Pondering Solutions to the King Snake Puzzle: An Adventure in Discrete Mathematics

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?