August 30, 2002: We were sidetracked again this week by an interesting project -  converting a differential equation solver to Delphi.   Don't let your eyes glaze over just yet.  There are lot's of academicians to supply us with the equations describing how things work.  We just need to be able to convert them to numbers we can print,  plot or otherwise play with.   Here's a  Runge-Kutta    program over in Math Topics with  procedures and test cases for solving  Second Order Ordinary Differential Equations with Known Initial Conditions.   Machines that follow Newton's Laws of Motion including projectiles, rolling or sliding objects,  pendulums, spring-mass systems, etc. can be described with equations of this type.   Useful indeed for those of us interested in computer simulations of the real world.    

August 25, 2002: I've been working on Linkages, a mechanical linkages simulator program this week, but it's going to take at least another week to get anything even close to working.  In the meantime here are a couple of others of the "Can You Find?"  or "T-Shirt"  variety  that somehow had never gotten posted.   Pandigital Numbers  introduces that topic and asks for the smallest pandigital that is a perfect square and the smallest number that, together with its square, contains all of the digits from 1 through 9.    Remainder of 1 looks for, (and finds), the smallest multiple of 13 that leaves a remainder of 1 when divided by integers 2 through 12.    We do this in a couple of ways and compare run times measured in microseconds.  (The smart way is about 100 times faster.)

August 16, 2002: An Oscilloscope program driven by sound card inputs has been on my list for quite a while.  I finally bit the bullet and did it this week.  Here's A Simple Oscilloscope program that is just that. 

 If you use a microphone for input and click your tongue and the "Stop Display" button at the same time, you can prove for yourself that there are really two distinct sounds generated - one when your tongue leaves  the roof and the other when it slaps the floor (of your mouth, of course  :>)).

August 11, 2002:  While developing  the "Know-Don't Know" program I fixed a silly timing problem in the U_Primes unit which tests for primality.  The IsPrime function now runs about 100 times faster than it did last week.   I posted the fix today over in Prime Factors 1  where U_Primes originally appeared. 

August 10, 2002:  Here's a program that solves "The Know-Don't Know Logic Problem", sometimes called "The Impossible Problem" or "The Sum-Product Problem".

Two integers, A and B, each between 2 and 100 inclusive, have been chosen.  The product, A×B, is given to mathematician Dr. P. The sum, A+B, is given to mathematician Dr. S. They each know the range of numbers. Their conversation is as follows:

P: "I don't  have the foggiest idea what your sum is, S."
S: "That's no news to me, P. I already knew that you didn't know. I don't know either."
P: "Aha, NOW I know what your sum must be, S!"
S: "And likewise P , I have figured out your product!!"

What are the numbers?    

It takes a little convoluted reasoning to solve it and  most explanations left me slightly puzzled.   My approach includes the best explanation you'll find  (he said immodestly ).

August 7, 2002: Well, it took 18 years, but here at last is the Logic Problem Solver program.   Actually, I haven't been working on it for that long but the original Turbo Pascal version was last compiled in 1994.   I converted it to Delphi and Windows and added the user interface a couple of years ago. This past month I finally worked up the courage to delve back in and make the 5000+ lines of code fit for posting.    

The program solves problems like: "Mrs. Anderson bought boots.  She has three more children than the mother (not Mrs. Counts) who used her credit card to buy shirts.    etc., etc.  ...... What item of clothing did each mother buy, how did she pay, and how many children does she have?". 

 In addition to solving these problems with pencil and paper, there are three ways to play with the program: as a "Solver" your job is to extract enough facts and rules from the included sample problems so that the program can figure out the solution.  As an "Author" you can enter  new problem descriptions .  And finally, as a "Programmer" you can try to figure out how the heck it works (and perhaps make it work better).