Sunday, June 08, 2008

Next Element

Title: Next Element
Author: Zielock Games
License: Freeware (donation requested)

Next Element is similar to Hex-a-hop and MASRDBE. It is not as good as the former, but better than the later. The object is to find a path from the start tile to the goal tile which passes through each of the numbered tiles that many times. There are two additional twists. First, the arrow tiles can only be entered from the tail of the arrow and exited in the direction of the arrow head. Second, there are teleporter tiles which jump you to another part of the board. An oddity of the rules is that these special tiles can only be used once, but you do not have to use them to complete a level.

There 30 levels which must be played in order. The level design is decent. Most of the levels are easy, but there are a few tricky ones. One key features is an unlimited (I think) undo feature. One minor misstep does not require a restart of the level, just hit 'u'.

The interface for Next Element is straight-forward, use the arrow keys. The graphics are simple but effective. I found the audio a bit annoying and turned it off . These is not much else to say. It is a fun freeware game worth playing if you like these sort of puzzles.

There is no level editor. If you make a donation to Zielok Games, they will allow you download Next Element Deluxe which contains 80 levels.

As I mentioned in my entry on MASRDBE, solving these puzzles comes down to finding a Hamilton path in a certaom graph. In any position, there are at most four ways to move and usually far fewer. Also, it is pretty easy to notice when things have gone bad. For example, the remaining tiles are disconnected, or there is a dead end. So, I am guessing that a depth-first search should do really well on these problems. Maybe a meet-in-the-middle search is needed for some problems. I am curious if a computer search could find some really tough puzzles. I am sure, as the size of the board increases, the problems become exponentially hard, but with 10 minutes thought I could not see a proof that they are NP-complete.


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