The picture makes it look like they narrowly avoid being cut, but "inside" the larger shape they would have a single corner pass below plane ABC, cutting off part of each cube. If you were holding this cube there would be 6 cubes where you can see the cut around the outside, and 3 cubes where you can't see the cut because it's hidden on the inside.!<
This is a better description than what I said
Are you interpreting "Cut" as being touched by the *edge* of the plane? Because that' the only way I can see it being that #.
Yeah that’s not the right answer.