Jigsaws & problem-solving

Do you enjoy doing jigsaws� or have you long given up such �childish� pursuits?  If you have not recently frantically forced �lug� into �eye� then I am not sure that I should really be encouraging you to take up the habit.  There are those who describe the pastime as therapeutic, an escape from the pressures and stresses of everyday life.  However, I am only too aware that the element of competitiveness that a jigsaw engenders can lead to its own particular brand of stress, not to mention the strain placed on a relationship if you attempt to solve a puzzle with someone else.  After all, it�s unlikely that you�re so well matched with your puzzle-partner that you will both want to employ the same jigsaw-solving strategy.  There are just so many different ways that you can set about those cardboard pieces.

Initially, with the pieces newly tipped from the carton and the dust blown away, first moves are deceptively reassuring.  Almost everybody (although there are still a few obstinate exceptions) agrees that a useful first move is to sort out all the pieces with a straight edge.  When sorted, you reason, these will help to delineate the boundary as well as providing some basic reference points for later.  Don�t be fooled.  Although �almost everybody� agrees that this is a good idea, the manner of execution remains a potential minefield.  Die-hard theorists will want to persist with sorting until every last straight edge has been found � and only then start to connect them into a frame.  Activists, on the other hand, are desperate to fit bits together, come what may, clutching at each new �straight edge� as it is discovered, pressing it into service (with sometimes undue force) so that a framework can be established as soon as possible.  I am still not sure whether either of these approaches is more or less helpful than the reflective approach that spends the first half hour studying the picture on the box-lid.

But it is only when the straight edges have been finally rearranged from frantically lop-sided to regular rectangular that the fun really begins.  Or should that be �feathers really fly�?  What strategy now?

There are those who work steadily inwards from the border, each successive new line of pieces gradually reducing the expanse of bare table-top until the last few square inches are filled with a sudden flurry of activity occasioned by the ever-increasing simplicity of the task.

Then there are those who focus attention on particular parts of the picture � �the beach then the boats then the bathers� � so that eventually, though they may be left with all the indiscriminate pieces, there are relatively fewer places for them to go.

Still others will sort out all the pieces that show a particular colour, albeit such pieces may well relate to red flowers, red coats, red noses, red sails in the sunset, red rag to a bull!  Red is closely pursued by blue, green, yellow, etc.  Their rationale is that such pieces are easy to find and that, once connected, these colourful splashes will form little islands just waiting to be joined.  I suspect that this particular strategy has a lot more to do with prettiness than its exponents would care to confess to.

As if we have not already considered enough differing approaches to make your head spin, we have yet to examine the graphical co-ordinates system.  Devotees of this particular procedure take random pieces from the pile and, after scouring the picture to identify its precise orientation and position, place each piece meticulously in place by means of a grid reference system.  (�Level with the soldier�s eye and as far to the right as the horse�s tail.�)  Eventually (and somewhat beyond the endurance limit of the average activist), there are sufficient pieces in place for some of them to actually join up, �Oh frabjous joy!�  Unless the system is rigorously applied, there are also likely to be a considerable number of pieces mere millimetres apart � desperately yearning to be conjoined to their prospective partners � but frustrated by the inaccuracy of a puzzler�s judgement.  Unless, of course, you actually go the lengths of drawing a co-ordinate grid on the box-lid and a corresponding grid on your baseboard.  Honestly, I�ve seen it done.

Then there are those who actually seem oblivious to the picture so carefully pasted to the front of each piece, relying rather on the shape of the piece to determine what joins to what.  Whereas this might be a necessary tactic when dealing with expanses of sky, it can be somewhat annoying to have to point out that the Queen does not normally have a feather up her nose and that corgis do not often wear tiaras.

So we come to the $64,000 question.  Which is best?  Does one particular method have the edge over the other strategies?  Is any one of these procedures likely to guarantee a swifter or more satisfying conclusion to the puzzler�s task.  It will, I suggest, depend on who you ask.  No doubt there are those who would be prepared to go to war (and may actually have done so, albeit only a family war) to defend their particular course of action as most suitable.

I would suggest that each of them has their benefits � and their drawbacks.  Even the (almost) universally agreed �straight edges first� approach is not a lot of use if you are trying to complete one of the new circular puzzles � though it is fairly easily adapted.  This apparently clear-cut first stage is considerably less useful if you are tackling one of the multiple-straight-edges puzzles.  Made up of frames within frames within frames these puzzles have more straight-edged pieces than the conventional �lug and eye� type.  It is a strange (but necessary) move to sift out all the �un-straights� as a starting point.

Similarly, the colour co-ordinated approach is not a lot of help when confronted with pictures of baked beans � or dice � or jigsaw puzzle pieces!  (Do designers of jigsaw puzzles have consciences?  How can they sleep easy in their beds?)  Neither is the graphical co-ordinates procedure a barrel of laughs when you have to contend with vast expanses of sky!

So, it�s �horses for courses� � which is the point I am trying to make.  Whether we are solving jigsaws � or any other kind of puzzle � we need to have in our armoury a range of different weapons that can be deployed, depending on circumstance and personnel as well as upon the nature of the problem to be solved.

So we need to develop logical, step-by-step problem-solving skills � as well as less structured brainstorming and creative thinking techniques.  We need analytical approaches � and �guesstimates�.  We need reason and intuition.  We need, above all, to be aware of the variety of approaches available to us � and a readiness to adapt.

In closing I should also mention some of those other time-honoured jigsaw-solving techniques that I have overlooked to mention until now.

The random matching technique (much favoured by 7-year-olds) involves picking out two random pieces from the pile to see if they fit together.  If not, they are tossed back disparagingly and another two pieces selected.  If they do match, then you would be well advised to purchase extra lottery tickets this weekend � because with that kind of luck you cannot fail.  Then there�s spreading out all the pieces on the coffee table until they gather enough dust to look as if some of them are actually connected.  Then there�s throwing the whole thing in the bin � or seeing what�s on the telly � or watching paint dry �