Lux: The Traffic Maze at Floyd's Knob

In Martin Gardner's excellent book, "The Unexpected Hanging and Other Mathematical Conundrums," I encountered many interesting puzzles. One that I particularly enjoyed was a puzzle by Robert Abbot, author of "Abbot's New Card Games." It goes like this:

"Because the town of Floyd's Knob, Indiana, had only thirty-seven registered automobiles, the mayor thought it would be safe to appoint his cousin, Henry Stables, who was the town cutup, as its traffic commissioner. But he soon regretted his decision. When the town awoke one morning, it found that a profusion of signs had been erected establishing numerous one-way streets and confusing restrictions on turns.
"The citizens were all for tearing down these signs until the police chief, another cousin of the mayor, made a surprising discovery. Motorists passing through town became so exasperated that sooner or later they made a prohibited turn. The police chief found that the town was making even more money from these violations than from its speed trap on an outlying country road.
"Of course everyone was overjoyed, particularly because the next day was Saturday and Moses MacAdam, the county's richest farmer, was due to pass through town on his way to the county seat. They expected to extract a large fine from Moses, believing it to be impossible to drive through town without at least one traffic violation. But Moses had been secretly studying the signs. When Saturday morning came, he astonished the entire town by driving from his farm through town to the county seat without a single violation!

"Can you discover the route Moses took? At each intersection you must follow one of the arrows. That is, you may turn in a given direction only when there is a curved line in that direction, and you may go straight only when there is a straight line to follow. No turns may be made by backing the car around the corner. No U-turns are permitted. You may leave an intersection only at the head of an arrow. For instance, at the first intersection after leaving the farm, you have only two choices: to go north or to go straight. If you go straight, at the next intersection you must either go straight or turn south. True, there is a curved line to the north, but there is no arrow pointing north, so you are forbidden to leave that intersection in a northerly direction."

I had just finished work on Illusion and was doing those puzzles to unwind, and since it was 1:30 AM I suddenly found myself thinking, "Hmm, that might make an interesting Lux map."

So, I got to work. I drew up a little picture of the map in photoshop, blew it up and loaded it as a background image. I divided each segment of street up into 4 countries in each direction. For the one-way streets I only used four countries in a row, and for the two-way streets I had two rows next to each other (it required making some pretty small countries, but not TOO too small). I considered making each intersection a country in itself, but I wouldn't be able to restrict turn directions in terms of straight and curved lines, so I just kept it to the streets. I also made each of the highways on either side of town separate country, and connected them with each other. Also, to increase the user-friendliness of the map just a little, I made it so you CAN make a U-turn once you're on the highway, meaning that you can get on one highway, then turn around and head back into town at the same spot you left.
The tricky part was identifying all the one-way streets. The obvious choices were to make one-way streets leading towards any exit of an intersection that didn't have a head of an arrow, since there was nowhere to go. However, there was more to it than that. You see that in some intersections, there are arrows leading out of the other end of what would be a one-way street. Robert Abbot included those extraneous arrows to make the puzzle harder to solve, but in this map they'd make a street with no origin. So I had to figure out which arrow heads to erase

I expected to have one jolly mess of a time making all the one-way connections, and guess what: I was right. But there were also plenty of obstacles before that as well, most of which I hadn't expected.

When I drew the two-way connections, I opened it up and started to play a game as a test run (to make sure I hadn't missed any countries), and I got an error message saying that country "null" didn't connect to any other countries. This had happened before, and each time I just opened up the board in text editor, looked for the country ID that had been identified, and edited the polygon locations to make it visible, then deleted it. But this time, the first time I tried it, something went wrong and the entire map was fouled up (it wouldn't even open up in the map editor), forcing me to redraw the whole thing again, from scratch.

Once I'd gotten the countries named, it was time to divide them up into continents. I decided to make each segment of each street a separate continent. This would make the two-way streets hard to take, since you'd have to find a separate route back onto the other side of the same street to take it. However, the one-way streets would be much easier, and with the one-way connections they'd be a prime shafting spot and attacking point.
The country names were simple, I just game them street addresses. I named each street and just wrote out some random sequential numbers for the addresses. I used a few numbers that have significance in my writing projects, and a few others were years of historical significance, but most of them were just random.
But when I started making continents, I ran into a problem. The map editor is contained in one window, and as you create more continents, the row of colored squares representing those continents reaches down that window. But the row of squares does not wrap around and repeats, it just keeps going down, so eventually the squares reach offscreen. And since I have to manually drag a line from a country to the square to place a country in that continent, I couldn't reach the last few squares. So, I had to open up the board in text editor and manually write the continent details into the java script itself, then move the country info into those continent paragraphs in there. I had to create 7 more continents this way, and it took forever. Plus, I made a mistake with the first tag and this time, when I got the error message, it wouldn't tell me which country or continent was causing the problem, so I had to search through the entire document in text editor and find what the problem was. That alone took over a week.

Once I'd gotten that mess settled out, it was time for the fun part: making the connections one-way. I got to work editing the tags in the text program (over 100 countries and each one needed at least one tag deleted, several needed more), looking up ID numbers and deleting them. Oh yes, and did I mention that several times I misidentified a country and had to redraw the connections along an entire continent again, and repeat the tag removal?

Those were the major obstacles, my college classes and Shakespeare performances were others. Altogether, the whole process took over four weeks.

The theme and artwork were easier, I just looked around the internet for a couple of days for an aerial shot of some farmland, played with the colors a little to make sure it wouldn't stand out too much and distract from the board too much, and used that as the background. I just put a black stripe around the roadways for asphalt, and to increase the contrast. I also drew semi-transparent arrows over the roadways to mark which roads lead where (I drew one arrow and copy-pasted it over each country, in the appropriate direction). After that I wrote a brief description of the map and a summary of the puzzle, and put that right by it. I used the magic wand to select the whole text, chose "expand selection" by 3, and filled the background with a wood pattern to make a nifty wooden sign on which to post the info. I put that on the right of the maze. After that it was just the title and name at the top and my logo at the bottom (I used three cubes this time, red, yellow and green, just like a traffic light!!!), and it was ready (FINALLY!).

I played a few games on it and I think I did reasonably well. Now I'm crossing my fingers.