The Seventh in the Lecture Series Sponsored by the
MATC Mathematics Club

"Some Binary Curiosities"
Professor Norbert Kuenzi

Professor Kuenzi and Sri confer before the lecture.


MATC students and teachers eagerly congregate for the last lecture in the Math Club series..

Get Professor Kuenzi's Handout here
pg. 1
pg. 2
pg. 3
pg. 4

Anyone who missed the lecture can email Sri to arrange to view the presentation.

Math Club's  fourth Spring presentation:
Speaker: Professor  Norbert Kuenzi
Department of Mathematics
When:  On May 2, Wednesday, 3:30-4:20 
Where: Room 322
Title: Some Binary Curiosities

Professor Norbert Kuenzi ( is a retired Professor of Mathematics from the University of Wisconsin--Oshkosh.  In 1959 he began his teaching career  as a high school mathematics and physics teacher. 

He received his Ph.D. in 1969 from the University of Iowa and then taught  mathematics at UW-Oshkosh  until the end of 1999.  He served as Chairman of the Mathematics Department from 1976--1991.  He served  10 years as co-editor (with the late Bob Prielipp) of the Mathematics Problem Department for the journal  School Science and Mathematics (1976-1986). 

He has been actively involved in the construction of the Wisconsin Section (MAA) High School Math Contest since 1978.  His interests include mathematical recreations, mathematics education, discrete mathematics, probability and statistics. 

Whole numbers are usually represented by using the digits 0 to 9.  The whole numbers can also be represented in Binary(Base Two) form by using arrangements of just the two symbols 0 and 1. Binary representation of numbers is associated with several interesting curiosities such as: 

Ethiopian multiplication
counting to a thousand on you fingers, 
cereal box mind reading cards, 
finding the right husband for King Arthur's daughter.
Learn more about binary numbers and binary arithmetic
  • Binary basics, history and links here or here
  • Convert a decimal number to binary here or here
  • Convert a binary number to decimal here or here
  • Add binary numbers in binary here or here
Counting in Binary


Professor Kuenzi discusses and compares numbers in binary and decimal form .  Then he shows how the binary representations can be done by grouping colored disks.


Professor Kuenzi shows "Ethiopian multiplication" done by repeatedly doubling the multiplicand and halving the multiplier, then adding doubles corresponding to halves with zero remainder. 

He demonstrates a binary card trick.

From: "Trygve Schadler" (College Algebra)
Subject: The May 2 Lecture
Fri, 04 May 2001 11:44:59 

     Professor Norbert Kuenzi opened his lecture by showing us some quotes that he thought were significant to the lecture.  He gave everyone a packet about his lecture that we could follow.  He then started talking about binary numbers. 

He first taught everyone how to count in binary, then made us do so.  Professor Kuenzi told us about Ethiopian multiplication and showed us how it was related to binary numbers.  Then he showed us how the cereal box mind reading game worked because of the knowledge of binary numbers. 

He showed us how to count up to 1023 on our fingers in binary but told us to be careful with the numbers 4, 128, and 132. 

The lecture that Professor Kuenzi held was overall pretty interesting.

Trygve Schadler

From: "Marian Villand"  (Trigonometry)
Subject: The Binary Curiousities Lecture
Date: Thu, 3 May 2001 15:05:31 -0500

Hi Mr. Garcia,

     I attended the lecture on Binary Curiosities along with my husband. I had invited him to attend along with me because he also enjoys math puzzles.

     I thought Prof. Kuenzi was very interesting.  How fun it must be to have a grandpa that so excited about math.  His enthusiasm is evident. 

     Prof. Kuenzi made the binary system easy to follow.  I wish he would of talked more about adding, subtracting, multiplying and dividing Binary numbers.  It was interesting the  small amount you had us do for the 10 point assignment.  It was also very interesting to learn about Ethiopian Multiplication, how it relates to the Binary System and how long the concept has been is use.  Once the concept is explained, it's very basic and logical. 

The Cereal box mind reading cards and the game of Nim, again take puzzling games and make very simple ways of figuring them out because they are based on Binary numbers.  My husband and I practiced counting in Binary on our fingers. It was a lot of fun, hard to get our fingers to do what we wanted them to do.

Marian Villand

Professor Kuenzi shows how to use fingers to count in binary.



Cheryl helps him with an impressive binary card trick.

Professor Kuenzi answers questions after his lecture as Sri and Associate Dean Marian Timmerman look on.
Date: Mon, 7 May 2001 16:42:26 -0700 (PDT)
From: Malissa Horlock <>
Subject: Re: bonus points
To: "Ray A. Garcia" <>

 I went to the binary curiosities lecture on wednesday May 3rd. I found it very interesting and the professor was informative as well as humerous. I thought the ethiopian multiplication was easy to remember because the need to double, and half, and know how to add.  That is the kind of math I like.I also enjoyed the puzzle box mind reading and I remember using it as a kid. It was an enjoyable short and sweet lecture and my fingers are working on counting in binary.

                           Malissa Horlock/Algebra Concepts Mon-Wed

From: <>  Rosie Moua
Date: Sun, 6 May 2001 21:53:35 EDT
Subject:  re: Lecture Report extra credit

The lecture at MATC about Binary numbers, by Professor Norbert Kuenzi, was an interesting and fascinating subject.  Professor Kuenzi explained how the Ethiopian multiplication works, the cereal box mind reading cards, and the counting over one thousand on your hands system.

The Ethiopian multiplication starts out by first: knowing how to double, how to half, and how to add.  For example, 85X42+ 170+680+2720=3570.  Although he explained how the technique works, I had a hard time understanding this concept.

Next was the Cereal box mind reading cards.  This is a game in which you can have up to 5 cards.  On each card there are four numbers across, and four numbers down the card, in addition, the numbers must be whole numbers from 1-31.  I'm not quite sure when the game ends or who determines the winner.  When he first started the game I had a hard time following the game.  The 
second time we played, I understood parts of it.

And last but not least, the counting to over one thousand on your hands system.  By using ten of our fingers and binary representation, we should be able to count from 1 to 1023 on all ten fingers.  This was a very funny game because I got lost at counting up to 20.  It was quite hard trying to form up the correct fingers.

I enjoyed the presentation by Professor Kuenzi.  I'm already teaching my husband the counting over 1000 on your hands system.  It's funny how useful 
your hands can be.

Rosie Moua

Professor Kuenzi opens and displays the gift presented by Associate Dean Marian Timmerman.



Professor and Mrs. Kuenzi with Sri at the reception at the end..


The end.



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