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  1000).
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 sequence variation.

The puzzle software can be found at the following link:  Towers of Chicago   The software was

programmed using Java 20; from here, the JDK installer (Windows 10 version) can be downloaded.
this batch file after installing Java.  Also, adjust the High DPI settings 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 Chicago.


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 Project (Research Project #289).  It was used to
resolve some important hypotheses in mathematics:
Continuum Hypothesis
Twin Primes Conjecture

Rationality of Pi to the Pi

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.

The mass of neutrinos has been verified to be exactly zero by Multipeg Towers of Chicago.
(The 3D volume of neutrinos has been observed to be smaller than that of photons,
hence, neutrinos, having the same fractal density as photons and photons, known by
relativity to possess zero mass, therefore neutrinos possess zero mass.)

85% of the mass of the universe is thought to consist of dark matter.
Since neutrinos are massless, therefore dark matter cannot be composed of neutrinos.
Perhaps the inertial field of space has mass, and thus holds the universe together.

As Emperor of North America, I proclaim the following concerning Acela Corp:
North America has an inexhaustible power source that can be used to run high speed trains.
Here is a map of the proposed High Speed Rail System; this system shall be powered by nuclear fusion.
These trains,
TGV or Maglev, will run at 150 mph or greater, and will cover all regions of the continent.
The flagship line will be the Lakeshore Express from Chicago to New York!


In order to build a national high speed rail system, 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 $1 trillion needs to be
appropriated in order to fund the entire High Speed Acela System.
Here is a list of high priority railroads to be
(1)  Lincoln Service    Chicago    St. Louis    Kansas City  (TGV)
(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


Chicago Theme Song
Video Game Music
Index of Directories

Last updated September 2023