Whit McMahon, a puzzle constructor, wrote to me recently to share a new kind of puzzle he created last year called Balance Quest®.

In these numeric logic puzzles, you fill in blanks so that the sum of each box is made by adding the numbers in the adjoining half-height boxes. Note that some of these numbers are negative, and may produce negative sums. Eventually you reach the center, in which the final sum is zero, representing a kind of equilibrium — you have achieved your quest for balance.

Whit has kindly provided two sets of printable puzzles, small and large, which contain more detailed instructions, a fistful of puzzles, and their answers. Here are the two sample sets:

9 Small Balance Quest Puzzles (pdf)

6 Large Balance Quest Puzzles (pdf)

If the symmetry of Galaxy puzzles pleases you, I suspect you may also like these, even though they are quite different. If you find you like ’em, visit the Balance Quest website for more.

Enjoy!

So, as I reported recently on my blog, I discovered recently that a maze that appeared on the back of packages of Kraft SpongeBob Macaroni & Cheese was based on one of my designs. When I notified @kraftfoods of this, via twitter, they put me in touch with Design Partners, an agency in Racine Wisconsin that was responsible for the packaging design. It is perhaps worth pointing out that Kraft (like most companies that outsource their design work) is indemnified against this kind of thing – any legal repercussions would fall on the agency responsible, not on Kraft.

Susan, the HR director at the agency contacted me with a very nice letter, apologizing sincerely for the mistake. She asked me how I would like to “resolve the matter”. I asked the agency to make cash donations to two food banks – $2,000 to their local food bank, the Racine County Food Bank, and $2,000 to my local food bank, the Los Angeles Food Bank. They were very happy to do so, and the donations were made Thursday morning.

I am personally very pleased with how this turned out. I’m aware that some of you (including one or two eager attorneys) were hoping I would try to get a substantially larger settlement. In my mind, this would not have been just. It would have been a reverse form of theft, taking advantage of one person’s mistake for my personal gain. While it’s tempting to blame the “big corporation” for this kind of thing, ultimately these kinds of mistakes are made by people who are prone to the same kinds of errors that you and I make every day. Also, my house is too cluttered with broken pencil sharpeners and cat toys, and I don’t know where I would fit a lifetime supply of mac & cheese.

So, I hope you like the way I resolved this. I feel I’ve turned lemons into actual lemonade. Or spilt milk into unspilt milk? I dunno, you figure it out.

If you are in the US, and you’d like to learn more about your local food bank, I suggest visiting the following directory:

Feeding America.

A big thank you to Josh Masur for advice and encouragement.

While grocery shopping this evening, I happened to notice a box of Kraft Mac & Cheese that was turned around, with a familiar looking maze on the back.

While this maze may look generic to you, it looks quite recognizable to me, because I spent quite a bit of time writing software that produces mazes in this style. If you look closely, you may notice the vertices form a fibonacci spiral. It’s a pretty unique design, but, just to be sure, I bought a box, took it home, and started looking through the collection of mazes on my website. These mazes are free for you to download, but definitely not free for you to reuse, unless I grant you permission.

Looking at my website, I found the original pretty quickly. The artist took Maze #1 from Book #1 (published in 2010) of my Intermediate Mazes, and turned it 90 degrees clockwise, and altered it in a handful of spots. Despite the addition and removal of about 7 line segments, the majority of the puzzle is identical to the original. Alas, he or she forgot to ask permission to use my design! They also failed to notice my copyright notice. I can only assume that they figured I wasn’t a consumer of Kraft Macaroni & cheese, or that I would never touch the SpongeBob variety that this maze appeared on (true – I prefer the classic elbow variety, which is getting increasingly hard to find for some reason). I admit I’m not terribly proud of my biannual craving for classic Kraft Mac, but sometimes, I like to pretend I’m 8 years old again.

Here’s the two mazes side by side, just in case there was any doubt:

A helpful note to the good folks at Kraft Foods, or any other multinational conglomerates that wish to use my content without my permission: If you’re gonna steal a maze, you might want to try stealing from maze book #47, and do a horizontal swap on it before you rotate it 90 degrees. That’ll slow me down some…

UPDATE: I’ve worked things out. The story continues…

For the past several days I’ve been enjoying solving successive levels of Euclid the Game, an online set of puzzles based on Euclid’s Elements.

You are initially given the equivalent of a stick, a straight edge and a compass (tools for drawing points, lines and circles), and are asked to construct an equilateral triangle. Once you’ve solved that, you now have a new tool that draws equilateral triangles, which you use to help solve the next problem. As you solve successive problems, you build up a collection of increasingly sophisticated tools, and solve increasingly difficult problems.

I’m currently on level 20. Not sure how far this goes, but let me know if you get stuck.

This is a new demonstration I’ve prepared of my Mirror Morph technique, discussed previously. It’s a simple 2D trick that can make still images look three dimensional.

Here’s a GIF version.

I occasionally get requests to add new puzzle varieties to the collection. I have to ignore a lot of these, because there are 24 hours in a day. However, the last request I received, for Masyu puzzles, was hard to ignore, since I’ve enjoyed solving these myself for the past few years, and I’d love to have access to a larger collection of them. So what the heck! I made a bunch.

Masyu puzzles are closely related to Slitherlink and other spatial reasoning puzzles. Like Slitherlink, the end result is a loop which is constructed from straight line segments.

Unlike Slitherlink, Masyu puzzles don’t use numbered clues. Instead, the clues are black and white circles, which I am told resemble pearls (although I think they resemble the stones in the board game Go). This gives the puzzles an elegant simplicity which is perhaps only rivaled by Galaxy puzzles, another great Nikoli-style puzzle.

Masyu puzzles use the following rules:

• Black circles indicate corners.
• White circles indicate straights.
• Black circles must be turned upon, but the loop must travel straight through the next and previous cells in its path.
• White circles must be traveled straight through, but the loop must turn in the previous and/or next cell in its path.

If you’d like to learn more about how to solve the puzzles, I’ve written a (hopefully) helpful tutorial, which you’ll find here. If you find the tutorial less-than-helpful, let me know, so I can work to improve it.

If you’re ready to try your hand at these puzzles, check ’em out!.

Roderick Kimball wrote to tell me about an interesting logic puzzle he’s developed called Path Puzzles.

In these puzzles, you must make a path that winds its way from one opening to another on the edge of the grid. The clue numbers tell you how many squares in each row or column are occupied by the path.

The more advanced versions of the puzzles involve more ambiguous clues, and multiple door choices; which makes them significantly more challenging.

If you’d like to try these puzzles out, check out this sample page that Roderick has provided to Krazydad readers:

Path Puzzles Sample Page

Want some more? Go to pathpuzzles.com.

And happy puzzling!

Emergent Orange describes the orange hue that is produced when you average together a bunch of randomly selected digital photographs.

The illustration shows 5 different sets of photos (randomly selected from Flickr) accumulating over successive rows. The first row is a single image. Then 2 images, 5 images, 25 images, and 100 images in the bottom row. I have cranked up the saturation to reveal the orange shift (unprocessed averages tend to look like dirt or milk-chocolate).

I stumbled across this effect in 2006, playing with Flickr, and have blogged about it a few times. Other digital artists who use the same averaging technique have also observed the effect. The reasons why it happens are not yet entirely clear, but I suspect it has something to do with chemistry and physics. Interestingly the same effect occurs with collections of human-generated synthetic, abstract art (not photos), such as fractals.

Over thanksgiving break I wrote an informal paper describing my findings to date, in hopes of attracting some brighter minds to the topic. Perhaps you are one of those minds? You’ll find my paper here.

If you prefer pretty pictures to words, here’s a Flickr set containing some of my image averaging experiments.