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+--- Thread: Little problem(s) 2022.08 (/thread-18629.html)
Little problem(s) 2022.08 - pier4r - 08-02-2022 08:26 PM
Inspired by this: https://www.youtube.com/watch?v=gNRnrn5DE58 and this.
Someone wants to order a set of 81 rectangular cuboids that can stick with each other, whatever is the face that we pick of the cuboid.
Those cuboids will be used for measurements.
#1
Define the dimensions of those cuboids with the objective to cover the largest number of possible consecutive lengths provided that we give a fixed interval between those.
I am not sure I wrote this properly so I give an example.
Say that I decide to design the 81 elements as cubes with edge of 1 unit (1/1000 of an inch, a millimeter, a digitus or what not); then with 81 of them and an interval of 1 unit, I can cover 81 consecutive lengths: 1,2,3,...,81
I hope the example helps.
#2
Given the devised set, it should be practical for an operator to compose a certain length with maximum 5 blocks. Thus which blocks could be covered combining at most 5 blocks given the 81 designed cuboids? (in general the limit of 5 could be seen as "limit of N blocks").
#3
What are the all possible covered lengths (consecutive or not) that one can assemble given the 81 elements that were designed?
#4
For each possible covered lengths, what is the shortest combination of blocks to equal that length and what is the longest?
RE: Little problem(s) 2022.08 - EdS2 - 08-03-2022 07:26 AM
Interesting one - do I take it each cuboid has three independent dimensions? It's a variation of the Sparse Ruler problem, I think.
RE: Little problem(s) 2022.08 - pier4r - 08-03-2022 11:00 AM
(08-03-2022 07:26 AM)EdS2 Wrote: Interesting one - do I take it each cuboid has three independent dimensions? It's a variation of the Sparse Ruler problem, I think.
Yes a cuboid could be designed to have 3 different dimensions. And I didn't know the Sparse Ruler problem, neat.