noosphere
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Counting knight moves - 2007/10/06 17:24
Quick! What's the minimum number of moves a knight on g6 needs to get to e4 ?
To answer this question, most chess players will simply start to mentally move their knight around, counting the moves, until it lands on the desired square. Let's say you counted 4 moves: e5-g4-f6-e4 That's one way to get there, and so is: f8-e6-g5-e4. But is there a shorter route?
To answer that question with some measure of certainty (as opposed to just guessing), most chess players would need to try a number of alternate paths to e4. This might take an inordinate amount of time in a game, and when the player has the answer, they might even need to go through the moves again to double-check their answer, taking even more time.
And what if the player was interested in more than one destination square for the knight, or in the minimum number of moves it would take for knights starting from two different squares to reach the same square? Depending on where that square was, coming up with an answer you felt confident in could really take a long time and be very error-prone using the ordinary method of counting knight moves.
Fortunately, there's a better way. I'm a fan of obscure chess books, so when I was at a local chess store the other day, the book "Knight Moves" by Charles Alexander caught my eye. In it he describes a relatively simple method, which he calls "Alexander's Technique", to count the minimum number of knight moves it would take a knight to move from any given square to any other square.
Alexander's Technique consists of a number of rules-of-thumb which the player would need to memorize and apply. The rules range from the incredibly simple -- such as learning that the only times it would take a minimum of 6 moves to get a knight from one square to another is if the knight starts on one of the corner squares (a1, a8, h1, h8) and wishes to go to the diagonally-opposite square (ie. from a1 to h8, h1 to a8, etc...) -- to a number of more complex (but quite easily learnable) rules.
It only took me a few minutes to start applying the rules after I'd read the book, and maybe another ten minutes to half an hour to completely internalize them... and after an hour or so of practice, I feel completely confident I'd be able to quickly (certainly under about 15 seconds, and often as little as a second or two) to figure out what the minimum number of moves it would take for a knight to get from any one given square to any other.
The method can also be used to determine the minimum number of moves it would take a knight to get to groups of squares. For example, if the knight is not on one of the corner squares, you immediately know that the minumum number of moves it would take to get to any other square can not be greater than 5. The minimum number of moves it would take a knight to move to other groupings of squares, such as any black or any white square, could also be easily counted.
Alexander's Technique does have its limitations, the most obvious one being that the presence of other pieces on the board might delay or completely stop the knight from reaching a given square in the minimum number of moves. For example, some moves might be illegal given the situation on the board at a given time (such as having a piece of the same color as the knight block one of the squares the knight needs to move to), or the knight could get captured on its way, etc... In these cases, the player is pretty much on his own in taking account of these possibilities. Still, he can be certain that the knight will not reach the destination square in less than the number of moves Alexander's Technique tells him it will.
Another limitation is that the player could still make a mistake in applying Alexander's Technique, perhaps requiring a double check of some sort (by either re-applying Alexander's Technique, or manually counting out the moves).
Still, given what Mr. Alexander set out to achieve with his method, I'd say he admirably reached his goal.
One other thing that I should mention is that this is a really thin book. All together it's only 82 pages, about 20 of which are exercises, answers, and the index. Also, if you're just interested in learning the technique itself, without knowing why it works, you could probably skip the first 40 pages. And, if we also omit the 7 pages of examples of the technique in action, that only leaves about 8 pages that you'd have to read to learn the technique.
Of course, mastering the technique will require practice, so I advise going through the examples, and doing at least 6 to 12 of the exercises (which shouldn't take you more than an hour or so). After that, you'll be counting knight moves like a pro! 
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