* * * * *
* * * * 4 7 7 * * * *
* * * 5 4 4 8 3 3 4 6 3 * * *
* * 1 4 5 1 1 1 4 5 1 7 1 3 5 * *
* * 4 9 4 9 6 7 5 5 5 8 7 6 6 8 5 * *
* 3 7 2 9 8 3 5 6 7 3 9 1 8 7 5 8 5 *
* * 1 4 7 8 4 2 9 2 7 1 1 8 2 2 7 6 3 * *
* 7 2 1 8 5 5 3 1 1 3 1 3 3 4 2 8 6 1 3 *
* 4 2 6 7 2 5 2 4 2 2 5 4 3 2 8 1 7 7 3 *
* * 4 1 6 5 1 1 1 9 1 4 3 4 4 3 1 9 8 2 7 * *
* 4 3 5 2 3 2 2 3 2 4 2 5 3 5 1 1 3 5 5 3 7 *
* 2 7 1 5 1 1 3 1 5 3(3)2 4 2 3 7 7 5 4 2 7 *
* 2 5 2 2 6 1 2 4 4 6 3 4 1 2 1 2 6 5 1 8 8 *
* * 4 3 7 5 1 9 3 4 4 5 2 9 4 1 9 5 7 4 8 * *
* 4 1 6 7 8 3 4 3 4 1 3 1 2 3 2 3 6 2 4 *
* 7 3 2 6 1 5 3 9 2 3 2 1 5 7 5 8 9 5 4 *
* * 1 6 7 3 4 8 1 2 1 2 1 2 2 8 9 4 1 * *
* 2 5 4 7 8 7 5 6 1 3 5 7 8 7 2 9 3 *
* * 6 5 6 4 6 7 2 5 2 2 6 3 4 7 4 * *
* * 2 3 1 2 3 3 3 2 1 3 2 1 1 * *
* * * 7 4 4 5 7 3 4 4 7 * * *
* * * * 3 3 4 * * * *
* * * * *
Starting from the central cell of this maze (there's a (3) in it), the challenge is to find a path that leads you off the maze, and to a "star" (*).
The number at each cell shows how many steps, in a straight line, you must take. You can travel horizontally, vertically, or diagonally, up or down, left or right.
(In reply to
re(2): ARE YOU GLAD, CHARLIE??? by Goldwing)
"There is no particular cleverness to be proud of and no mutual enjoyment of a puzzle when someone lets the computer do their thinking for them."
Of course computers cannot think. My solution depended on finding an algorithm to solve the problem, and putting that algorithm in a form that the programming language on the computer could understand. The presentation of my algorithm did not preclude either further, better, computer algorithms to be developed or by-hand methods from being developed. In fact, goFish did just that: he came up with a better algorithm to find a solution to this problem--in fact, the shortest path, directly.
goFish's algorithm could equally be done by hand or by computer. I personally do not see the extra value to be gained by doing the actualy grunt-work of tracing back from the end by hand. The array of distances from the end that goFish produced could easily have been programmed into the computer. The enjoyment of solution was, for goFish, in thinking of the method of going back from the end, not in actually carrying it out.
Of course, you could say that the availability of a computer for solution leads to an unnecessary satisfaction with an inefficient algorithm, merely because a computer can do it faster. Indeed, that may be a valid criticism of my algorithm, as goFish described it as "rubbish". However, goFish's algorithm, while elegant and leading to a minimal-length solution quickly, does not allow for maximal-length solutions. That was an area of exploration opened up by computer solution--in particular the computer algorithm I used. The puzzle itself does not ask for the minimal length path.
But to answer the essence of pcbouhid's objection: as mentioned, the presentation of one solution does not preclude better solutions from being found, as goFish's comment shows.
In that regard, I consider a "solution" to be the method or algorithm used, not just the final answer--in this case, not just the path found. pcbouhid's official solution just presents the answer without giving the methodology for finding it. The comments--mine and goFish's--show the methodology; they are in fact solutions, and not just answers. The former was less efficient, going from beginning to end of the path; the latter more efficient, going from end to beginning. But the former also allowed for further exploration of longer paths, to see how to make them as long as possible, rather than short.
But certainly the use of a computer does not preclude thinking.
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Posted by Charlie
on 2005-10-02 14:18:22 |
re(3): ARE YOU GLAD, CHARLIE???
