Nodes: advanced connecting dots

Nodes.pngVery many interesting games and puzzle concepts are being developed by the flash-gaming community. An example of such an interesting puzzle is Nodes, developed by Eggy (Bradley Erkelens) with the assistance some not further clarified person named Frank. The goal of the puzzle is to position the nodes of a graph in such a way that the vertices cross through a set of small circles. This game is also available on the iPhone, though unfortunately not through Eggy, nor with his consent.

Picture3Nodes.jpg Nodes (iTunes Link) from the ukrainian company Olmob is the most direct copy of Eggy’s game. Eggy explained:

“Then that guy made that recently and I emailed him about it asking if he copied me, he says he didn’t and it’s a coincidence…I find it hard to believe to be honest…but nothing I can do either way.”

I also don’t believe a word of the story that Olmob got onto the same game independently. The name of the game, the gameplay, the level design, and even the visual design of the puzzle is too similar to Eggy’s original. Don’t spend money on such a rip-off!

IMG_0004Laser-Puzzle (iTunes Link) uses the same puzzle-principle, but at least the styling and the name are completely different (see screenshot to the right). The really great improvement of this implementation is that you can use multi-touch to solve it! This is really a breakthrough development. It might sound like a small change, but actually solving these kinds of puzzles becomes so much more fun when you can move both ends of the line at the same time.

IMG_0005In the latest update there is now also (finally) an ‘easy’ puzzle-mode without time pressure. I still don’t get what is so interesting about time-pressure in puzzles. I have said it before, but I’ll repeat it again: time pressure is only necessary when the puzzle-design is too simple to be enjoyable in itself. In this case, time pressure is simply completely unnecessary. For example, the solution to the puzzle to the right is shown to the left here. It surely is not trivial, and I got a nice ‘aha’ when finding the solution.

As an aside, this kind of puzzle actually has a long history. Both the old grandmasters of puzzle design Sam Loyd and Henry E. Dudeney made some puzzles that are strongly related to Nodes, though I guess that none of the current developers had any knowledge of this origin. In Dudeney’s Amusements in Mathematics (1917), there are various puzzles in the section Dynamical Chess Puzzles (specifically “Star Puzzle”, “Yacht Race”, and “Scientific Scater”) in which the objective is to find a route that passes through all points in a rectangular grid of 8×8 points. The route has to consist of straight lines, and the question is to find the route with the least amount of turns. Sam Loyd’s puzzle Going Into Action is of the same type.

4x5closed.gifThe solutions to these old puzzles were actually not very interesting, but many new solutions were found for different grid-sizes in the wake of a challenge posted by Ed Pegg Jr. on Mathpuzzle in 1999. It turns out that minimal solutions get really interesting once you let go of the assumption that the route has to be inside the grid (see for example the 4×5 solution with only 7 lines to the right). For a summary of the findings from this challenge, see Ed Pegg’s summary.

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