Here’s one method, drawn out in Sketchup. The arrows indicate where the contiguous colored sections stay connected to the base.
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Sorry! Blurred now. 
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Easily.
Cut the square into a spiral shape nine small squares in length. Then, moving outward from the innermost small square, as you cross each line, fold
- Inward
- Inward
- Inward
- Inward
- Outward
- Outward
- Inward
- Inward
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Nice solution, thanks for blurring too, even before one of us could drop in instructions on how to do.
Also: Welcome to the BBS!
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I was about to upload some hand drawn instructions with my solution but realized that in just 30 minutes so many people had already sent theirs. Still, mine was as well a different one like @john_c suggested that would happen.
Btw, long time BB reader but just signed up today to reply for this thread. Nice to be here! Greetings from Spain
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All are welcome!
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No matter how fast you are, there’s a brilliant boinger who will get there first!
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And perhaps too much time on my hands or a desire to procrastinate to solve a fun puzzle with scissors.
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Yes! It’s actually a general solution, not just the S shape mentioned above. Here are the parameters:
[spoiler]
- Cut one line two segments long
- Cut two lines one segment long each[/spoiler]
Ta da! So long as no pieces fall off, you’ll have a shape that can be folded around the cube.
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Hmm… does this help?
… maybe not.
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If that’s the case…
Red = cut
Blue = fold
[spoiler]
This is one of those situations where something done is much easier than the same thing to be said.[/spoiler]
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Is this supposed to be difficult because there are no 1x2 squares perpendicular to the bottom edges of the cube?
Look, I’m obviously #verysmart but it took me longer to figure out the puzzle than the answer.
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YES! I suspected it could be articulated simply. Kudos for describing the principle before the particulars!
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I guess I’ll be the one to write the dissenting opinion here: No, I’m sorry to say that it is not possible. Sorry to burst all of your bubbles, but it just cannot be done.
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Welcome to the BBS 
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Yeah, if we ignore condition #1 and use 45° folds, then I think the alternative solution would be more appealing. No cuts are necessary.
<img src="//cdck-file-uploads-global.s3.dualstack.us-west-2.amazonaws.com/boingboing/original/3X/1/2/12847c3b6f47473d57603a478be3aa882058915b.jpg" width="500 height=“375”>
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Is that a Rubik’s cube solved and with the edges inverted?
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Nope. It is not a superflip (all edges flipped), it is simply a checkerboard pattern: M2 E2 S2 (or U2 D2 F2 B2 L2 R2).
I meant edges flipped, not edges and corners.
Checkerboard would be a better way of describing it
