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One solution is Thought process:


As an addendum to the answer from @Arnaud:


My first guess would be because Of course, this assumes I don't think


The puzzle asks for a maximal sum for the numbers on the edges, so...


If your three dots at the end would mean that 3 elements left then the pattern is the palindromic one. However if we don`t know how many elements are left, we cannot state this.


I get Because


The problem is not really about products, more about finding an arrangement of digits 1 to N-1 (for base N, since digit N does not exist in base N), that conforms to the criterion that any pair in the arrangement is part of the set of single digit products. There could be a better way to solve this, but I wrote a small program that creates a table of ...


The answer is: Because the filled-up pentagon looks like: The sum in each edge is 38. This is the maximum I got after several trial & errors.


After @SteveV's progress: Then, given the language tag, we now Giving Meaning (approximately)


Short and Concise solution, Finally,

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