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

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. :slight_smile:

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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

  1. Inward
  2. Inward
  3. Inward
  4. Inward
  5. Outward
  6. Outward
  7. Inward
  8. 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 :sunny:

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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="//discourse-cloud-file-uploads.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