All you Math Wizzes, Here is One For You

[altenbach]

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@GregFreeman wrote:

PVC Pipe Length L=30, we will call the right edge 0, so with holes at +6 and +25 inches, a solution may be a 7 inch piece from the right, and 7 inch piece from the left. Another solution may be a 27 inch piece from the right and yet another solution just a 27 inch piece from the left. 

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So the "inserts" are required to be flush with one of the sides? (Else another solution would be to use a 19" piece covering the two holes and the space between them. What is the diameter of the holes (is it significant compared to the other measurements or are these just pinholes)?)

Do you have an unlimited supply of inserts of each lenght? What is the maximum number of holes?

Are you trying to build a saxophone? 😄

[mikeporter]

This whole thing reminds me of a story I heard once about a beautiful woman, a mathematician, a philosopher and an engineer...

The punch line was something about, "...a close enough approximation to make life interesting..."

Mike...

[johnsold]

I still do not understand the full scope of the problem.

- What are the minimum and maximum numbers of holes in the outer pipe?

- What are the constraints on the position and spacing of those holes?

- Is L always 30 or are other lengths possible?  What is the range of lengths?

- Expanding on altenbach's questions, must the inserts remain in contact with each other (if entered from the same end) or can one or more be "isolated" in the middle (assuming that a suitable length was available for pushing it into position)?

Lynn