The following galaxy-like shape:
can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps.
How can it be done?
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asked Jan 27, 2020 at 6:38
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2$\begingroup$ rot13(Gur gbgny nern vf 102, fb rnpu jnyy unf na nern bs 17 - ner lbh fher gur funcr naq cebcbegvbaf ner pbeerpg?) $\endgroup$– Michał WójcikCommented Jan 27, 2020 at 10:59
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$\begingroup$ rot13(17 nf gur fhesnpr bs gur fdhner ybbxf n ovg fgenatr, fb V jnagrq gb znxr fher) :) $\endgroup$– Michał WójcikCommented Jan 27, 2020 at 15:34
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$\begingroup$ Nah, it's exactly the sort of number I was expecting :-). $\endgroup$– Gareth McCaughan ♦Commented Jan 27, 2020 at 16:57
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$\begingroup$ @MichałWójcik rot13(Lbh unir pnyphyngrq pbeerpgyl. Gur nern bs rnpu fvqr vf vaqrrq friragrra.) $\endgroup$– plasticinsectCommented Jan 27, 2020 at 17:33
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1 Answer
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The galaxy should be folded like this
The grid steps by 4 in one direction and 1 in the other
This gives a side length of $ \sqrt{4^2 + 1^2} = \sqrt{17}$
This is a crude model I made of the cube, with the joins highlighted (might have missed one).
First of all I spotted the 4 quarter-grid parts, which I assumed (and was right) would be the centre of the opposite face. After a few false starts the penny suddenly dropped as to where the $17$ area comes from, and from there I produced a model.
OP previously said he would make these puzzles harder, and it was. Unlike others, there is no obvious place where the corners of the top side will be. The centre part does not include any of the corners of that face.
answered Jan 27, 2020 at 18:53
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$\begingroup$ I love seeing these solved with physical folded paper! Well done. I imagine this one was especially tricky to fold, because rot13(nf lbh cbvag bhg va lbh nafjre, lbh qba'g unir nal ersrerapr sbe gur gbc pbearef hagvy nsgre gur sbyqvat vf zbfgyl qbar). And yes, I admit I did this on purpose to make the puzzle harder. My previous puzzles were getting answered too quickly. :) $\endgroup$ Commented Jan 27, 2020 at 19:46
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$\begingroup$ rot13(Ol wbvavat gur prager bs gur onpx snpr jvgu gubfr sbhe dhnegre-cnegf orsber znxvat nal sbyqf, V fhfcrpgrq jurer fbzr rqtrf bhtug gb wbva, ohg pbhyq abg frr ubj. Jura V ernyvfrq nobhg gur fvqr yratgu vg orpnzr pyrnere. Gung jnf nsgre frireny fxrgpurf bs fhccbfrq sbyqf naq gjb snvyrq zbqryf. Avpr chmmyr!) $\endgroup$ Commented Jan 27, 2020 at 19:55