No! Not a firing squad nor the need for a continuous line to cross all line segments just once!
To each vertex labeled A to L apply a different value from 1 to 12. Let V, W, X, Y and Z be the sums of their respective surrounding vertices.
Provide at least one example where V=W=X=Y=Z, or offer a reason why this, like the continuous line, is impossible.
I tested using nested loops, for some efficiency though not total optimization. (1) First varied ABCEFGH for 1 to 12 without duplication: testing for V=W; (2) Then varied DI, testing for V=X, finally (3) varied J, testing for V=Y=Z. Testing each vertex for nonrepetition shortens the execution time if not the coding process. The whole process took only about a second or so of execution time. Everyone gains when the problem statements define terms -- in this case "vertex" which is popularly thought of as "corners" of a multilateral, but which has technical definitions which allow other points (though usually as intersections or interceptions). I often avoid problems altogether if there is too much uncertainty.
efficiency
