Pattern #5 – Puzzles to Solve

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Why is it that the puzzle section of your local newspaper prints sudoku, chess and crossword puzzles, but not algebra problems?   I love chess puzzles. While working on one the world around me completely disappears. It is as though I am hanging in deep space alone with the puzzle.  My wife and I do the New York Times crossword daily.  But don’t ask me to balance my checkbook, much less solve a trigonometry problem, for fun. Why? These are all puzzles. What are the design elements that make one kind of puzzle compelling but another repulsive? 

There is no doubt that humans are drawn to puzzles. Consider the enormous market for puzzle books and puzzle apps. Among mobile apps, games are the most popular, comprising 25% of active apps according to a recent survey.   The second-place category wasn’t even half that number. (source)  And among mobile games, puzzles are far and away the most popular category.  

Nor is the love of puzzles a recent phenomenon. The Book of Games was one of the best-selling books of the medieval period, (Mohr 1997).   One of the oldest known written documents, the 3,600-year-old Rhind Mathematical papyrus scroll, is a collection of brain teasers. (Danesi, 2002)

Management Science Professor Michael Pidd at the University of Lancaster in England makes a distinction between the different kinds of challenges we face at work. He breaks them down into what he calls puzzles, problems, and messes.

Of the three types of challenge, puzzles are the simplest. They have one correct answer, and usually one way to solve them. Think Sudoku or crosswords. 

Problems are more complex. They have more than one correct answer, and it is up to the solver to decide which answer is right. There may also be more than one way of solving a given problem. For example: How do I help my daughter get into the right college? The answer to that question starts with determining what “right” means. Once that is determined, there are many different ways of pursuing admittance to those schools.

Messes, according to Pidd, are complexes of interconnected problems. They are ill-defined, ambiguous and often associated with strong moral or political issues.  Global warming, for example, is a mess. 

Most challenges we encounter at work fall into the categories of problems or messes. But puzzles are the ones people do for fun. Can business leaders design work such that the problems and messes that people face at work feel more like puzzles? And can people modify how they approach problems at work to make them more interesting?  

A puzzle-based work pattern 

The most compelling puzzles contain recurring design elements; examining these elements gives us insight into how to better design working experience for ourselves and others:

A clearly correct final solution. The most compelling puzzles have precisely one detectably correct answer. They provide a complete denouement that leaves no residual doubt about whether or not the solution has been achieved. This requires that the objective of the puzzle be clearly set out up front. 

Incremental wins. The puzzles to which we are most powerfully drawn grant us small wins along the way toward the final solution. If we had to study a jigsaw puzzle for ten hours before solving it all in one go, we would never do it. We are willing to work on a jigsaw puzzle for days because every few minutes it provides that incremental reward of successfully fitting one piece to another.  Each confirms that we are making progress towards the solution. In the same way that the overall solution must be detectable, each small win must itself be detectably correct. 

Difficult but not impossible. An ideal puzzle is difficult enough that achieving a solution is in doubt, but it cannot feel beyond reach. This is part of the narrative tension created by a puzzle: are we smart enough? Can we beat it? It is a bet in which we wager our ego, and failure results in a loss of self-esteem. However, when we do succeed, the greater the perceived difficulty, the greater our pleasure.

The New York Times crossword gets more difficult each day of the week, with Monday the least difficult and Saturday the most.  Those of us who do crosswords know which day of the week is our sweet spot.  Solitaire, which is very popular (although not a pure puzzle because it also incorporates chance) allows only 1 win out of 11 tries. 

Self-contained. It is in part because puzzles are a test of our minds that the best puzzles require no external reference. Puzzles like sudoku or crosswords demand satisfaction of an entirely internal consistency. It isn’t necessary to go to an external source to solve either. This is why so many mystery novels, examples of an art form built around puzzles, are set in in locations isolated from external sources of influence: a train, a boat, a snow-bound mansion, or a locked room. Puzzles are most satisfying when our successes are attributable to our own prowess. 

Beautifully constructed. Many puzzles are themselves great works of ingenuity, and a pleasure to look upon. If you had never seen a crossword puzzle, would you have imagined that even one could be created, much less one for every day of the week year after year? Whether or not you solve a chess puzzle, the structure of the game manifests an organic balance and simplicity that is an aesthetic marvel. Mathematicians, some of the most driven of puzzle solvers, often comment on the beauty of their problem-space: Bertrand Russell provides an example of the ardor of a puzzle solver in his description of mathematical beauty: 

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.  (Russell, A History of Western Philosophy, 1945)

Provides a glimpse into the eternal. Russell hints at this in the quote above when he says there is a sense in math of being “more than Man.” Mathematicians know more than most the special satisfaction of reaching a more general solution, such that solving one puzzle results in solving all puzzles of the same type. As one goes through the process of solving a puzzle, a part of the mind is cataloguing the techniques that can be used to solve others.

Understanding a puzzle completely, especially those involving numbers, feels like touching a deeper part of the universe. This explains why Sangaku, the Japanese geometrical puzzles and their solutions, were left as offerings at Shinto and Buddhist temples during the Edo period (source). Pythagoras, in the sixth century BC, founded a religion based upon the idea that number is not just descriptive, but is actually generative. Gazing so deeply into the puzzle of math, he and his disciples perceived divinity in number. The greatest puzzles provide a glimpse into what Pythagoras saw.

Elegantly solved. Sometimes it’s not enough just to solve a puzzle; real satisfaction comes from arriving at an elegant solution. To some extent, pursuit of elegance is a way for solvers to achieve the appropriate level of difficulty. Solving a puzzle inelegantly may be too easy, so pursuing the most simple, effective, and clever solution raises the level of difficulty and satisfaction in success. 

Application to the design of work

Optimize the market.  There is a finite number of puzzles to solve at work, and they have value. This forms a market for this scarce resource. Such a market can be either efficient or inefficient. Pay attention, therefore, to how puzzles are distributed. Take time to understand the preferences of individuals, and, whenever possible, give them work that contains the type of puzzle they favor. 

I can provide an example from my own team. Dawn and Jim are both Senior Analysts. Sometimes, for fun, Dawn takes the logical reasoning portion of Graduate Record Exam practice tests. For fun, Jim completes the Sunday New York Times crossword every weekend. It takes him about twenty minutes. They both hire their job to give them puzzles to solve.  But Dawn and Jim don’t like the same kind.  Dawn likes the big, green-field, nobody-has-ever-solved-it-before kinds of problems. Jim likes small, knotty, Rubik’s-cube-like puzzle involving numbers.

Instead of assigning team members to new projects at random, I try to be conscious about allocating Dawn and Jim the kinds of puzzles each of them likes best.  I match the degree of difficulty to their different abilities, such that the challenges are difficult but not impossible. The easiest way to do this is to let team members select their own work. It’s part of my job as a leader to seek out and win new work that contains the most interesting problems, so that there are more puzzles to go around.

State clear outcomes and incremental wins:   Take the time to clearly identify the outcomes sought, so that successes are easy to see. This can often be achieved by following project management best practices, like drafting a charter that sets out clear objectives.   For those puzzles that take longer to solve, shine a light on incremental wins. Again, project management can provide tools by defining milestones along the way to the final solution. 

When a puzzle is not successfully solved, be clear about that too, because unsuccessful attempts sweeten successes that follow. Remember that failures are also part of pursuing more general solutions. 

Take a moment to admire the beauty of business problems. It’s there.  Look past the messiness of incomplete information, politics, and human weakness to identify the pure nature of the puzzles that work provides. Sometimes it’s necessary to incorporate messiness into the body of the puzzle. For example, if a person in one organization thinks she may have the solution to a particular problem but someone in another organization is blocking her ability to test it, that person can be perceived as either a hindrance extraneous to the puzzle or an unexpected part of it. The first is a frustration, the second can be seen as a new and interesting challenge. 

Problem solving spaces: Some environments are better for solving problems than others. Given the freedom to move, individuals will seek out good places for thinking: big white boards or quiet areas.  Provide a variety of spaces in which to work, and the freedom to work in different spaces, including beyond the walls of the organisation.  Betsy Boroughs, a consultant on innovation and the neurophysiology of insight, points out that solutions most often emerge from hidden parts of the brain when the conscious mind is idle. She actually runs innovation workshops on the train from San Francisco down the California coast to Santa Barbara. 

Henri Poincaré’s description of his discovery of the principle underlying the theory of automorphic functions is a great example of the situations in which the most difficult puzzles are often solved: 

Just at this time I left Caen, where I was then living, to go on a geological excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Countances, we entered an omnibus to go someplace or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’s sake I verified the result at my leisure. 

Seek a solution to the meta-puzzle:  In the first (and last) computer science class I ever took, we were given an assignment to write a program that would play the game of matchsticks against a human. To play, a row of matchsticks is laid out. Two players take turns removing one, two, or three. The player who must take the last matchstick loses. The game itself was of mild interest, intellectually on a par with tic-tac-toe.  But to write a program to solve for all possible game play – that was fascinating.  This is what I mean by a meta-puzzle.  Although many puzzles in the workplace may be too trivial to be compelling, every puzzle instance can be seen to be one of a type.  Directing our attention to solving for all puzzles of a type is more challenging. This can be designed into work by agreeing to write up best practices, or building a mathematical model of the problem space, or attempting to automate the solutions. 

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Dart Lindsley

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