Latest page update: 1998 May 5.
Answers and hints are given for odd numbered exercises only.
The exercises in this chapter may be attacked either using the Web, or not using it. (I've had a student ask me how to search without using the Web -- a sign of the times.) It is interesting to give the assignment first without the Web, then pick some of the more difficult questions for work on the Web.
1. While Donald Knuth is well known for his computer science publications, his first published work was not in that field. It was "The potrzebie system of weights and measures," in MAD Magazine, Issue #33, June 1957, pp. 36-37.
3. The first problem here is to understand what joinery is. It is the art of putting wood pieces together, as in cabinet making. Once that is understood, coming up with a bibliography is not a difficult task. This question arose from an attempt to learn more about a particular kind of relatively rare dovetailing, which seemed to be in use for about ten years. That is still a more difficult question to answer, as the usual furniture and antique books do not go into that kind of detail. It took me nearly thirty years to find someone who knew the answer.
5. One student reported that he searched long and hard, but couldn't find this listed in Dissertation Abstracts. Actually, it is a humorous essay by Charles Lamb, the English author who wrote under the pen name of Elia. Apparently the idea came from a conversation that Lamb had with a friend.
7. This is a difficult question, arising from a comment that von Neumann had
given up on this problem because it was too difficult.
One problem in hunting down the answer is that the problem has two different
names -- common set transversals, or common systems of representatives.
Apparently von Neumann never wrote anything on this problem;
at least the person who was assembling his collected works after his death
knew of no such writing.
The only reference that I have ever found is a comment toward the end of a
chapter in Paul Halmos' book on vector spaces, to the effect that von Neumann
considered the problem and felt that it seemed to present some difficulties.
This, of course, does not say whether von Neumann ever seriously worked on the
problem.
One student, however, came back with this response: "For three or more
collections of sets John von Neumann had to say that common set transversals
for them could be associated with every set by taking weak closures of
appropriate unions."
9. The obvious source of information is the local social security office. The first three letters indicate the region in which the number was issued. The next two seem to be random, and the final four are serially assigned to applicants.
11. Melongena (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) (the plant) is more accurately called Solanum melongena. It is the common eggplant. Thus, while many species of Solanum are toxic, including the Deadly Nightshade, S. melongena is harmless and tasty. However, there is also a genus of mollusks named Melongena.
13. The custom seems to date back to an early use of a star to denote a gentlemen's facility, and a cresent moon to denote a ladies' facility. Eventually the star lost out, perhaps because of the extra labor involved in building two outhouses.
15. This is attributed to Abraham Lincoln.
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13. For aaa, the initial a is in the interval 0.000... to 0.333.... The second a puts the code in the interval 0.000... to 0.1666.... Finally, the third a puts the code in the interval 0.000... to 0.1000....
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1. The number of combinations of four out of seven terms is C(7,4) = 35.
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1. For n = 1 the slope is -logeb; for any larger value of n the slope is 0.
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