Pondering Solutions to the King Snake Puzzle
An Adventure in Discrete Mathematics
by
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Who Needs This Book?
First, let me introduce Harry. He is the main character in this book. “Harry” is the name of the Microsoft Excel Macro, coded in the Visual Basic programming language, that generates solutions to the King Snake Puzzle. And now, who needs this book?
● The puzzler with the puzzle on his hands – The King Snake Puzzle is such a complex puzzle I
am amazed that any human being can solve it. Yet, I know it’s done. Every copy that has come to me
has arrived in its solved state in a cubic box.
Look at this picture of the snake in chaos on my dining room table. The puzzler with a snake
in that state is in trouble.
(1) He can’t put the thing together.
(2) He doesn’t want to throw it away. It would be fun to offer it, in its solved state, to Uncle Harvey and see what happens. Besides, it cost a lot of money.
(3) It’s embarrassing to have the thing still sitting on the dining room table every time another visitor looks at it and says, “What is that?” To get himself out of trouble, this puzzler needs a copy of one of Harry’s annotated lists specifying twenty-six steps for placing the sixty-four cubes into solution.
● The student of computer programming – Harry, the macro that generates the solutions, is coded in the programming language named “Visual Basic”. The language offers a variety of methods for specifying data elements and a basic list of program control structures. I used several of these programming features in building Harry: integer data, double integer, one-dimensional and twodimensional arrays, arithmetic assignment statements, “if” statements, compound “if” statements, loops, sub-routines, etc. The code is heavily commented with the hope that a student only just introduced to programming languages will be able to follow its logic.
● The student of Discrete Mathematics – Many examples of “discreteness” arise in the study of the King Snake Puzzle. An example is the graph: When Harry successfully places the sixty-fourth cube of the snake in the 4x4x4 array, Harry has specified a three-dimensional graph with sixty-four nodes. The graph shows the snake’s path within the 4x4x4 array of solution. Another example is the algorithm for transposing a digital solution from one octant of origin to another.
● The curious puzzler - Not the least of the bunch is the curious puzzler - Like me. How many solutions are there to the King Snake Puzzle?
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About the Book
Plan of Attack
- For 10 steps in assembling the 27-cube snake puzzle, see Appendix 1. If the terms are puzzling, too, look them up in the Glossary, Appendix 7.
- For 26 steps in assembling the 64-cube King Snake Puzzle, see pages 7-8 in section 3.6 “The Puzzler with the Puzzle on His Hands”, and see Appendix 3, pages 4-5
- Computer Programmer? See “Harry”, the Visual Basic macro that generates paths of solution to the King Snake Puzzle. Harry’s logic is described, and his source code listing is presented in Appendix 6, “All About Harry”.
- To indulge in the labyrinth of the whole of the titillating adventure, jump in at page 1, section 1.0 “The Challenge”. See the development of discrete algorithms that (1) generate and examine Harry’s 192 paths of solution, (2) identify similarities and differences among the 192 paths, and (3) group the paths into families of 24 siblings.
- For a succinct summary of the adventure see page 15, section 5.0 “Finale, Digital vs. Physical” where the mystery of the King Snake Puzzle is revealed.
About the Author
One Sunday afternoon in 1947, in a Chinese restaurant in Jacksonville, Florida, Ms. Starbuck was given the little wooden elephant puzzle. She has been attracted to take apart/put-together puzzles since that time. Her current favorites are the six-piece burr, Stewart Coffin’s “Three-piece Block,” and the snake puzzles, the 27-cube snake as well as the 64-cube.
Ms. Starbuck’s formal studies include Mathematics at Florida State University, B.A. 1958, and Computer Science in the School of Engineering at U.C.L.A., 1968-1970.
In 1959, Ms. Starbuck went to work for the System Development Corporation* in Santa Monica, California, with the job title “Computer Programmer”. Her first computer was the AN/FSQ-7,* an “automatic” device in the SAGE* system (Semi-Automatic Ground Environment*). She spent the whole of her professional career developing software systems, primarily for agencies of the Federal Government.
Shortly after Ms. Starbuck went to work in Santa Monica, she wrote to a school buddy whom she had left back home in Florida, “Come work with me. Come help us build this software system. It’s like solving puzzles all day.”
To contact Ms. Starbuck, send e-mail to CuriousPuzzler@outlook.com.