I solved the riddle! (Whew.)  The solution occurred while I was drinking coffee this morning at a McDonald’s restaurant after having fiddled with numerous trials and erroneous attempts.  I guess insight played a role in my solving it since I had “found” the solution without realizing it the night before and had rejected it — by which I mean that I had discovered the correct shape (thinking of this as a drawing exercise) but had the scale wrong (a common problem in drawing)  Thus a slight attitude adjustment was needed to capture the solution, requiring several hours of sleep as well as relaxing distractions plus a fresh morning perspective.  (No doubt the coffee was helpful, too.)

The work of solving the riddle presented many intriguing corollary questions.  While solving it feels nifty, I wonder who created the puzzle and what questions lead someone to an invention like this.  Discovering a puzzle requires a higher and brighter curiosity, I think, than solving a puzzle that is already well received.  While artists complain of the difficulties they face in the market place, imagine the plight of a riddle inventor!  Certainly one must have very pure motives to spend one’s days in devising riddles and puzzles knowing that one’s reception is so marginal.

Other ideas passed through my mind as I toiled away at the puzzle.  I was aware of having seen its solution once, but recollection did not come very handily to my aid.  Even knowing that the lines had to meet somewhere outside the figure did not help much psychologically.  I still felt compelled to try various ways of connecting the edges of the box.  Finally, I realized that an element of trust was required.  Could Kitsune have tricked me?  Was there a solution?  And another kind of trust was needed, too.  I have counseled various persons about confidence in regard to their drawing.  Drawing in art, making “mistakes,” can be discouraging and I have told people many times that you must go through the problem and not give up on it.  It is the passage through self-criticizing thoughts that leads ultimately to the promised land of art.  Here I was with a knotty problem — a drawing problem, I decided to think of it in those terms — and I could have given up, but I decided to follow my own advice and press on.

I am still not convinced that it is not more math than art, though I chose to use art as much as I could to solve it.  But unlike most the art I do, I did not know what the thing I was drawing looked like.  The reasoning here was exactly opposite what I typically do.  Usually I look at something and from a massive wall of perceptions, I am choosing certain ones and ignoring the rest.  Here I had very limited means, four lines, and with them I had to discover something I could not see, trying to bring it into visibility by following a set of instructions.

As I was leaving McDonald’s backing my car out of a parking space, perhaps it was then I had what felt like a real “insight” moment.  As often happens in art, drawing something or looking at other artists’ drawings will change the way we view the world.  It struck me as more than a little ironic the number of arrows that seemed to be everywhere around me after I had found the figure that solves the riddle.  A big arrow painted on the asphalt pointed the direction out of the parking lot and as soon as I noticed that big arrow, why it seemed that the world was littered with arrows!  They might have been like hints (unless of course there’s more than one solution!).

[Top of the post:  photograph of a McDonald’s restaurant napkin upon which I solved a riddle posed by a reader, Kitsune, on the post Alice Drew a Maze, photo by Aletha Kuschan]

8 thoughts on “Good news, Kitsune

  1. Hello, Aletha!

    I am glad you solved the problem 🙂 Thank you for writing about your experience of discovering the solution. I am a fox, but not an evil one – I would never trick you 🙂

    It is not known with certainty who created the problem, but some sources suggest that it might have been Sam Loyd (Yes, he was a “recreational” mathematician).


    I find your comment about the wall of perceptions and choice intriguing. I think it highlights how different artists work. Sometimes it is impossible to see clearly an abstract concept. Icon is a good example. I think it is one of the most difficult tasks that an artist can face because of the value people place on it. You know that you want to draw, let’s say Holy Trinity, but how to draw it is a problem. An artist has to search her/his soul to find an answer. Thinking about it reminded me of the film Andrei Rublev by Tarkovsky.

  2. I was just relieved I could solve it. I had a serious “yikes!” experience until the solution appeared, as I had an unpleasant flashback to high school math.
    I didn’t really ever suspect you of playing a trick. It was, I think, more a doubt that creeped into my thought because the solution was elusive. Better to blame you than me! Doubt and confidence play important roles in outcomes. However, I decided that trust and confidence were things I could choose.

    I like this example better than Jackson Pollack, who had a strong motive for rationalization since chance played a pivotal role in his imagery. However, the old masters painting the Holy Trinity is a wonderful puzzle because the artist creates an image with considerable conscious deliberation (and sometimes with instructions by the patron) that lies outside normal experience. As a consequence, artists copied conventional stereotypical forms, and motif played a huge role in religious painting. How does the first instance come about? What lends the image to stereotype later on? Once a particular iconic visual idea gained acceptance it was recycled generation after generation. And also revealing and intriguing is that these images, as regards Christian art, sometimes had non-Christian roots in the art of antiquity.

    The history of motif, and changes in motif in art, provides a ripe topic for psychological criticism. How do images transpose from one culture into another while sometimes acquiring radically different meanings? And what accounts for the appeal and durability of certain images? What marks a winner? What happens when an image falls on hard times and no longer resonates?

    Copying plays a big role in art. Even in modern “abstract” art artists copy various motifs that become standardized. Imitation is such a big part of human behavior. And people imitate each other often without being aware.

    Do the gestures have meaning in their own right? Platonic ideas? There’s the rub!

    Thank you for providing the puzzle that led to these fun ruminations!

  3. Carl Jung is often studied in art departments due to his hypotheses on unconsciousness and symbolism. One of the important concepts in his view is an archetype – innate and universal disposition that generates basic themes of human life. We do have some support for such innate dispositions. For example, snakes and spiders can be more easily identified in an array of pictures and serve much better as a fear inducing stimulus for conditioning rather than such harmless creature as a butterfly. Perhaps, it is those symbols and themes that developed in humans through evolution that resonate the most with the spectators.

    How various cultures view the same concept is a very interesting question. For example, red and green color have very different meanings in some cultures.

    Indeed, coping is a very good exercise and sometimes it happens unconsciously. A book came out recently called The Dumbest Generation by Emory English Professor Mark Bauerlein. I have not read it, but some of the comments on Amazon made me sad. One of the reviewers wrote that the book mentioned a young artist that does not know who Michelangelo and Rembrandt are, but, what is much worse, does not care…

  4. I often wonder what happens in today’s art departments; glad to hear the Jung is part of their study. While motif is a little different thing than Jung’s idea of the archetype, it certainly lends support to it.

    I also think it’s sad whenever young artists claim that they are not interested in old masters or in basic skills, though what that means depends upon who says it. Rembrandt claimed he couldn’t be bothered to go to Italy because he was too busy painting. In his case, it didn’t matter that he avoided what was thought to be the richest education in serious art then available to his generation. He no doubt felt himself firmly grounded in Netherlandish art forms, found rich sources of invention around him in Amsterdam. He was a very alert admirer of Rubens and got the Italian thing indirectly through Rubens, and he made wise use of all the other “Italian” moments that came his way. So, for an artist like Rembrandt the dismissal spurns the “hip” thing of the moment in favor of one’s own lights and standards. It worked for him.

    But a lot of young artists make a different mistake, probably akin to what the author intends when he describes a generation as “dumb.” (Let’s hope he exaggerates. Every generation criticizes the young crowd that’s taking over.)

    A prevalent stereotype of today is that art is about change — change for its own sake. Linked to that, yet unspoken, seems to be a yearning for celebrity which young artists perhaps think they’ll be lucky enough to get. It’s like wanting to be a rock star (which is very different from wanting to make music, even rock music).

    When I hear artists of any age say they have no time for drawing, I translate that as “they don’t know how to draw.” And they believe the difficulty is beyond them. The skills seem too high, too hard and their goal is not even the use of the skill to explore life, but the acquisition of a designer label for ingenuity. To be thought an artist has cachet. I don’t know why. Being an artist involves one in plenty of mundane (though delightful) kinds of work.
    Why does no one want to be a dentist or an accountant? The schools that teach these skills should work to make these occupations seem more glamous! (Sexy though emotionally volatile dentist who is mysterious and brilliant, sought after by women, misunderstood by other dentists –mere ordinary dentists — because his dentistry boldly goes beyond anything they ever imagined or dreamed possible ….) Ditto accountant. Whatever.

    I tried to write about all this once in a funny way. This inspires me to reprint it here.

  5. Don’t know if he exaggerates or not… Here are some facts quoted in the book:

    – Sixty-three percent of test takers couldn’t find Iraq on a map

    – Fifty-two percent of high school seniors picked Germany, Japan, or Italy as allies of the United States in World War II


    Accounting was the most boring class I have ever taken, and I don’t want to look in someone’s mouth all day!

    Artists saying they have no time for drawing… Well, I have a story about that issue. I have a friend who is an art director. I saw some of her work, and she is very talented. However, she stopped painting for herself. The only thing she does is art for work. She is quite busy with work and has a small baby. Exhausted after work she does not have the energy and willingness to paint. Perhaps, in a few years her baby will be older and she’ll have more free time, but I just feel sad that she stopped painting.

    Thinking about it I recall one psychological experiment. Kids used to play close to a house of their neighbor. They used to laugh and scream loudly while having fun. The person really didn’t like all that noise and disturbance. He came up with an ingenious solution. Every time kids came to play by his house, he gave them small amount of money. A very interesting thing happened. After a few days, kids stopped playing by his house. Why it happened? This was just an anecdotal evidence, but there are other experiments showing that once you start paying people for what they really like to do they make a new association and do the activity not for fun, but for the money…

  6. You are among the young, are you not, Kitsune? How do you find your generation? Perhaps your judgment is more nuanced than what one learns from statistics. If it offers comfort, there’s probably as many dummies in my generation as yours. Context is important. Prior to the present Iraq war I might have been hard pressed to locate Iraq with precision, not withstanding Iraq 1. And I remember thinking it odd that al Quida would have influence in Somalia until I consulted a map, then it didn’t seem so odd. Most French people probably couldn’t locate Wisconsin with precision, since no cheese coming out of Wisconsin is likely to impress the French!

    Usually we know the facts that matter to what we do. What I find troubling in people of any age is a lack of curiosity. We can learn new facts all the time, but curiosity comes prior to any kind of knowledge that has real depths.

    Doing art for money has come to be seen as “selling out,” and indeed often it is. Side by side with the stigma of selling out is the notion of the avant garde, removed from its 19th century French context and applied broadly to art everywhere. Among the folks that I disparagingly refer to as the hipster class, “real” art is “avant garde” which usually means that average people are scratching their heads wondering what it is. Sometimes its obscurity alone is thought to qualify it as genuine, a distinction that I think is more aptly called snobbery. Not that art must be transparent either … it’s complicated.

    Ironically the avant garde artists who are championed as the “real” artists are financially doing quite well, even ridiculously well. Damien Hirst is the highest paid artist in human history, and you can probably guess I won’t gush over his products.

    It would be extremely difficult to work as an art director and try to take the product up to the level of high art. Constraints of time and multiple pressures probably make that impossible except on very unusual projects. Still some visual abilities criss-cross the boundaries of commercial art and fine art. Having a baby, in addition, probably makes your friend’s life very complicated. I was a stay at home mom with my daughter in her early years, and I couldn’t do much art. Sometimes I just drew on paper on the floor while my daughter crawled around and she scratched out parts of my drawing, thinking to join me in my fun…? But kids grow fast and I found that anything that was even almost art helped keep my visual imagination going.

    Sometimes money kills art, becoming a substitute for what art is supposed to provide which is life. People buy life instead of living it. But as always there are exceptions to the poor artist. Rubens were he living today would be Rubens Inc., he was so wonderfully successful. For a time, Rembrandt couldn’t crank out portraits fast enough to satisfy wealthy Amsterdammers’ clamoring. And the great English painter Turner was a money man from his lanky youth and made himself a fortune. Nevertheless Turner became truly a visionary artist whose work influenced countless artists coming after him even unto today.

    I rather hope that I can become rich! I realize that some of what I want to do with my art requires largish sums of money since I want to paint certain of my pictures in a more monumental scale, one that requires space and materials and probably occasional helpers.

    Art is such a big deal, and is so because life is a big deal. The artists are supposed to teach us that, to connect us with our humanity. But money can easily confuse the mind, that’s for sure.

  7. Hello, Aletha!

    Yay! You solved it! 🙂

    ‘I had “found” the solution without realizing it the night before and had rejected it’

    Same thing happened to Einstein. He actually found the solution to the problem, but discarded it. He came back to it eventually, and did solve it correctly. It took Einstein about eight years, while Hilbert also solved it much faster and around the same time. https://en.wikipedia.org/wiki/David_Hilbert#Physics

    ‘several hours of sleep as well as relaxing distractions plus a fresh morning perspective’

    Sleep is extremely helpful! We tell our brain to do something, it does its thing, and we get a solutions a few hours later or in the morning – it’s great!

    Some riddles come from research needs. A particular phenomenon may need an investigation, and the appropriate means to test hypotheses could be developed.

    ‘I decided to follow my own advice and press on.’

    Yes, that’s the key! The agony and the ecstasy! Art and science are very much the same in that sense!

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