86 of 100: Mental Folding

Geometry Level 1

The figure above can be folded into a cube. When the cube is formed, which edge will the red one (marked with a question mark) be in contact with?

Time to put your visualization skills to the test.

Yellow Blue Orange Green

8 solutions

Atomsky Jahid
Aug 24, 2017

Oh boy! Animating things is hard!

However, you put in the effort to make this and karma will reward you back... just look at all these upvotes ! See, you deserve it! :)

William Huang - 3 years, 9 months ago

Thank you! I also tried to make a GIF. But, that would be too hard. Still pictures were the best I could offer.

Atomsky Jahid - 3 years, 9 months ago

NOT FAIR I AM A BIT COLORBLIND AND THE ORANGE ONE SEEMED GREEN

Liviu Vigu-Giurea - 3 years, 9 months ago

@Janae Pritchett , please consider naming the sides along with coloring them.

Atomsky Jahid - 3 years, 9 months ago

The orange and the green one seem very similar to me, i have Deuteranopia, also the yellow one seems to me as a greenish-yellow, rather then a normal one.

Liviu Vigu-Giurea - 3 years, 9 months ago

@Liviu Vigu-Giurea – Actually, I am not the one who set this problem. I have mentioned the problem setter in the previous reply. I am sorry that you had to face this difficulty. Hopefully, they might name the sides in future.

Atomsky Jahid - 3 years, 9 months ago

@Atomsky Jahid – Well my condition isn't that common, i hope that i didn't cause you or the setter any problems, and in the end i made a fuss abut this for nothing, the big problem was when i wanted to get my driver licence and for my case the law says it is up to the doctor to decide if i am able or not, and the doctor needed a little "perpetuation" to choose in my benefit. Still i thank you for your kindness and i would want to thank the problem setter if he fixes it.

Liviu Vigu-Giurea - 3 years, 9 months ago

fantastic Superb animation

Soham Chitnis - 3 years, 9 months ago

Robert DeLisle
Aug 24, 2017

Marking all the corresponding sides:

( All quick and dirty using MS Paint. )

David Hairston
Aug 25, 2017

I made a chart, which made the visualization of the sides in 3-D much easier for me. The six sides of the cube are designated by a capital letter as: Left, Front, Bottom, Right, bacK and Top. This is the large letter in the center of each face in the chart. Next, I labelled the edges of each face with two letters. The first letter, in the edge designation, was simply the letter of that face (and completely redundant but useful for bookkeeping). The second letter, in the edge designation, was the letter of the other face shared by that edge. This was relatively easy to do since the faces were more or less obviously adjacent to certain other faces. The only visualization needed for me is shown as the blue double-arrow lines shown in the chart, otherwise the edge designations could be deduced because of the obvious relationship to another face or, when it wasn't obvious, because that face was opposite an obvious face. The opposite faces are, of course: front-back, left-right and top-bottom. The last step was to label the red edge (left-top) and the other colored edges. It worked out that orange was top-left and thus was the edge shared with red .

This is very close to my solution. In short, cut the L and T squares from the diagram and then re-identify the edges you've marked with blue arrows. The red and orange edges are then opposite sides of a row of four sides, so using the geometry of a cube, they must be identified.

You've obviously shown a bit more (for instance, my method doesn't explicitly say where yellow goes), so thumbs up to you.

Brian Moehring - 3 years, 9 months ago

Your solution would visually be more compelling. I wish I had seen it like that. Thumbs up to you!

David Hairston - 3 years, 9 months ago

Gabriel Käppeli
Aug 29, 2017

There are 3 times 2 boxes horizontal aligned. You can move the bottom one to the top, so the shape remains the same.

Mohammad Khaza
Aug 24, 2017

as there is only six surfaces so it will be a $1 \times 1 \times 1$ cube.

suppose, the given diagram is a matrix .now we can try to make a cube.

at first, folding $11$ & $12$ to make a positive angle with $21$ .now folding $22$ with the diagram.

and now, closing the boxes surrounding $21$

so, now,the $32$ matrix has 3 colors in the upper side of the cube--blue,yellow and orange.as the orange color is on left side & the red color is also on upper red side,so, red will definitely match with orange.