Jigsaw Completion Strategies: Jigsaws — they ain't for wimps
by J. Zimmerman, Sorter and Inner Joiner
on the Mandala 1000-piece Jigsaw-Puzzling Team.
Index
Strategies
In general:
- Get a table top big enough for the size of the finished jigsaw!
Better still, get one at least twice the size, to hold piles of sorted pieces!
- Pick out and pile up similar pieces -- the edges, pieces with particular colors or lines or
patterns. Try to enlist others to help with this process! Channel your Inner Sorter.
See
extra sorting for speed edging.
- Make serendipitous joins as the piles start accumulating.
- After you reach a 'large enough pile' of edge pieces (or can't bear to wait any longer),
start joining the edges.
The easiest thing to do is the edge: let anyone else be
the Edge Joiner (the one to focus on edging).
In particular, award this role to the youngest person or any person skeptical that this is a delightfully
rejuvenating game.
Once the Edge Joiner rises to the Edge Challenge, excitement builds
as the edge lines form, start to be positioned correctly (on top, bottom, and sides), and get joined together.
- If you're lucky enough to have a team, the person with the strongest
Inner Sorter can keep sorting the pieces in the box and
putting pieces into relevant piles on the table. The more pieces get put into those
piles, the fewer pieces need to be sorted through.
- Meanwhile, an Inner Joiner can take any of the piles and begin constructing
internal patches of the puzzle.
- If your team has a Master Joiner, they will resist such useful strategies as
doing "Edges First" or sorting pieces. Tell them to get their own 2000-piece puzzle and
their own table, and challenge them to finish before you.
They probably will ... but you will have more fun.
- Mid-game:
- Take lots of snack and refreshment breaks.
- Switch with someone so you can work on a different activity or part of the puzzle.
- Put in some couch-potato eye-resting time while the rest of the team continues.
Be sure to praise them when you return (despite your secret conviction that you could have made a lot more progress).
- Leverage the established lines and sections, finding patterns that connect to them.
- End game (last 25%) of a difficult puzzle requires the Geek's Approach: shape-sorting.
The Inner Sorter (or the Inner Compulsive)
comes into her own for the trickiest areas:
she can sort each pile of same-color-pattern shapes by "innies"
and "outies":
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% |
- The final piece: right to put in the final piece is traditionally obtained some
secret action early in the game, such as:
- Slipping a piece into your pocket. Traditionally this is done by each
participant, and at least one of those pieces ends up in the laundry a few days later.
- Dropping a piece on the floor and then "finding" it at the end.
Use of the cover picture
Some Joiners find the cover picture extremely helpful to solve the puzzle:
- Especially when puzzles get large (to quote skilled Joiner R.H.):
"anything that contributes to their
completion is fair game (provided the pieces are separated and randomized first)".
- The cover picture can be particularly valuable initially for
positioning the edges correctly.
- However, for the most part, use of the cover picture seems to slow down this Joiner:
but she is happy to have others use it.
Extra sorting for speed edging
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.
Multi-box Strategy
A really great addition to the sorting technique is:
- Acquire three or four small cardboard boxes (like check books are mailed in).
- When sorting the pieces initially for the edge pieces, assign to the boxes whatever look like vast swathes of fairly similar colors:
one for sky, one for water, one for grass, for example.
- Obviously, in addition to pulling out the edge pieces, pull out any pieces that are of striking difference from the rest of the picture
— the leopard, the pink spoonbill, and the warrior maiden are likely candidates.
- Once your team has got the edge in hand and the leopard and similar, your small boxes will probably contain less than 200 pieces each (for
a 1000-piece jigsaw), with a small bunch of "mystery meat" pieces left over in the main box for the end game.
It is so much easier to find one piece in 100-to-200 than one in 1000.
Bottom line: Time to complete
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)
|
Biopsychology.
