[988]from "AH"-24 April 2003:
Hi,
I'm a post-graduate student at Rhodes University, Grahamstown, South
Africa. As part of the year's work I have a research project - the
automatic solution of jigsaw puzzles by computer.
Thus far computer puzzle solvers are not very capable: the largest
puzzle solved to date is a 204 piece puzzle (but, it only took 20
minutes, for comparison a 100 piece puzzle took 3 minutes). People have
been trying to solve this problem since the 1960's. Some non-scienticts
suggest that we shouldn't be trying to solve this problem as it 'defeats
the purpose of puzzle building' - But, puzzle solving is a very
interesting problem and impacts on a number of problems within computer
science, specifically artificial intelligence, computer vision, image
analysis, pattern matching, it also delves into computational theory.
What makes puzzle solving especially intruiging is that it has been
proven to be an NP-complete problem (as pieces are added the
computational complexity increases rapidly - a 500 piece puzzle is not
just 10 times harder than a 50 piece puzzle).
Most computer algorithms solve 'apictorial' puzzles - by analogy a
puzzle that is of a single color - most computer solvers also place
strict limitations on the shapes of pieces.
As an aside to my main research I am interested in attempting to develop
some means of classifying puzzles by difficulty. Thus far it seems that
the picture has the most impact, followed by number of pieces, and
cutting style (color-line, etc.)... I have seen some references to
'what makes a puzzle difficult', but there doesn't seem to be much
consensus or directed discussion. When a puzzle is produced it is
normally targeted at a subject audience (by age, for example) - is this
done completely subjectively, or is there some mechanism in place?
I would be most grateful if you could perhaps pose these question to
some of your puzzlers, or point me towards more information on the
topic.
Thank you,
"AH"
***************
I'm not sure that I or
many of our community will be able to help with the mathematical
side of this question, but we do have some opinions about what makes
a puzzle difficult! As you say, the pictorial content can make a
puzzle more or less difficult, and the number of pieces is an obvious
factor in difficulty. Many people find puzzles more difficult if
the pieces are all very similar in shape, less difficult if there is
great variety in shape. Color-cutting makes a puzzle more difficult.
There is a great variety of other "tricks" which the puzzle maker can
introduce to increase difficulty: extra pieces; irregular or unusual
borders; double-sided; double-sided with the same image on both sides,
but rotated! What are some other aspects of difficulty, folks?
Thanks,
Jim McW
***************
from Keith--28 April 2003:
Hi A.H.
Fascinating ! I wish you well.
The progress of the dissected educational toy into challenge puzzle has
provoked quite a bit of discussion among the collectors of older puzzles.
The early puzzles were of hand-cut wood and by studying the methods people
used to assemble them, then introducing deceptive devices to upset these
methods became a game between the cutter and the assembler.
So the first objective was to assemble the straight edges of the borders,
it is in fact very difficult to assemble a puzzle made up of straight edged
pieces, think of the well known plain small square puzzle that has been a
classic for hundreds of years and goes back well before dissected puzzles.
The corner pieces if cut at an angle can also be disguised, this was taken
even further and edges had V pieces introduced making it difficult to link
up the borders and straight pieces added to the centre area to further
confuse. Then straight borders were eliminated at first with wavy lines
then simply followed the shape of a cut out figure. Now that has gone one
step on with areas of the centre being cut out in the most challenging of
todays puzzles.
Shapes were made identical at first by stack cutting areas of the puzzle
together so that certain shapes became identical, this was taken to the
ultimate with cardboard press cut puzzles having all pieces identical in
shape, usually interlocking, in fact pushfit puzzles are usually more
difficult than interlocking.
Colour was at first divided into areas of similar shade the easy pieces
being the divide between contrasting colours, cutting between these divides
( colour line cutting) in some cases does make for a degree difficulty but
may not always succeed. I happen to find dark colours harder to assemble
than light, I am not sure how common this is but for sure light is a factor.
Some puzzles were double sided this could be a factor depending on how well
the reverse sides are matched, some modern puzzles have the same picture on
the reverse.
I almost certainly have left some important factors out and have ignored
number of pieces firstly because it is a mathematical factor and many very
small puzzles with quite few pieces can be much more of a challenge.
This may give you something to think about, I am sure some cutters will
think of other factors, I wish you success with your project and hope we
get to know your conclusions.
Regards
Keith
***************
from Nancy Ballhagen--29 April 2003:
Hi Jim,
I read the letter from So. Africa. For me the most difficult thing is pieces shaped the same, and
monotonous colors such as blue skies, lots of tree branches, leaves and that kind of thing. To
give you an idea of what I consider difficult, we did the Springbok stained glass puzzle and it
took 2 or 3 weeks, we actually put it away once to make room for Thanksgiving dinner, and didn't
get it out again for a couple of years. Another one was by Hoyle called Diamond in the Rough, it
was one raw piece of coal, and the rest was hundreds of sparkling diamonds, I thought it would be
fun and pretty, but sure wouldn't want to do it again. It is hanging in the "museum ceiling gallery"
of our puzzle store. I know some people like to do puzzles as a challenge and the harder the better,
I like to do puzzles for fun and have a nice picture when finished. My husband works mostly by
piece shape and he doesn't seem to care too much about the picture
unless it is one he really doesn't like. He is very good at it. Number one son Mitch likes photo
cityscapes mostly but will work at almost anything and is very good, I think he uses the shape
of pieces mostly.
Number 2 son Richard (RBPuzzles) is also very good and I think works mostly
by shape of pieces also. He also will do most anything. I bought him a hand cut puzzle made of
masonite the first time I went to a AGPC convention in Bloomington, In. I think I paid $5.00 for
it on the auction they had. The pieces were less than 1/2 inch and there must have been at least
1000 or maybe 2000. The pieces were almost all alike with a little knob then a v shape then
another knob, not really interlocking. Richard said it took a while but he finally got it done.
We are working on one now called "The Blue Staircase Maze" it is all very small staircases with
little doorways, rounded sort of like Southwest, and some people walking up or down the stairs.
There are a few potted plants and in many of the doorways and windows are lights otherwise it is
all blue. We used to carry it in the store (it was made by Golden) and always thought it would be
fun, not so. It has been on the table for more than a month and we have worked on it only 2 or 3
times.
I hope this gave you an idea on what puzzles we think are difficult.
Nancy
***************
from LA--1 May 2003:
I've been mucking about with some older
Springboks lately that I think are good examples of really tough puzzles... and of course Springbok
pieces are not quadrangular, which makes them tougher:
"FLAT BANANA"
- all the same shade of yellow
"ABOUT A MILLION MARBLES"
EQUIVOCATION ii
I've also included a picture of a puzzle from Buffalo Games billed as "The World's Most
Difficult Jigsaw". ("400 pieces; feels like 4,000").
"Devil's Dilemma"
It was designed by the former president of Tuco puzzles... It is two-sided, identical on both
sides, with one side rotated 90 degrees... What makes it more difficult than other puzzles of its
type is that, with most two-sided puzzles, you can tell by feel which side is which.... but these
pieces are cut in an alternating fashion, with the horizontal cut with one side up and the
vertical cut with the other side up.
Keep on puzzling (and thanks, Jim, for the forum)
"LA"
***************
Respond or comment (note inquiry number)
"Autumn"
print
"Sunshine and Shadows"
"FLAT BANANA"
"ABOUT A MILLION MARBLES"
EQUIVOCATION ii
"Devil's Dilemma"
