Kitonum

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Consider two sets in the Euclidean plane, each consisting of 4 points.

First set:  A(0, 0),  B(3, 4),  C(12, 4),  E(4, -1)

Second set:  F(0, -8),  G(12, -4),  H(9, -8),  K(4, -9)

It is easy to check that the set of all pairwise distances between the points of each of the given sets (6 numbers for each set ) are the same. At the same time it is obvious that there is no any...

We assume that the length of a match is 1, then the perimeter of a polygon is equal to the number of matches N. If a match can be located at arbitrary angles to each other, then at a given perimeter of the area can take on any value between zero and the area of a regular polygon (for even number of matches) . For an odd number of matches the lower bound equals to the area of an equilateral triangle of side 1. For any given area within these boundaries will be infinitely many solutions.

Maple has  combinat [composition] (n, m)  command, which returns all possible lists of positive integers of  m  terms, the sum of which in each list is n. But there is no similar command for multiplication.

Wrote recently procedure  Factoring, which solves this problem. Formal arguments:  n> 1 - an integer, m - an optional parameter...

My answer in this topic does not load for some reason, so I had to create this post.

Variant of solution:

At first I wanted to post this message as a response to a question

http://www.mapleprimes.com/questions/136153-AnimateDisplay 

But for some reason the message is not loaded.

Look at the example of animation of astroid. First you need to create animation frames as separate graphical structure (in my example - it is E[k] ). And only then by  plots [display]

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