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.

(In reply to Impossibility by brianjn)

I see that your program evaluates all the sums within a loop that goes through all 12! = 479,001,600 possible sequences of A - L.

Speed can be gained by doing the P(12,8) = 19,958,400 possible sequences of A, B, C, D, E, F, H, I first to greatly narrow down the possibilities via X = V and D>A before continuing on with the 4! = 24 ways of arranging the remaining 4.

In fact, even though not taking advantage of this in my program due to the initial misunderstanding of the problem, once those 8 vertices are checked you could also check W before proceeding and cut down on the time even more.

Edited on May 1, 2010, 1:28 pm

Posted by Charlie on 2010-05-01 13:26:15