Tuesday, January 16, 2018

Jigsaw Puzzles

We have a family tradition of doing jigsaw puzzles over the winter holidays, going back at least a decade. My 3 daughters are always involved, my wife usually, my son sometimes, me not so much.

Last year I screwed up - I bought 3 2000 piece puzzles. 2000 pieces is too many - very little progress was made.

So this year, I bought a 1000 piece puzzle that my wife and I had seen at the Portland (OR) Fine Arts Museum when we were visiting our daughter in Oregon in August. I didn't want to fly the puzzle home, so I took a picture of it, found it on Amazon, and had it shipped to FL.

There was also a suggestion to get a 500 piece puzzle, so I got one of those from Amazon as well. And finally, my son and his wife gifted another 1000 piecer.

The 500 piece puzzle was titled "Barcelona". My 3 daughters made short work of it, finishing it in an afternoon.

Next up was the 1000 piecer from our son, "Wanderer's Cove". It was interesting in that it was based on a night scene. My wife and I did it in around 4 days.

I figured I'd go on and do the other 1000 piecer. (Yes, I am definitely retired). It took me 11 days. Its title is "Geometric Herb Garden".

Doing it on my own, I payed attention to the solution algorithm:
  1. Sort the interior pieces by color and pattern while sorting out the edges and corners. Both 1000 piece puzzles I missed 3-5 edges during this sort.
  2. Put the edges and corners together.
  3. Add interior pieces based on the most distinct patterns and colors. The garden puzzle has ~42 different patterns/regions. Because the puzzle has perspective, the top (further away) sections were less distinct and harder to match.
  4. Finish it off - when you have mostly only a few colors left - by sorting the remaining pieces into the 6 shapes of interior piece and matching based on shape.
The picture below shows the 6 shapes of interior pieces and the 4 shapes of edge pieces. The number at the start of each row is the number of "outies" on the piece, the number over each piece is the number of unique rotations of that piece. There are 16 total interior piece rotations (2^4) and 8 total edge piece rotations (2^3). Corners can have 3 shapes: 0, 1 (2 rotations), and 2 outies - 4 rotations total, 2^2; the garden puzzle had all 4 corners as 1 outie pieces.

So in step 4, a completely enclosed missing piece can be matched by only 1 shape. A missing piece enclosed by 3 pieces can be matched by only 2 shapes; bordered by 2 pieces, 3 shapes; bordered by 1 piece, 5 shapes.

Ha ha, yes, I am definitely retired. Plenty of time to fiddle with numbers. I'm sure there is much can be learned about jigsaw puzzles - say from this very informational Wikipedia article - around since 1760, who knew? - but it is nice to not have to be serious about everything.

Oh, I almost forgot. I took a picture of the garden puzzle every day and then used Gimp to create an animated gif. I didn't do a very good job, but here it is nonetheless.

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