Arlie's Blog
Wednesday, 21 December 2016
Unpuzzling Puzzles
Mood:  quizzical
Now Playing: The Uncomfortable Pastor
Lately the luxury of thinking about assembling jigsaw puzzles has been mine.  For example, I placed on Facebook a request for the formula that serves to clarify exactly how many successful connections a person must make with any given puzzle in order to completely assemble it.

One’s mind can go far astray by considering that corner pieces (at least in a rectangular puzzle) typically have two straight sides that require no connection.  And all the other edge pieces have one straight side.  Then you can take a piece from the middle and connect it to four other pieces.  Each of those four pieces will now have three sides exposed (at least where pieces are four-sided), but one needs to be careful here, because two sides may be used up by one connection.  So it all becomes very confusing.

Really, the formula is quite simple.  C (number of connections) = P (number of pieces) - 1.  There you have it.  You can check this out with a very simple puzzle of, say, nine pieces.  One does need to be careful to find the exact number of pieces.  Right now I am working on one whose box says 1000 pieces, but the actual number is 1026.  So 1025 is the minimum number of connections that will complete the puzzle.

This particular puzzle is challenging, and I am assembling it without referring to the picture on the box.  But a question came to mind:  Why is it that for a period of days I can look at a group of pieces that by color will fit into the same general area and have very little success then, but another day I will approach the puzzle seeing where they fit and having great success?  I have been pondering this and will offer a few suggestions.

One answer might be that the number of possibilities is dwindling.  With this particular puzzle I did the edges first and then proceeded from the top down--sky, vegetation, water, etc.  So by the time this difficult area became doable I had used almost half the pieces.

Another answer might be that by now I have looked at the pieces long enough, even one by one, that suddenly in my mind the picture is coming together.  My brain is recognizing the familiarity of each piece.

Another answer might be that in order to assemble a puzzle, you have to have something to which you might attach something else.  That something was not there earlier in the process, but now that it has been established by working down from the top, there is more of a context for the current stage which previously was not well established.

Another answer might be that the food I ate or the exercise I took predisposed me better for puzzling on that day than on other days.  This may be difficult to prove (but then so are the others).  Maybe a certain emotional state is better for puzzling.  I don’t know, but the phenomenon is curious.

And that is it for my current state of considerations on puzzling.

Posted by turbooster at 1:25 PM MST
Updated: Sunday, 15 January 2017 9:59 PM MST

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