Knight’s jump mazes: nothing really there yet

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By using special rules for movement, simple mazes can become complex multi-state maze-puzzles. A well-known special kind of movement that can be used for such puzzles is the knight’s jump from chess. There are two puzzles available in the app store that use this kind of movement, but neither of them offers really nice puzzles yet. However, this could easily be changed for the better.

The app Knights Run (nicely misspelled) offers the basic knight’s tour problem: try to reach every square of the chess board with the knight (and preferably return to your starting point). This problem dates back at least to the Book of Chess by Abu-Bakr Muhammad ben Yahya as-Suli (c. 880 – 946). As a mathematical problem, this puzzle has been extensively discussed, and not much now is to be gained from this problem in its classic form. I don’t see any reason to try this app.

A much more interesting approach is to change the form of the board. Traditionally, many different rectangular boards have already been considered. However, why not just take an especially designed selection of squares to be toured? This is exactly what the app Super Horsey offers (shown in the illustration at the top of this post). Each level consists of a selection of squares to be toured by the chess knight (though differently from the knight’s tour problem you are allowed to pass through a square more than once). You can only see a part of the squares: only by moving the knight will the rest of the ‘board’ be revealed. The puzzles offered are really nice, with various squares that can only be reached through a particular ‘entrance’ square. When you miss this possibility, you will be hopping around the board, unable to enter the remaining squares. At such a moment, the maze-structure of such puzzles becomes exceedingly clear.

So far, so good. Unfortunately, Super Horsey is presented as an arcade game, and not as puzzle. Every level has a restricted time for it to be solved, and when the time runs out, you have to start all over again. This is extremely unfortunate because the time-restriction is very strong, so it is difficult to reach the higher levels. And having to do the same levels over and over again is just boring. The solution is simple: just offer a second possibility to play this game: the puzzle mode. Levels can be chosen freely, and solved without any time pressure. As an extra twist, it might also be interesting to offer the minimum number of moves necessary, so real aficionados can search for that special solution as well. For the arcade lovers, this puzzle mode might be considered ‘practice’, because even when all levels are theoretically solved, quickly remembering the right solution in the arcade mode will still be a challenge!

Finally, both these apps should consider to offer real mazes. Instead of asking for a complete tour of all squares, the goal in such a ‘maze mode’ will be to simply reach a particular goal square. Various designs of such knight’s jump mazes have been made by Andrea Gilbert, and are available online as knight tour mazes. I am sure she will be delighted to cooperate and bring these designs to the iPhone.

[Update 21 January 2009] Another basic knight’s tour implementation just became available on the app store: Knight’s Tour. Nothing new, nothing of interest.

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