For Fun Newsletter #33
They say time flies when you're having fun, so I must be having a ball! Our last newsletter was at the end of May, but summertime provides some valid reasons for the delay. Delphians could probably care less, however this newsletter is the only way that distant relatives and old friends know that I'm still kicking, so here is my list of excuses. The garden is coming along - beans are in, cucumbers will be ready this week, corn is tasseled out and it looks like a bumper crop of tomatoes coming along (all 6 plants). We bought a new car last month, which accounted for a couple of weeks of research and dealer visits. We moved up to a Mercury Mountaineer from a Ford Explorer this time. I told the dealer that if the market held up, we would be back in 10 years for an Aviator! I've decided that all car dealers are the same, but in their defense, it must be a tough business.
Itís making me tired all over again, just thinking about it!
Here are the rest
of the "What's New" items
since last time.
23, 2003: I
just wanted to let any interested viewers know that the MATHCOUNTS
national finals will be televised on television station ESPN on May 29th at noon
Eastern Time. MATHCOUNTS is
an organization that sponsors math competitions for 6th, 7th, and 8th
grade students here in the USA. We are trying to get the program
established in our county schools next fall. You can check it out at
Just enough time to squeeze in one more program for this month. The
Counterfeit Coin program solves, or lets you solve, an old coin
weighing problem with several variations. The problem is to use a balance
pan scale to identify the bad coin from among 12 by its weight being different
from the other 11 . The most challenging version is to solve
the problem in three weighings and to identify whether it is light or heavy when
that fact is unknown. It's not surprising that author/mathematician
Martin Gardner is responsible for the algorithms implemented here.
Summertime things are not leaving much spare time for programming this month,
but I do have a request. The other day, a viewer asked if I could
design a a Knight's Tour that starts and ends on specific squares.
I'm not aware of a specific algorithm for this,. but maybe one of our
knowledgeable viewers does. If you can shed any light on this variation of
the problem, please
use feedback link to drop me a line. In the the meantime, I'm going to refresh my memory
and take a look at our existing
Knight's tour program to see if it can be easily modified to target a
specific square as the final move.
Here is #7 in the numeric t-shirt series. These hypothetical
t-shirts are primarily programming exercises. The back of this shirt
reads: "The only set of prime numbers containing all of the
digits 1 through 9 and whose sum is a 3-digit number." And the
front of the shirt reads:See
the answer and check out the code at T-Shirt
An alert user recently spotted a bug in our Multi-Pile
Nim program. In the "last token losesĒ version, the
computer could lose if the human played well - but proudly announced: "Computer
after losing!. The replacement version posted today may still
lose but now he at least admits it.
June 12, 2003: A simple modification to the Knight's Tour program was posted today which allows users to specify an ending square as well as a beginning square for program solution searches. In most cases a procedure similar to that used for "closed tour" searches will find a solution in a few hundred trial moves. However, a test case starting at square (1,1) and ending at square (8,1) was stopped after 10,000,000 trial moves, so there is obviously room for a smarter method!
Alert viewer Charles Doumar sent code to correct the "corner"
problem with yesterday's Knight's
Tour posting (specifying any corner for an end point results in long search
times). I posted the revision today. It looks like
the problem with "next to corner" end points remains though (any
end point one knight move removed from a corner). Charles will be
working on it this next week - and I'll be at the beach on vacation!
(Well, I will have my laptop with me in case of rain <g>.)
See you in a week.
A replacement version of the Spring
Mass 1 program was posted today. It's an animated demo program of a
simple spring-mass system with user-controlled parameters. Fellow Delphian
Don Rowlett had spotted a bug or two and suggested some changes. I fixed
the bug and added a couple of other features as a bonus. The
exercise reminded me that I had planned a Spring Mass 2 program to handle
multiple coupled springs and masses. It's back on the active list
(which still may stretch into next winter).
10, 2003: I
posted a minor correction to the Golf
Course program the other day. The program is just a little combinatory
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
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:
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.
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.
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 is another one adapted from "Wonders of Numbers", Clifford Pickover
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 expressions must 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 havenít
heard back yet. I decided to post the program so the exercise
wouldn't be a total loss.
problem has in it the seeds of its own solution. If you don't have any
problems, you don't get any seeds..." -- Norman Vincent Peale
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