Hour Maze

Mike Reilly with Jenks Norwalk

Science is often a form of puzzle solving, and mathematics, pardon the expression, is riddled with puzzles. Some are solved, and some are not. In fact, mathematical games and puzzles have occasionally led to the development of mathematical theories. Some of these are number games, combination puzzles, geometric puzzles and networking puzzles.

The earliest known record of a puzzle is a papyrus from 1850 BC, in Egypt called the Rhind papyrus. Supposedly this is a story puzzle involving houses, cats, mice, and grain similar in structure to the fox, geese, and bean riddle. These are called transport puzzles.

Although I have a strong interest in both science and mathematics, I am neither a scientist nor a mathematician. Most of my work is focused on creating games and puzzles with some employment in the movie business, which many consider one big game and puzzle.

I started making games and puzzles for my daughter after she was born. At the time I was employed in a woodworking shop and had access to tools and materials. This hobby developed into a life long habit.

Speculation and opinions abound about why people like to solve puzzles. Solving most puzzles requires seeing patterns, trying different combinations, formulating plans, choosing alternatives, and applying our experiences to reach a goal. These are all skills we use in daily tasks. Puzzles, in some ways, allow us to practice these life skills.

Many serious studies about puzzles focus on their simulation of real world problem solving. They may act as tools to help the mind comprehend relationships between physical objects and spatial relationships. And since our bodies, which house those minds inhabit the physical landscape, interaction with puzzles help us to tease out answers to questions not so clearly presented in every day life.

It is also postulated that the activity of solving puzzles helps us to deconstruct preconceived relationships within our mental maps. Puzzles are now considered essential to brain health, especially as we grow older. They also provide a type of pursuit that can create meditative brain wave states in some individuals.

And, then again, maybe just the simple joy of solving is enough.

The History of "Hour Maze"

"Hour Maze" is the outcome of twenty five years of puzzling and one brief moment of "Aha!" Jenks Norwalk, my business and writing partner, and I were looking for a puzzle seed to plant in the lush landscape created by the success of Sudoku. We knew that this concept would need to incorporate number logic and something else.

We were also receiving a lot of encouragement and incentive from our agent, Howard Fleischer of Royaltypros. At this time we were also working on some maze designs to present to a number of his clients.

Six months later, Jenks and I were trying to catch an Ouroboros. Actually, we were working on a story about someone trying to catch an Ouroboros. An Ouroboros, if you didn’t know, is a circular symbol of a snake or dragon devouring its tail, standing for infinity or wholeness.

One of us had a vision of this snake going around in a maze chasing its tail, and the other one of us wanted to know if it was lunch time yet and, well, the rest is history, "Hour Maze" history.

We invested hundreds of hours in the next year producing three to four hundred "Hour Maze" puzzles to test. From 6 x 6 grids to 12 x 12 grids and some unusual shapes too. We also devised a variation called "Poker Maze," which is based on playing cards. In the next six months, we built a web site to demonstrate a proof of concept for the puzzle as a print version.

Then we found Rod Pierce at his excellent mathematics site, MathsIsFun. Rod volunteered to help build the flash version. Several months later, after we assembled the parts via email – by a method that I can only describe as badminton-programming – the interactive flash version of ‘Hour Maze’ was released in early September 2007.

I build most of my puzzles backwards. Maybe reverse is a more apt word. The best way to explain this process is to take you through it step by step. In fact, with a few simple materials and some time you can build your own version of my "Weaver’s Puzzle," which I'll describe in the next installment of The Citizen Scientist. With patience and diligence, you can build a very difficult puzzle, and build it very easily.

Sample Mazes and Rules

Three sample Hour Mazes are shown in Figs. 1-3.

Figures 1-3. Shown here are three sample Hour Mazes. (The solutions are given at the end of this article.)

Place any number, from 1 to 12, in each square of the puzzle maze.

Numbers must run in some sequence from 1 to 12 or 12 to 1, like on a clock face.

Each number's neighbor — any square above or below, to left or to right, not separated by a maze wall (diagonals are not neighbors) — must be one of the two numbers nearest on a clock. For instance, a 6 can only be next to a 7 or a 5. The number 12 can have either an 11 or a 1 as neighbors, and a 1 can only have a 12 or a 2 next to it. Almost all the puzzles include hints.

Each maze requires a certain number of complete sets of 1 through 12, according to its grid size. For instance, a 6 x 6 requires 3 sets of 1 through 12, a 6 x 10 requires 5 sets of 1 through 12, etc. However, the sets do not have to be in twelve continuous runs of 1 through 12. Please see web site www.hourmaze.com for details.

After you try solving the mazes in Figs. 1-3, compare your results with the solutions given in Figs. 4-6 at the end of this article.

Some Links

http://en.wikipedia.org/wiki/Puzzle
Wikipedia is a good source for puzzle information.

http://reilly4puzzles.googlepages.com/home
my personal site with links to some of my games & puzzles.

http://www.mathsisfun.com
Rod Pierce’s quality math site and lots of fun!

http://royaltypros.com/
Our agent, Howard Fleischer. Please mention that you read about him in The Citizen Scientist if you contact him.

http://www.counttonine.com/sudokuGame.htm
An excellent Sudoku site and friends of ours!

http://www.channelcraft.com/oops.htm
They manufacture ‘American Made’ toys, games & puzzles, including my ‘Oops’ and ‘Oops Again’ puzzles in wood.

http://www.clickmazes.com/
A great collection of maze puzzles.

http://www.logicmazes.com/
Robert Abbott’s outstanding collection!

http://www.johnrausch.com/PuzzleWorld/jerry_slocum.htm
World class collector of mechanical puzzles.

http://www.puzzles.com/
A commercial puzzle company.


Definitions & Citations

puz-zle - [puhz-uh l]

–noun
1.) a toy, problem, or other contrivance designed to amuse by presenting difficulties to be solved by ingenuity or patient effort.
Dictionary.com Unabridged (v 1.1). Random House, Inc. 25 Sep. 2007. <http://dictionary.reference.com/browse/puzzle>.

2.) Something, such as a game, toy, or problem, that requires ingenuity and often persistence in solving or assembling.
The American Heritage® Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company, 2004. 25 Sep. 2007. <Dictionary.com http://dictionary.reference.com/browse/puzzle>.

3.) puzzle (v.)
c.1595, pusle "bewilder, confound," possibly frequentative of pose (v.) in obsolete sense of "perplex" (cf. nuzzle from nose). The noun meaning "state of being puzzled" is recorded from 1607, from the verb; meaning "perplexing question" is from 1655; that of "a toy contrived to test one's ingenuity" is from 1814.
Online Etymology Dictionary. Douglas Harper, Historian. 25 Sep. 2007. <http://dictionary.reference.com/browse/puzzle>.

Maze - - [meyz]
-noun
1.) a confusing network of intercommunicating paths or passages; labyrinth.
Dictionary.com Unabridged (v 1.1). Random House, Inc. 25 Sep. 2007. <http://dictionary.reference.com/browse/maze>.

2.) A graphic puzzle, the solution of which is an uninterrupted path through an intricate pattern of line segments from a starting point to a goal.
The American Heritage® Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company, 2004. 25 Sep. 2007. <http://dictionary.reference.com/browse/maze>.

3.) c. 1297, "delusion, bewilderment," possibly from O.E. *mæs, which is suggested by the compound amasod "amazed" (see amaze). Perhaps related to Norw. dial. mas "exhausting labor." Meaning "labyrinth" first recorded c.1385.
Online Etymology Dictionary. Douglas Harper, Historian. 25 Sep. 2007. <http://dictionary.reference.com/browse/maze>.

Ouroboros (pronounced oo-ro-BOR-os)
Noun: a circular symbol of a snake or dragon devouring its tail, standing for infinity or wholeness; also written uroboros or Ouroboros
Etymology: 1940 < Greek 'tail devourer'.
Webster's New Millennium™ Dictionary of English, Preview Edition (v 0.9.7). Lexico Publishing Group, LLC. 26 Sep. 2007. <http://dictionary.reference.com/browse/ouroboros>.

See also http://en.wikipedia.org/wiki/Ouroboros

Three sample mazes are shown in Figs. 1-3.

Figures 4-6. Here are the solutions for the three sample Hour Mazes in Figs. 1-3