What's New - July 2003
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July 30, 2003: A user email the other day asked me check his solutions to some problems requiring the smallest integer values for given nine-digital expressions containing fractions. The must expressions contain all the digits 1-9 exactly one time. I wrote the program Pandigital Fractions and sent him the correct answers, (he had 1 of the 3 correct), but haven't heard back yet. I decided to post the program so the exercise wouldn't be a total loss.
July
25, 2003: The Cupid's
Arrow puzzle: Selecting from the numbers 1 through 9, place
one digit in each of the circles representing points on Cupid's
bow according to the following rule:
Each pair of digits connected by a black line must form a 2-digit
number that is evenly divisible by 7 or 13. You
can consider the 2 digits in either order and no digit may be used
more than once. A special bonus if the numbers
connected by the bowstring also satisfy the condition.
This another one adapted from "Wonders
of Numbers", Clifford Pickover
July 18, 2003: Here's a "Brute Force" version of the Knights Tour, Knights_BF. It was converted from a C version written by viewer Kurt White. Kurt questioned whether the Warnsdorf Heuristic was really necessary if a fast depth first search was used. His code is very fast, the Delphi version runs about 11 million move tests per second on my 2.4ghz P4. And starting at square #1, it starts finding solutions very quickly. Unfortunately an hour's testing starting at several interior squares found no solutions. Further proof of the futility of trying to overpower an exponential growth process with speed. Warnsdorf wins again! In the meantime though, converting the C code to Delphi was an interesting exercise.
July 14, 2003: The Book of the Month is "Wonder of Numbers" by Dr. Clifford Pickover (also available in paperback). It contains 100+ problems and puzzles that so far are all new to me and seem oriented towards computer solution. In fact the publisher, Oxford University Press, has a web site with solutions for selected problems in Basic. Maybe we can get Cliff to add Delphi for future editions <g>. Here is my first little program based on a problem in the book: Klingon Paths.
By the way, the book title links above are to Amazon.com. The only way to add such links was to be come an associate, so if you happen to buy the book using one of the above links, DFF will get a buck or so to help support the site.
July
10, 2003: I posted a minor correction to the Golf
Course program the other day. The program is just a
little combinatoric exercise written to answer the idle question:
"How many potential arrangements of par 3, 4, and 5 holes are
there in a course that has X holes and par score of
Y?" Viewer Don Rowlett pointed out that
large hole counts produced erroneous results, so
course size is now limited to 19 holes.