# Can we wrap a 1x1x1 cube with the blue 3x3 piece of paper, cutting along some edges without disconnecting it?

Originally published at: http://boingboing.net/2017/04/11/can-we-wrap-a-1x1x1-cube-with.html

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Can we?

You have my permission to go forward with that.

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May we?” ~ Your elementary school teacher, probably

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One of the sides will have 2 sections covering it but I can’t quite grok the cut to make the fold to go over the top.

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I was thinking diagonally.

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And I would be wrong.

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Yes: Cut in a s shape, wrap starting from one end of the s, folding every piece towards the cube / the smaller fold. On last strip, instead of folding towards the cube, fold the second to last piece back away from the cube back on top your strip. You’ll have just enough to reach the last side going that direction.

It’s also a challenge in describing an answer. Geeze.

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Three.

There are 5 sides to cover, 8 available squares

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Oooh yes that would do it.

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Makes you kinda feel some respect for the person who draws IKEA assembly instructions, right?

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I thought we’d concluded a while back that with puzzles like this the solution is always to rotate it by 45 degrees first…

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It works with a spiral shape too. Hmm, I wonder how many unique solutions there are.

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Great! Firstly, I never trust the puzzle the way it is given to me anymore, move that box around. I had the S, but I couldn’t quite figure out how to get to the last side. I knew I had enough area because 9-6=3.

[spoiler]Spoilers follow:

Puzzle as presented, move that box!

Cut the “S”

Start wrapping from on end

Almost done, watch that last bit

Fold it backwards and complete.[/spoiler]

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Yes We Can.

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Blur it! My eyes! Neither solution given by us all thus far is the one on the website, we are all so clever!

(I also appreciate the same nondescript solid surfacing material of your work desk as mine.)

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This is what I came up with

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…because mathematicians always take it too far - and then how many unique solutions given an n-dimensional (hyper)cube and an n-1 dimensional wrap allowing only folding and cutting (which I don’t know how to define outside of my boring 3 dimension+time that I live in). Somebody call a topologist!

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Heheh. Yes, it’s true!

Actually, all my questions have now been answered: http://cs.hood.edu/~whieldon/whieldon_papers/cubesurfaces.pdf

There are 126 solutions using 18 distinct cut patterns. If you want a little bit more of a challenge, assume the two sides of the paper are different colors. There are 21 solutions that leave only a single color showing.

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