Outside the Box: From Sudoku to recreational mathematics

By Moristotle

Hardly anything calms me more than sitting down alone in a quiet place to solve a fresh Sudoku puzzle. At least, it calms me when I don’t screw up the puzzle. Let me recast the opening statement: Hardly anything calms me more than sitting down alone in a quiet place and flawlessly solving a Sudoku puzzle.

    The calming effect puts me in mind of that scene in Claire Danes’s 2010 biopic film, Temple Grandin, in which she portrays the calming effect on [the autistic] Ms. Grandin of confining herself in a “hug box” when she is feeling anxious. Sitting down to a fresh Sudoku puzzle is for me perhaps like confining myself in Temple Grandin’s hug box.
    I thought of that scene recently upon reading the NY Times article “The Importance of Recreational Math” (Manil Suri, October 12, 2015​). Although the author acknowledges that “‘recreational math’...can broadly include such immensely popular puzzles as Sudoku,” he seems inclined to exclude Sudoku because it “always has the same format and gets easier with practice.” He favors “disparate puzzles that...require different, inventive techniques to crack [emphasis mine]. The solution in such puzzles usually pops up in its entirety, through a flash of insight, rather than emerging steadily via step-by-step deduction as in Sudoku.”
    And he provides an example, which I in turn provide to you: “How can you identify a single counterfeit penny, slightly lighter than the rest, from a group of nine, in only two weighings?”
    ...
    Not got it yet?
    ...
    Ah, that’s more like it! Nice! In its own way perhaps as calming as flawlessly solving a Sudoku?

The NY Times article extols Martin Gardner’s “Mathematical Games” column, “which ran in Scientific American for more than 25 years, introduc[ing] millions worldwide to the joys of recreational mathematics.”

Mr. Gardner’s great genius lay in using such basic puzzles to lure readers into extensions requiring pattern recognition and generalization, where they were doing real math. For instance, once you solve the nine coin puzzle above, you should be able to figure it out for 27 coins, or 81, or any power of three, in fact. This is how math works, how recreational questions can quickly lead to research problems and striking, unexpected discoveries.

“Unexpected discoveries” – that seems to be the rub. And the idea behind this new recurring column, “Outside the Box,” is to highlight areas in life where we may be overly inclined to restrict ourselves to one box or another precisely for the sake of rendering the world “expected” to ourselves, to protect us from being (unpleasantly) surprised or disturbed by ideas that we aren’t comfortable with. Such boxes abound, in the forms of

• habitual thinking patterns, modes of communication, transportation, economy, entertainment, diet....
• automatically following the ways or traditions of one’s own family, tribe, peers, neighbors (such as the Joneses), political affiliations, religious affiliations, city (like Pamplona, Spain’s barbaric “running of the bulls”)....
• adopting the opinions of experts who are widely regarded as authorities, like forensic scientists, medical doctors, financial advisers....
• “impersonal” psychological factors that have some influence on almost everyone, like confirmation bias, wishful thinking, the tendency to skew perceptions to minimize cognitive dissonance....

    Those boxes aren’t necessarily comforting, or comfortable to be in - or the results of acting from within them may not be comfortable. (Or it might not be comfortable being prevented from acting because one is in them.) Wishful thinking, for example, can land you in various fantasy lands. And the following assortment of boxes can be quite uncomfortable, for both oneself and others:

• personal psychological factors, like inflated or deflated self-image, addictions, procrastination, “writer’s block,” neuroses, even psychoses....

We invite you to consider that our first offering of “Outside the Box” might be to help you discover that you can put a little excitement in your life simply by trying a new kind of puzzle.
    In today’s googly world, you don’t even need to buy anything. Just google on “math puzzles.”
    (And you can go outside that box and think of other phrases to google on. There are lots of places outside boxes!)

[Note: With graditude, I acknowledge Jim Rix’s suggestion of the name for this column, which grew out of our discussions of the possibility of a column that would be science-oriented. And thanks to Jim, and also to Vic Midyett, for their contributions to the bulleted list of sorts of boxes that we humans are prone to.]

Copyright © 2016 by Moristotle