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Logic Mazes

written by Robert Abbott

The following are pointers to everything that is on this site.

Five Easy Mazes:
	Most of the mazes on this site are pretty complicated—so, here are some easy mazes you might want to try. You can start with Easy Maze 1 and then follow the pointers to the other mazes, or you can go directly to Easy Maze 2, 3, 4, or 5.

Eyeball Mazes:

There are 12 interactive mazes here. They use a simple concept—you travel to a square that has either the same symbol or the same color as the square you just left—but there are added complications and some of the mazes are very tricky.

These mazes are currently being used as a contest by the Catalan Culture Ministry. See the note at the end of the instructions.

Alice Mazes:
	This is a series of twenty interactive mazes that I created and programmed in JavaScript. These are called “Alice” mazes because they recall the scene in Alice in Wonderland where Alice eats a piece of cake with the sign “Eat Me” and grows larger, then she drinks from a bottle marked “Drink Me” and becomes smaller. These mazes won’t make you larger or smaller, but the distance you travel in a move will get larger or smaller.

Sliding Door Maze:
	This is programmed in Java by Oriel Maximé and is based on a maze from my book SuperMazes. It is very difficult. There is only a single layout, mostly because I haven’t been able to design a second layout (creating that first layout was hard enough). But at the bottom of the Sliding Door page, I refer to a series of similar mazes by Jorge Best. There are twelve layouts in that series.

Tilt Mazes:
	These are four mazes by Andrea Gilbert. You will be able to try both a non-interactive version and an interactive Java version of each maze. (And I try to explain why anyone would want both a non-interactive version and an interactive version of a maze.) There is also news about a walk-through version.

Number Mazes:
	These are the first programs I wrote in JavaScript, and the mazes have been on this site since time immemorial (that is, 1999). There is a small 5x5 number maze (it’s a recent addition that is part of the “Five Easy Mazes” section), there is a 6x6 maze that is still fairly easy, and there is a fairly difficult 7x7 maze. There is also the quite difficult, but interesting, Changing-Rule Number Maze and the way-too-difficult No-U-Turn Number Maze. Someday I should add a solution to that last maze.

Things That Roll:

Another interesting part of this web site is a collection of rolling-block mazes. For the most part, these mazes are not interactive. Instead, you’re asked to print the maze, tape some dice together to form a weirdly-shaped block, then roll the block across the maze. The mazes were created by many different people in the kind of collaborative effort that could only happen on the Internet.

I also have a collection of rolling-cube mazes. These involve rolling a single die across a page. They were predecessors to the rolling-block mazes.

The Bureaucratic Maze:

I call this a maze, but it could also be called a piece of performance art. Once it gets started, there can be about 30 people carrying forms between bureaucrats seated at five different desks. The forms give you a limited choice about which desks to go to, and if you make the right choices, you’ll reach the goal (though at the beginning you don’t even know what the goal is). Here is my write-up of the maze.

This maze has been tried a few times by me and other people. Wei-Hwa Huang ran a variation that he disguised as a registration process. The participants did not even know they were in a maze (at least, not at first). Eric Shamblen turned a variation of the maze into an on-line program that you can play on your own. The Bureaucratic Maze may (or may not) appear again at some time in the future.

Starry Night Maze:

This is a maze of mine that appeared on the cover of GAMES magazine—the issue of December, 2006. It’s a little like the Eyeball Mazes, but with hexagons instead of rectangles. It is, however, an advance for me because for the first time I was able to use real art in a maze.

What I had submitted to GAMES was an abstract maze drawn on a grid of hexagons. Jim Malloy, the magazine’s art director, came up with a theme for the maze and he created the art for the cover. I then programmed an interactive version of the maze and I incorporated Malloy’s art. It looks quite good. And not only that, if you solve the maze, the program has a winning display where all the stars twinkle. I can stare at that for hours (well maybe at least two minutes).

My interactive version is on the GAMES site, at this location.

Theseus and the Minotaur:

There are now three ways to play these mazes. The first is a modification of Toby Nelson’s original Java applet, which you can play on the Theseus page of this site. The applet has three training levels to help explain the mazes, then seven fairly tricky levels. It should take you about a week to get through those seven levels, and they provide a good introduction to the game.

Second, there is the Kristanix download. This has 87 large-screen levels for computers. Its price is $9.95, but you can download the entire game for free, then play it for a while before you decide whether to buy it.

Third, there is the version for the iPhone and the iPod Touch. It has the same 87 levels and only costs $3.99. There is also a free version, Theseus Lite, that has a sampling of levels from the full version.

The Theseus page has more about the three ways of playing these mazes. It also has a long history of the mazes, which goes back to my original print version in 1990. There is also a discussion of Toby Nelson’s layout-generating program, and there is an amusing updating of the Theseus myth.

A booklet you can order from me:
	My mail-order page is at this address. There used to be more here, but now everything is sold out, except for my booklet Auction 2002 and Eleusis. Auction is the latest revision of an old card game of mine, and it was presented in Games magazine (in the issue dated April, 2002).

Links:
	Be sure to visit my page of links. It has pointers to the sites of others who are working with this form of maze. There are also pointers to other game and puzzle sites.

Articles, essays, reviews, and a lecture:

Some of these articles generated many e-mail responses, some of which I added to the end of the article. Often, the responses are better than the article itself.

Walk-Through Logic Mazes:

Small walk-through logic mazes can be found outside of many of the large cornfield mazes, and others are beginnng to appear on their own in other locations. They are designed by me and also by Adrian Fisher, Andrea Gilbert, Dave Phillips, and John Taggart.

This site has two sections about these mazes. The first section describes how this concept developed from 1993 through 1998.

The second section is just pictures—showing the mazes during the summer of 1999.

Mazes in Cities:

Walk-through logic mazes first appeared on farms, but they are now spreading to cities. Logic mazes appeared in June 2009, at the World Science Festival Street Fair in Manhattan, in January 2010, at Mathematics Games Day at a school in Hong Kong, and in May 2010, at FESTIMATE in Lima, Peru. Here is a write up of these three events. Similar events are being planned for the future.

The basic purpose of these festivals is to show kids the fun side of mathematics and logic. They usually have tables or booths with collections of small puzzles. And they can also have some very large puzzles, like one of my walk-through mazes or one of Andrea Gilbert’s mazes.

How to Locate a Good Cornfield Maze:

There are now hundreds of these mazes, and this provides some help in sorting through them.

Mazes We Visited — Summer of 2007:

This starts out like a journal, but then I get into reviews (good and bad, but mostly bad) of various mazes. I explain what they do right and what they do wrong, and I give my own opinion of what a maze should be. I have a brief history of the rise and fall of wooden fence mazes, and I think I have a good explanation of why they disappeared. I also warn that cornfield mazes could suffer the same fate.

Mazes to Visit:

This is an old article (from 1998) that gives my thoughts and some recommendations on full-size (conventional) mazes you can walk through. The article is mostly about fence mazes. Fence mazes are great, but there aren’t many of them left.

The Garden Maze at Luray, Virginia:

This is a short write-up of a hedge maze—the only large (well, fairly large) hedge maze in America. We are way behind England in this regard.

Sacred Labyrinths:

This article is something of a “non-believer’s guide” to sacred labyrinths. I argue that single-path labyrinths are interesting even if you aren’t on a spiritual quest. The article was inspired by Annette Reynold’s beach labyrinth, shown here.

New Age Flim Flam at a Labyrinth in Santa Fe:

This is something of a rant. It’s about a labyrinth with a strange echo effect at its center. At first, I thought this effect was a magic trick some New Age whackos had added to fool people into accepting their beliefs. And what made me really mad was I couldn’t figure out how the trick was done. Well, the truth was more complicated (and weirder) than I thought. After I posted the essay, I received several letters (also posted here) that explain how the trick is done—and it isn’t really a trick.

What Logic Is Not:

I’ve always had questions about plane geometry and symbolic logic, questions like: what exactly is an axiom and how many logics can there be. I think I stumbled on some answers to these questions in my work with mazes. I put my ideas together in a 10-minute lecture that I presented on March 16, 2006, at the Gathering for Gardner (it’s a conference for people involved in various forms of recreational mathematics). I’ve also posted the text here.

Spoiler alert: in order to illustrate some points in the lecture, I show the solution to a maze I worked on. This is the Twisty Maze. You might want to try it before you read the lecture and see the solution.

Numb3rs about Logic Mazes:

At our house we used to watch Numb3rs every week, and we were excited when they had an episode devoted to logic mazes. They got a few things wrong, but that is unavoidable in any television show. I wrote a discussion of the episode and complained—a lot—about the mistakes, but I still think it was a great show.

Video Games are Incredibly Stupid:

This is an essay I posted in 2001. It gave my opinion of today’s video games, and it became rather famous. The “incredibly stupid” part really just referred to modern video games. I contrasted these games with the great video and arcade games of the 1970s and 80s, and I lamented that the classic games had all but disappeared. Recently there has been renewed interest in the old games, and at the bottom of the first page, I added a postscript about this renewed interest.

Reviews:

This has a review of Dave Phillips’ new maze book, along with two mazes from the book that you can solve here. There is also a review of a book that has nothing to do with mazes, but I wanted to review it anyway.

Plain Old Solitaire—Maybe It Isn’t as Dumb as Everyone Thinks:

This is an article of mine that appeared in the April, 2010, issue of GAMES Magazine. I argue here that Klondike solitaire generates interesting puzzles, and I also present a strategy that lets you win one out of three games. Of course, it may be that the world doesn’t really need a strategy that helps people win more games of solitaire.

And finally:

I have an explanation (sort of) of the term “Logic Mazes.”

My site has reviews of my books SuperMazes and Mad Mazes. These reviews have some samples of mazes you can try solving.

Maa.org, the web site of the Mathematical Association of America, has an article on Multi-State Mazes. It has a lot of nice things to say about me and about this site.

Serhiy Grabarchuk’s Age of Puzzles has a page about me. The page includes a long discussion of a 3D maze of mine that was in Martin Gardner’s column in 1963. When he was young, Serhiy was impressed with that maze and built a transparent model of it. With various tilting and nudging, you can coax a ball through the model. It would be great if someone manufactured this, but that’s unlikely to happen.

PuzzleMonster.com has an interview with me along with review of this site.

Before I became entranced with mazes, I used to invent card games and board games. Here is a section devoted to my games.

To send me an e-mail, please use this address:

Unless otherwise noted, all material on this site is copyright © 2011 by Robert Abbott.