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A cubical box is required to contain a set of wooden blocks (N right parallelepiped solids that fits in without spaces) which have different edges and colors. No two blocks have the same edge linear measurement. All blocks have unique dimension (integer units), thus no square faces.

What are the smallest box's inside dimensions SxSxS ?

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  • $\begingroup$ Are you looking for a solution involving $n$ solids fitting the constraints? $\endgroup$ – Thomas Markov Dec 13 '19 at 19:46
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    $\begingroup$ It's probably a good idea to clarify: a dimensionless box is enough to contain (and exactly fit) an empty set of 1x2x3 blocks. A 3x3x3 box is enough to contain a single 1x2x3 block. Yes, there's space left over, but filling the box isn't a stated requirement. Does the "dimensional measurement" mean volume, side length, side area, total area or maybe all of the above? Also, what do the colours have to do with anything? $\endgroup$ – Bass Dec 13 '19 at 20:20
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    $\begingroup$ "No two blocks has the same dimensional measurement" Does that mean no two blocks have a common side length, or no two blocks are congruent, or no two blocks have the same volume? $\endgroup$ – Magma Dec 14 '19 at 0:03
  • $\begingroup$ What do you mean by "inside dimensions"? As opposed to outside dimensions? $\endgroup$ – Magma Dec 14 '19 at 0:05
  • $\begingroup$ No two blocks has common edge or side distance..and box haa thickness $\endgroup$ – TSLF Dec 14 '19 at 0:20
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4x4x4

Because

Given there was no constraint to the number of right parallelepipeds, I chose two. Since each solid has pairwise unique side length (and it was not specified that we could not have repeats between solids), the solids in the box have dimension 1x2x3 and 1x2x4. These clearly fit within a 4x4x4 box.

And if side length is pairwise unique between all solids,

7x7x7 with solids 1x2x3 and 4x5x6, which again clearly fit. (Originally said 6x6x6, derp.)

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  • $\begingroup$ Yeah, thats why I added an answer that considers that constraint (which is not clearly stated). $\endgroup$ – Thomas Markov Dec 13 '19 at 21:27
  • $\begingroup$ Derp, 7x7x7 obviously. Thanks. I still dont really understand what the problem really is though lol. $\endgroup$ – Thomas Markov Dec 13 '19 at 21:32
  • $\begingroup$ Yeah thats what I assumed in my first answer. $\endgroup$ – Thomas Markov Dec 13 '19 at 21:34
  • $\begingroup$ I didn't assume that the solids fit together to have the same dimensions of the box. I assumed we could just put two of them in the box. It wasn't specified in the problem, another issue with its construction. $\endgroup$ – Thomas Markov Dec 13 '19 at 21:36
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    $\begingroup$ I'll stop commenting until the question is clarified. At this point, I neither know what the objective is nor do I know what the constraints are. $\endgroup$ – JS1 Dec 13 '19 at 21:36

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