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In general:
Pieces are not always 4-sided, but usually they tend to be, giving these combinations of "innies" and "outies":
Side 1 | Side 2 | Side 3 | Side 4 | Total 'In' |
In | In | In | In | 4 |
In | In | In | Out | 3 |
In | In | Out | In | 3 |
In | Out | In | In | 3 |
Out | In | In | In | 3 |
In | In | Out | Out | 2 |
In | Out | Out | In | 2 |
Out | Out | In | In | 2 |
Out | In | In | Out | 2 |
In | Out | In | Out | 2 |
Out | In | Out | In | 2 |
In | Out | Out | Out | 1 |
Out | Out | Out | In | 1 |
Out | Out | In | Out | 1 |
Out | In | Out | Out | 1 |
Out | Out | Out | Out | 0 |
On average, then, some pieces are more rare:
If pieces had random distribution
of 'innie' and 'outie' sides | 0 'In' | 1 'In' | 2 'In' adjacent | 2 'In' opposite | 3 'In' | 4 'In' |
Average number of 16 pieces | 1 | 4 | 4 | 2 | 4 | 1 |
Average percentage of 16 pieces | 6.25% | 25% | 25% | 12.5% | 25% | 6.25% |
In particular, if you find a slot that needs "4-innies" or "4-outies" you'll only have a couple of options in a pile of 30.
More practically, when filling in, you can count on only a few places where two adjacent sides have been completed.
However, if there is an excess of the traditional jigsaw shape (two opposite innies and two opposite outies), the one-innie-one-outie-corner combination is particularly common: Even if a space has more than one side completed, it will usually have a large number of candidates to pick through, making it time-consuming to fill. This hazard befell for the blue-sky of the Bavarian puzzle a quick count of the final 97 pieces of blue sky showed that the "2-opposite-innies" format appeared with over four times the random probability: this is disastrous for speed in shape-fitting in the end game:
Blue sky of
the Bavarian puzzle
(97 pure-sky pieces). | 0 'In' | 1 'In' | 2 'In' adjacent | 2 'In' opposite | 3 'In' | 4 'In' |
Number of 97 pure-sky pieces | 0 | 23 | 9 | 47 | 15 | 3 |
Average percentage of such pieces | 0% | 24% | 9% | 49% | 15% | 3% |
Some Joiners find the cover picture extremely helpful to solve the puzzle:
If you are puzzling with either a very inexperienced puzzler (who is happy to do ANYTHING helpful) or else an over-the-top Compulsive Inner Sorter, then the shape-sorting (so useful for the end game) can also be applied to the edges.
While an edge piece has (by definition) one smooth side, these are the combinations of "innies" and "outies" (for the typical approximation of 4-sided pieces):
Side 1 (edge) | Side 2 | Side 3 | Side 4 | Total 'In' |
Smooth | In | In | In | 3 |
Smooth | In | In | Out | 2 |
Smooth | In | Out | In | 2 |
Smooth | Out | In | In | 2 |
Smooth | In | Out | Out | 1 |
Smooth | Out | Out | In | 1 |
Smooth | Out | In | Out | 1 |
Smooth | Out | Out | Out | 0 |
On average, then, some pieces are more rare:
0 'In' | 1 'In' | 2 'In' | 3 'In' |
1 | 3 | 3 | 1 |
In particular, if you find a slot that needs "3-innies" or "3-outies" only one-in-eight will fit either slot.
However, because the edge pieces are usually the first to be added, the shape of the side opposite the edge-side tends to be unknown. So, four (not eight) sorting groups are useful:
Side 1 (edge) | Side Left of Edge | Side Right of Edge |
Smooth | In | In |
Smooth | In | Out |
Smooth | Out | In |
Smooth | Out | Out |
On average, then, one in two of the edge pieces can fit any other single piece. And one-in-four of the edge pieces can fit between two particular edge pieces.
Bottom-line advice: Don't bother with this step unless you need to keep other hands busy ... or you are doing the dreaded Magritte's Castle in the Air, the world's most evil jigsaw.
A really great addition to the sorting technique is:
Time to complete increases with difficulty of puzzle and decreases with experience of puzzlers both in general and with the particular puzzle at hand. Here are some sample numbers:
Pieces | Subject | Team size | Work-hours taken | Pieces per work hour | Comments |
1000 | New to all participants: Mandala | 3 | 27 | 37 | Somewhat like a jigsaw of a Pollack. |
1000 | New: National Geographic Bavaria; | 1 | 10.3 | 97 | Helpfully the shapes are irregular. The multi-box strategy was useful. Everything was going so well until the pure-blue-sky endgame, when the rate fell to about 50 pieces per hour for the last 100 pieces (due in part to similarities of piece shapes). |
499 (1 of the 500 pieces has been missing for 49 years) | 50-year-old QE II coronation (circular) jigsaw | 1 | 2.3 | 217 | Familiar (done several times previously) |
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