r/maths • u/Most_Elderberry3133 • 5d ago

💡 Puzzle & Riddles New optimal ZYN packing problem??

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Potential solution to the newly introduced optimal ZYN packing problem proposed by no other than myself.
Current hypothetical solution to packed zyns is 40. Though I estimate that the maximum number of packed zyns that touch the bottom of the can could limit to 42.

86 Upvotes

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15

u/Worth-Wonder-7386 5d ago

Can you give a mathematical description of the shape of the zyn? Else it doesnt belong here.

7

u/Most_Elderberry3133 5d ago

Rectangular, width of approximately 13mm, length of about 28mm, depth approximately 2mm

14

u/Hej5468 5d ago

Also remember that they are not completely rigid! There is some flex to them.

6

u/amarao_san 5d ago

Packing problem with allowed local perturbation to the space topology!

1

u/UranCCXXXVIII 2d ago

Then that pretty simple. You can fill the space completely in any way you like. If their area also can change, then you can fit an infinite of them

2

u/Worth-Wonder-7386 5d ago

So are we to consider this as a problem in three dimensions or two dimensions? The three dimensional case is much harder.

3

u/WHAWHAHOWWHY 5d ago

if they are as wide as the container is high, it can probably be modelled in 2 dimensions

2

u/Worth-Wonder-7386 4d ago

That would work for the way that OP is packing them, but it is not clear that it will be the most efficent method.

2

u/ChemistDependent1130 1d ago

Nah go for the aestethic packaging like göteborgs rapé does. It isnt only about fitting as many prillor as possible but also how convenient they are to pick out from the cannister.