Rubik's Cube

Logic Level 1

What is the maximum number of faces that you can see in a Rubik's cube at a time by holding it in a stable position? (You are allowed to hold at any position so that you see the maximum faces)

Details and Assumptions :

No mirrors or other tricks are involved.

Image Credit: Flickr Bryan Ng .

6 5 2 4 3 1

2 solutions

Daniel Liu
Jan 30, 2015

Obviously you can't see two opposite sides.

Now, if you can see side A, the you can't see the opposite side, say side A'.

Similarly, if you can see side B then you can't see B' and if you can see side C then you can't see side C'.

But now we're run out of sides to see: we can see sides A, B, and C but not sides A', B', and C'.

Thus the maximum answer is 3.

It remains to prove that this is possible. However, looking at a rubiks cube from a vertex satisfies viewing three sides, so the answer must be 3.

It does specify "any position so that you can see the maximum sides", so what if one held it in a position that happens to be close to several conveniently placed mirrors? That would meet all of the problem's requirements, yet one could see all 6 faces simultaneously.

Caleb Townsend - 6 years, 4 months ago

Well, that would kind of be stretching the problem a bit. Regardless, I heeded your complaint and edited the problem a bit.

Daniel Liu - 6 years, 4 months ago

The answer is not 3.

When I hold the standard-sized Rubik's cube, I can still see four faces. This does not use any tricks, just two eyes and careful placement of the cube within my hand. I can see the the relative bottom face, left face, right face, and a miniscule part of the top face.

Doesn't really make sense how you can say the answer is three based on vertices, since people have different physical abilities, and may be able to see more

Eddie Spagnoli - 5 years, 8 months ago

People are not supposed to have eight balls for eyes so i auctually like this

Bailey Spears - 5 years, 8 months ago

Goodness that made me laugh!

Though I don't have eyes the size of eight balls, I am quite tall and large, but no camera can catch what I saw. I'll tell you that with the cube solved, I saw four different colors, plus the black outline, which is four sides.

The problem is ingenious though, since people who are more normal than myself will only ever see three sides at the same time, due to the visual spectrum.

Eddie Spagnoli - 5 years, 8 months ago

@Eddie Spagnoli – Oh you thing...HA you also made me laugh! You think that the black outline is a side?

Bailey Spears - 5 years, 8 months ago

@Bailey Spears – Huh?

edit:

No, I said that I saw four colors PLUS a black outline. I saw a total of five colors, and the black outline is just the outline behind the stickers (yeah, I have an old Rubiks Cube). I'm not that big of an idiot. ;)

Eddie Spagnoli - 5 years, 8 months ago

Stereo Not a trick!

I do not agree that the answer is 3. Please try again. You should be able to see a maximum of 4 sides using two eyes; this is not a trick. I tried and gave an answer of 4. Remember to take only small cube for maximum.

Lu Chee Ket - 6 years, 4 months ago

We are talking about a standard Rubik's Cube size, I assume the author is saying.

Daniel Liu - 6 years, 4 months ago

I observed my Rubik's Cube of usual size.

Lu Chee Ket - 6 years, 4 months ago

@Lu Chee Ket – You could see only 3

D Kartikeyan - 6 years, 4 months ago

@D Kartikeyan – Nope, you can see four. We can't take a picture of it, because a camera has only one lens. if you are looking at an actual cube, your right eye can see the right face while your left eye sees the left face. Remember to get close enough to the cube.

Nathan Ramesh - 6 years, 4 months ago

@Nathan Ramesh – Yes, I know it works for sufficiently small cubes. However, the problem writer had a clear intention that this was based on an orthogonal projection (imo) so the answer would be 3.

In fact, with your same argument, a person with especially wide-set eyes (or just a big head) can see 5 sides of the cube in a stable position.

Daniel Liu - 6 years, 4 months ago

Yes it is of standard size

D Kartikeyan - 6 years, 4 months ago

Nathan Hauspurg
Oct 6, 2015

While I got the "correct" answer of 3 I'd have to disagree with that solution because we don't see from a single point. If the distance between your pupils is greater than the width of the cube, you could see a maximum of 4 sides.

Rubik's Cube

Image Credit: Flickr Bryan Ng .

2 solutions

0 pending reports