What's New - July 2004
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July 27, 2004: This problem was published by Marilyn vos Savant in her "Ask Marilyn" column in the weekly "Parade" magazine last Sunday.
A clueless student faced a pop quiz - a list of 24 Presidents of the 19th century and another list of their terms of office, but scrambled. The object was to match the President with his term. He had to guess every time. On average, how many terms would he guess correctly?
I couldn't figure out how to solve it analytically, so I wrote this simple Random Matching program to find the answer experimentally. 40 lines of code make it a good Beginners level program.
On the Kirkman front - I can now identify the unique solutions! I hope to get the code integrated to make Kirkman2 in the next few days.
July 23, 2004: Michael from Demark wrote the other day asking about adding Civil Twilight times to our Solar Position program that has an option to display Sunrise and Sunset times for any date and location. I posted the change today. He's working on a program to display hours of daylight for pilots flying under Visual Flight Rules. They figure that there is enough light to fly when the sun is 6 degrees or less below the horizon.
(Other than that I'm still trying to identify those darn 7 unique Kirkman solutions. I can filter out many, but not enough of the hundreds that the Kirkman1 program produces)
July12,
2004: Here's Kirkman1,
version 1 of a program to solve Kirkman's Schoolgirls
Problem described last week It finds lots of
solutions, but cannot yet determine which are unique and which are
merely renamed & rearranged versions of solutions already
found,
July 7, 2004: For the past several weeks most of my spare programming-for-fun time has been spent working on Kirkman's Schoolgirl problem. I haven't cracked it yet, but I will. It's time to share the problem so that all you hotshot Delphi programmers can try your hand.
Fifteen girls at a boarding school go for a daily walk. In order to prevent cliques from forming, the school mistress has declared that the girls will walk each day in 5 rows of 3 and that each girl will walk in a row with each other girl exactly once. Since each girl must walk aligned with 14 other girls and she walks with 2 different girls each day, it will take seven days to complete the cycle if one exists. The question is how to line the girls up each day to implement the schoolmarm's wishes.
In fact, there are seven distinct solutions to the problem - English amateur mathematician Thomas Penyngton Kirkman published the problem and the solutions in 1850! One DFF viewer, who happens to code in C++, found a brute force solution after about 5 days of CPU time but there are surely more efficient ways. I just haven't found one in Delphi or Pascal yet. There is lots of information on the Web and the solutions are all known, but the journey to finding even one solution should fill lots of pleasant hours. How did Kirkman do it?
In the meantime, I posted a modified version of
our "Crossword Helper" word completion program and available from
the WordStuff1 page or as
part of WordStuff2.
The new version includes an "excluded letters" list
to reduce the number of words returned when a partial
word is entered. Not helpful in solving
crosswords, but there is an application in finding hidden phrases
in the "Flip Words" commercial game that seems to
be floating around the web. Viewer Frank,
who probably spends too much time playing the Flip Words,
requested the change because he's addicted and determined to
get a high score..