| ©1990-2005 by Stewart T. Coffin For questions or comments regarding this site, contact the chief metagrobologist:  |
[Home] [Contents] [Figures] [Search] [Help]
[Next Page] [Prev Page] [ Next Chapter] [Prev Chapter]
Perhaps this would be a good point at which to pause for a moment and review our progress thus far. Practically every puzzle design described in this book might be regarded as a systematic dissection of some geometrical form into bits, usually identical, which are then partially recombined into puzzle pieces. The superficial perception of this strange pastime is that all of this is so that a second party can then enjoy the confusion of trying to reconstruct the original solid. In point of fact, there is often no clear dividing line as to where the design process stops and the solution begins, or who is the designer and who is the solver. They may be one and the same. In some of the plane dissection puzzles in Chapter 1, discovering the dissection is the real puzzler, after which the pattern solutions are relatively easy. In those like the Octahedral Cluster Puzzle, as presented, the design becomes the solution. In the Jupiter Puzzle, the intriguing design overshadows the straightforward solution because it is much the more interesting of the two. Some puzzles foisted upon the reader in previous chapters (if only one could write in a whisper) may not even have solutions!
It is common practice in most puzzle books to include the solutions somewhere. Perhaps some readers will be annoyed not to find them in this book. Solutions are fine when they serve some purpose. Certainly a book of riddles would be dull reading without the clever answers included, while answers to crossword puzzles may be educational. In the case of most combinatorial puzzles, including the solutions would add nothing new or interesting. There are exceptions, and note that some solutions have been included in the text. Here are four more of them:
| 1. | Karl Essley's two misplaced pieces were of course identical and triangular, but we will never know who got them, will we? |
| 2. | In the puzzling pairs of Tangram figures in which one appears to have a piece missing, the pieces are always rotated 45 degrees from one to the other. |
| 3. | The mini-Tangram set of five pieces forms seven convex figures, five of which have multiple solutions. |
| 4. | Beeler's proof of the impossibility of a 3 x 20 rectangular Cornucopia solution is to count the empty squares on either side of the piece placed and note that they are never divisible by six. |
| 5. | The reader was asked to judge which of two Cornucopia patterns was more pleasing and to identify four flaws in the other one. The following is of course not an answer but merely collective opinion. See if the reader agrees. Of the half dozen persons polled, all preferred the pattern on the right. One objectionable feature of the pattern on the left is the long horizontal line that nearly dissects the pattern. Another is the vertical line intersecting it and creating two "crossroads". (Could it be only a coincidence that a fundamental rule of good stone masonry construction is to avoid both long straight lines and crossroads for reasons of structural strength?) The two long parallel pieces at the bottom are also a distraction. A fourth flaw is that the first three flaws are all asymmetrical, creating a sense of unbalance. Having determined that this pattern is bad, it is interesting how many other objectionable features reveal themselves. The four vertical lines at the top lead the eye off the square, the T is upside down, the piece at the upper left is a pointing gun, and so on. Do you sometimes wonder what goes on (and off) inside the human mind? |
What some readers may find even more perplexing than omission of solutions is that in many cases even the designs themselves are not shown in this book but instead left for the reader to ponder. The reason of course is that the design is the puzzle, so why spoil it by giving the answer. Publishing everything known on a subject may be a good idea in some fields, such as medicine. But in recreational mathematics, a gluttony of information is probably worse than none at all. With only a few exceptions, the policy in this book has been not to include the details for any puzzle designs or solutions that have not previously been published. Instead, they have been left purposely in the dark so that the inquisitive reader may have the joy of rediscovering some of them. This book is intended to be merely a glimpse into the puzzling world of polyhedral dissections and not an open pit excavation. If every known geometrical recreation were to be dug up, extracted, and refined, would it not leave a rather barren landscape behind for future generations?
The very idea that mankind might possibly be better off with some knowledge left unpublished probably sounds as far-fetched today as did the notion a century ago that some parklands ought to be left undisturbed. The compulsion not only to publish but to be the first to do so pervades the academic world. Added to that, we now look forward with some apprehension to the day when all of this and much more will be stored and analyzed to death in some gigantic computerized retrieval system, with all the answers instantly accessible at the touch of a keyboard. But answers to what?
Computers and Puzzles
Abstraction and Reality
The Universal Language of Geometrical Recreations
Games
| ©1990-2005 by Stewart T. Coffin For questions or comments regarding this site, contact the chief metagrobologist: |
[Next Page] [Prev Page] [ Next Chapter] [Prev Chapter]