Gianni A. Sarcone - Impossible Folding Puzzles and Other Mathematical Paradoxes

A world without problems is an illusion, so is a world without solutions.

G. Sarcone

We often confuse inability with impossibility. Sometimes, even if we have all the necessary skills, the lack of sufficient information can kill our motivation to do something or solve a problem. Other times, it may be that our inability is due to the fact that some things are simply impossible to do. We learned at school that every problem has a solution, yet, though humans are remarkable problem solvers, there are problems that still remain unsolved.

When a child (or an adult) experiences many failures in a given area, a phenomenon known as cognitive dissonance starts to set in his mind. The child will then assume he is not (or is no longer) able to perform in this area, and eventually accepts this condition by hiding behind excuses such as anyway, its a useless waste of time!.

Curiously enough, a child (or an adult) who wrestles with paradoxical problemsthat is, deceptively easy problems that have no solution, or problems that seem at first impossible, but which have a very simple solutionwill put his or her supposed inability into perspective and will look at any upcoming challenge with new eyes.

Intriguing puzzles or magic tricks share a principle called violation of expectation; the more the solution or the magic trick is unexpected or unpredictable, the more the reader or the spectator will become involved and enjoy it! Surprise can actually be a powerful ingredient to stimulate interest and a motivator for learning.

Many problems of understanding in mathematics (not all!) can be reduced to a problem of attention or misdirection. We can draw a parallel between mathematical puzzles and conjuring--both share the same keystone element: attention! The stage magician, like the creator of puzzles, plays with our attention. His goal is to divert our attention so that we overlook the real procedure or technique that underlies the magic effect.

Neuroscientists liken our attention focus to shining a spotlight on something we pay attention only on what is lit, and lose focus on everything else. Magicians and puzzle authors exploit this tunnel effect to perplex us.

One of my inspirations in puzzle making was the French writer Anatole France, who said Awaken peoples curiosity. It is enough to open minds, do not overload them... Put there just a spark! I like to combine art, psychology, cognitive sciences, and recreational mathematics to test peoples ingenuity. I know by experience readers enjoy counterintuitive or paradoxical surprises!

As an author of recreational math games and problems, I particularly love those puzzles that look deceptively simple or that require very few pieces, giving the illusion they can be easily solved. Paradoxes, too, can be a creative tool. In fact, playing with paradoxes can sharpen attention, and foster focusing on the solution and not the problem.

I created or revisited the games and puzzles featured in this book. They are surprising in their effects and amazing in their simplicity. But it is precisely their simplicity that highlights some mental blocks or conditioning we put ourselves through while attempting to solve a problem.

My goal, as a puzzle creator, is to create a disjunction in the readers mindthat is a violation of expectaton that will stimulate and encourage him or her to think outside the box.