Update: Logic problems, Part 2

I knew that updating the logic problems for the new website would be a big task. Several logic problems were never posted to the last version of the website, and those that were still needed updated graphics and, in some cases, updated detailed solutions. I decided to break the logic problem update into pieces, so that I could better manage the work and post updates more frequently. The first update was back in March, 2015. Here’s what’s new in the second update:

Logic problem #6 – Marbles
All the changes here were to the detailed solution explanation. Some of the language was clarified. A mathematical error found in one of the explanation’s graphics was corrected. The biggest change was replacing an argument concerning the divisibility of the number of Andrew’s marbles with a more direct fractional explanation. This not only made the explanation more straightforward (with new equation graphics), but also enabled me to provide an explanation of (commonly misunderstood) fraction multiplication in the solution.

Logic problem #7 – Corn Maze
From the second update group, this problem needed the most work. Since I wanted this particular puzzle to appear in the fall in order to introduce a recurring blog feature on corn mazes, it also set a timeframe for when the entire update should be posted.

Undertaking a major update to the website presents opportunities to make significant changes, as well as fixing minor yet thorny problems. The graphic for the corn maze was the latter. At the time this puzzle was originally made (Fall 2006), my unsophisticated knowledge of Adobe Illustrator meant that I wasn’t capable of designing an acceptable corn maze graphic, one that would look like an actual corn maze from above. My aunt, who is a writer and artist, graciously stepped in to help. I sent her the outline of the maze and she sent back an illustration in the style that she uses for her books.

Corn Maze for Logic problem 7, version 1

This is what was published in the magazine and what I posted on the website until now. Although I am grateful to my aunt for her assistance, I was never completely satisfied with the result. (One thing I absolutely love, however, is that bridge.) It just didn’t look like a corn maze to me, although it took me a long time to figure out why I felt that way.

The main issue, I realized, was that the path size to corn size ratio was incorrect. A corn maze has thin paths compared to the patches of corn separated by those paths1. The outline of the maze I originally designed had a path size to corn size ratio of 1:1, that’s what my aunt used as a template for the above illustration, and that didn’t look right. With thinner paths, the corn maze would feel appropriately bigger.

Corn Maze for Logic problem 7, version 2

Even after I had identified this problem, fixing it was still a challenge. I first attempted to draw the new, skinnier paths on a green background representing the corn, but could not get the path corners to appear correctly rounded, as they would in an actual corn maze. After exhausting much time and effort on that method, I then decided to try a different approach, using expanded versions of the patches of corn on a background of brown dirt. The gaps in the patches of corn would thus result in the paths. Rounding the corners of the corn patches that do not have straight edges was still a challenge, since this is not natively supported in Adobe Illustrator 6 and earlier. After exploring my options, I ultimately chose to use the Round Any Corner script, which has mysteriously disappeared in the past few days.

One of the other issues I had with the original illustration was the stroke weight of the details representing the corn. I think my aunt’s intent was to represent the leafy texture of the corn plant, but photos of corn mazes show a more grainy texture where those details of the individual plants all blend together. Thus, I wanted to make my corn maze illustration have this sort of texture as well. While I was satisfied with the textures I could apply in Illustrator, I have not figured out how to successfully export these to an SVG file (so that the texture will still appear sharp on high-resolution displays). Thus, I dropped the textures altogether, as you can see above.

Finally, neither a graphical illustration of the correct solution nor a detailed solution for the problem were ever posted on the website. I had never actually thought through a detailed solution at the time I created the puzzle, so all of that needed to be worked out as well. It was tricky to figure out how to represent the path segments graphically in a way that didn’t need a lot of explanation. I also wanted a way to show the choices you needed to consider in picking which path segment to use next. The solution path shown is made up of several pieces, layered below the corn patches and above the brown dirt background. The toughest part here was getting the correct path thickness at splits and intersections. There is an intersection that is visited twice, and in order to clearly communicate which way you turn the solution path shouldn’t intersect or overlap itself there.

Logic problem #8 – Flight Plans
The solution graphics were slightly modified to better support non-high resolution displays. This problem was one of the first to be written after the sixth version of the website debuted, and as such required few updates.

Logic problem #9 – Writer’s Group
Increased the size of the graphics representing the circular table at which the authors meet, mostly to support a larger, more legible font. Also brought the table to the foreground to make the author positions (circles) look more like chairs, and to better highlight the two important author positions (poetry, screenplay) that are rotated midway through the solution to find non-problematic overlapping positions of clues.

Logic problem #10 – Castaway, Part 2
To better match the overall aesthetic of the website, reduced the stroke weight for the stick-figure graphics representing the rules on how the castaways lie to each other. I fixed the gradient backgrounds representing in-progress groupings in the detailed solution (or rather, I learned how to create them properly). The solution graphic font was changed to be more legible. Name cards, matching those from the updated first Castaway logic puzzle, were added to the solution graphic. Finally, a minor error in the detailed solution (switched a name) was corrected.

The third, final, and largest update to the logic problems is still to come. There is a lot of work that needs to be done in order to bring that group of logic problems to the website for the very first time, so it will take quite a while to complete. In the meantime, enjoy these problems and others on the site!

  1. This is mostly to prevent people from cheating by cutting through the corn, I think. Compare this to a hedge maze, where the shrubbery is denser, and the path size to hedge size ratio is closer to 1:1.