new puzzle challenge

[Claudio L.]

(03-30-2015 02:34 PM)Claudio L. Wrote:  There's 19 unknowns, and unless I'm mistaken we can write 15 linearly independent equations, so there's only 4 independent variables, not 10 I think.

I spoke too soon.
Writing the equations in matrix form and row-reducing the resulting matrix, 3 of the 15 are dependent equations, so there's a total of 12 independent equations with 7 independent variables.
The row-reduced form shows something interesting: variables 1-9, 12, 13 and 17 are dependent on 10,11,14,15,16,18,19.
In a graph, this looks interesting as the independent variables also form a smaller hexagon (variables numbered as in the diagram below):

Code:


     1      2     3
  4     5     6     7  
8    9    10   11    12
 13   14    15   16
     17   18   19