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 puzzle; 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 (1300
  x  900).
The Towers of Chicago uses a dynamic algorithm to compute the optimal partition numbers, and then
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 19; from here, the JDK installer (Windows 10 version) can be downloaded.
Run this batch file after installing Java.  Also, adjust the High DPI setting for the Javaw executable
located in the system folder.  Here is the JDK documentation.  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.  Furthermore,
here is a scholarly paper about
the mathematics behind Multipeg Towers of Hanoi.

Also, I wrote software that solves problems in Boolean Logic:  Meta Theorem
Curiously enough, 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 50 million years!

The 4 countries that run nuclear fusion are America, Canada, Japan, and Haiti.
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 two supertowers were built in Chicago
using my
Automated Reasoning software:
  —  Completed in 2009 @ 1388 ft
  —  Completed in 2020 @ 1191 ft

This is the new symbol of Christendom.

As Emperor of North America, I proclaim the following concerning Acela,
which will be the national high speed rail corporation:

North America has an inexhaustible power source that can be used to run high speed trains.
Here is a map of the proposed Acela System; this system shall be electrified under nuclear fusion.
These trains will run at 150 mph or greater, and will cover all regions of the continent.  Intercity
electric high speed trains, like the Acela Express, get power from 25000 volt AC catenary.
The Midwest is the next logical region to get this rail service, after the Northeast.  Here are
some of the railroads that should be electrified in order to run at high speed:
(1)  Lincoln
Service    Chicago    St. Louis    Kansas City  (LGV)
(2)  Hiawatha
    Chicago    Milwaukee    Minneapolis  (TGV)
(3)  Lake Shore
Express   Chicago    Cleveland    New York  (LGV)
(4)  Crescent
    New Orleans    Atlanta    Charlotte  (TGV)
(5)  Coast Starlight    San Fransisco to Los Angeles  (LGV)
(6)  Pacific Cascades
    Seattle to Portland  (TGV)
(7)  Texas TGV
  —  Dallas to Houston
Of course, the flagship high speed railroad will be Chicago to New York!

In order to build a national high speed rail network, we need the U.S. military to
withdraw from a variety of foreign lands and restore development on American soil.
The Biden infrastructure package is insufficient in terms of intercity high speed rail;
$12 billion is not enough to compete with China.  At least $200 billion needs to be
appropriated in order to fund the entire Acela System.

Chicago Theme Song
Video Game Music
Index of Directories

Last updated February 2023