Towers of Chicago
Robert Swartz
I am a mathematician and computer programmer from Chicago.  I have a BA in Mathematics from
Northeastern Illinois University, and I'm also Sun Certified.  Since 2000, I've been working on the
Towers of Chicago; I programmed the multipeg version in Java.  The multipeg version involves
4 or more pegs, as opposed to the usual 3.  These pegs are enumerated as follows:  the initial peg,
the final peg, and 2 or more auxiliary pegs.  This applet can display up to 50 discs by 10 pegs
with the default window size (1250
  x  850).

The Towers of Chicago uses a dynamic algorithm to compute the optimal partition numbers,
and then a
recursive algorithm to compute the moves.  This program is an example of
Automated Reasoning, especially since it has a reverse feature.

The puzzle software can be found at the following link: 
Towers of Chicago.  The software was
programmed using
Java 16; from here, the JDK installer (Windows version) can be downloaded.
Run this batch file after installing Java.  The original version of my Towers of Chicago software
won 5th prize in the
Quest for Java Contest.




Here are some screenshots, and here is an applet that calculates the number of moves in the
multipeg problem.  Here is another applet that calculates the number of top-level partition
numbers in the
multipeg problem.

Also, I wrote software that solves problems in Boolean Logic:  Meta Theorem
It turns out that any statement in mathematics can be reduced to a statement
of Boolean Logic.  My treatment of Boolean Logic includes 64 variables,
truth constants, 6 operations, and perfect syntax checking.  Here is a list of
logical sentences that can be used to test Meta Theorem.


Meta Theorem was developed at Argonne National Laboratory under the
Automated Reasoning research project.  It was used to resolve some
important hypotheses in mathematics:
Continuum Hypothesis
Twin Primes Conjecture
Odd Perfect Numbers

My math applets are generating 500 Gigawatts of D-D-T Fusion Power:
D + D             T + H + 4.03 MeV
D + T      
      He4 + n + 17.6 MeV
This power source will last for 10 million years!
Here is the

and here is the imperial city skyline, Chicago, USA.

Here is a list of Chicago's top 20 skyscrapers.

It turns out that was
built using my Automated Reasoning software.

This is the new symbol of Christendom.

As Emperor of North America, I proclaim the following concerning Amtrak:

The United States has an inexhaustible power source (D-D-T Fusion) which can be
used to run high speed trains.  Here is a map of the proposed high speed rail network.
These trains will run at 150 mph or greater, and will cover all regions of the country.
Electric high speed trains, like the Acela Express, get power from 25000 volt AC catenary.
The Midwest is the next logical region of the country to get this rail service, after the
Northeast.  For example, the following routes should be electrified:
(1)  Lincoln Service
  ―  Chicago to St. Louis
(2)  Great Northern
    Chicago    Milwaukee    Minneapolis
(3)  Lake Shore Express
    Chicago to Cleveland

Chicago Theme Song

Video Game Music

Index of Directories


Last updated May 2021