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Jigsaw puzzle solving

I got involved in a Facebook conversation with a friend from HS about jigsaw puzzle solving. I hate to post long comments on Facebook where I'll never find them again, so here's my take on this. Enjoy…

One cool thing about being human is that if you do some task several times, you pretty much can't help learning how to do it better. Doesn't matter much how "smart" or knowledgeable you are, or really even whether you're paying attention. It just sort of happens. Jigsaw puzzles are a great example of this.

Most of the jigsaw puzzle solving rules are fairly obvious, and I'm horrible at solving them, so I won't presume to tell you how your jigsaw solving should be done. However, here is an example of a less-obvious rule you can think about...

At any given time, you will have some "corners" to fill, in the sense of a place where you need to place one piece that will contact two or more other already-placed pieces. In a typical non-fiendish interlocking jigsaw, most pieces will have four edges, and each edge will be either a "tab" (sticky-out bit), "blank" (place to put a tab), or "flat" (just a straightish edge). Assume that you have started by building the frame, so that any flats are interior.

OK, start by separating all the pieces with flats into their own area. Put the pieces that aren't really four-sided in this pile also. Typically, there won't be so many of those. Next, separate the remaining pieces as follows:

  • Pieces with no tabs.
  • Pieces with one tab.
  • Pieces with two adjacent tabs.
  • Pieces with two opposite tabs.
  • Pieces with three tabs.
  • Pieces with four tabs.

You now have seven different collections of keyed pieces. Depending on the shape of the corner, you can look in just a few piles for a needed piece. If the corner is blank-blank, then look in the no-tab, one-tab, two-adjacent-tab, and irregular piles. If the corner is tab-tab, look in the four-tab, three-tab, two-adjacent-tab and irregular piles. Otherwise, look in the one-tab, two-opposite-tab, three-tab and irregular-piles.

The cool thing about this plan is that sections you build from color and texture of the puzzle picture typically have lots of corners, and these corners are typically bland-looking and hard to find. The sorting technique described above will help you narrow down on exactly the pieces you need.

Have fun! Fob

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