The experienced jigsaw player uses several clues to speed the solving rate.

In particular, finding edges and corners can greatly increase the rate of progress, since to a first approximation it divides one large pile with n*(n-1)/2 piece combinations into two piles, with m*(m-1)/2+(n-m)*(n-m-1) combinations. For example, for a 1,200 piece (40 by 30) jigsaw there are naively 1200*1199/2=719,400 piece combinations, whereas if pieces are sorted into sides and centres there are 40*2+(30-1)*2=138 sides (and corners), with a mere 9,453 combinations which can be performed first, leaving a sub-puzzle with only 563,391 piece combinations.
The centre would then generally be solved by attempting to divide-and-conquor in other ways, such as comparing pieces with similar overall colour or other obvious details.

Clearly, these practices must be stamped out. Therefore the maximal difficulty jigsaw attempts to confound these expectations:
* The edges of the jigsaw also carry knobbles.
* The shape of the jigsaw as a whole is not rectangular.
* The pieces are not designed to a regular grid.
* The image used is carefully chosen not to have any large, easily distinguishable areas.
* A fraction of the pieces do not have a knobble on one side - these are usually (but not always) internal.
* Where possible, piece edges follow significant boundaries of the image, and 'obvious' details are entirely contained within a piece.

-- Loris, Mar 04 2012

is knobble a word? http://dictionary.r....com/browse/knobble
Knobble : /noun/ a small knob. [Loris, Mar 04 2012]

Impossipuzzles http://www.google.c...0l0l0l0l43l81l3l3l0
I think they don't have 'edge' or 'corner' pieces either. [neutrinos_shadow, Mar 05 2012]

Shmuzzles http://shmuzzles.com/
The pieces have the same salamander shape. [AntiQuark, Mar 05 2012]

is nobble a word?
-- po, Mar 04 2012


//these practices must be stamped out. // As, indeed, are jigsaw puzzles.
-- MaxwellBuchanan, Mar 04 2012


Research in the jigsaw labs appears to be leading to "silly putty" pieces, that not only have flexible shapes, but can have their image shifted as well.
-- normzone, Mar 04 2012


For Loris: a gift - the un-jigsawed Puzzle.
It consists of perfectly square featureless black tiles. These tiles have no obvious orientation, even front and back. Internally, they contain RFID chips and sufficient circuitry to identify their neighbors. When queried, each chip will report whether it has the appropriate neighbor on each of its sides (or no neighbor, if *that* is appropriate to the tile). A scanner queries each of the tiles, and if they all are correct, the scanner beeps, blinks a green LED, says "Yes", or other congratulatory message. Any other configuration says "No", so you get only a single bit of information from each arrangement attempted.

As you lay out the n tiles, there are n! orders to lay them in (I will grant that you know the finished dimensions in advance, such as square, or 1*n, or whatever), and there are 8 different orientations in which each piece can be laid. Therefore, there are 8^n combinations of orientations, yielding 8 possible orientations for the final completed puzzle. So your chance of getting it right are 1 in n!(8^(n-1)).

For Loris, I think the 4x4 piece puzzle should suffice: your odds are around 1 in 7.4x10^26.
-- lurch, Mar 04 2012


There was a puzzle back in the '90s that was billed as 'the world's most difficult' jigsaw puzzle; it was a big red circle with about 2000 pieces or something, and a number of them were nearly identical in shape. I remember thinking that a puzzle with no discernable edges would be even more difficult.
-- Alterother, Mar 04 2012


//is nobble a word?//

It is, but it's the wrong one! Fixed.

I should say that the idea is not to make the puzzle practically impossible, but rather to challenge jigsaw enthusiasts in an interesting way. There still would be logical clues available to make the problem solvable, just not the immediate ones they're used to.
-- Loris, Mar 04 2012


is knobble a word? finial has a classier sound to it.
-- po, Mar 04 2012


//not to make the puzzle practically impossible// ok, I took you a bit too literally on "maximal difficulty".
-- lurch, Mar 04 2012


Sounds sort of like the Eternity II Puzzle.
-- AntiQuark, Mar 04 2012


[lurch] The puzzle you described is not, in fact, the most difficult possible jigsaw. The minimum- information jigsaw would be like yours, except the user wouldn't know the value of "n" (total number of pieces) beforehand.
-- mouseposture, Mar 04 2012


I believe edge-less jigsaws already exist
-- simonj, Mar 04 2012


Can't find it but I'm pretty sure I've seen an edgeless puzzle of popcorn like this.
Completely maddening.
-- 2 fries shy of a happy meal, Mar 04 2012


I've heard of edgeless puzzles with a few superfluous pieces thrown in. Diabolical! I've also seen puzzles where there are no edges and every piece is the identical shape with the only clues being the image which is usually something like a mass of earthworms or such.
-- AusCan531, Mar 05 2012


There are existing puzzles with (IIRC):
No edge or corner pieces
Repetitive image (see linky)
A few extra pieces (as per [AusCan531])
The same image printed on the back of the pieces (rotated 90 degrees I think)

There's also the Wasgij, in which the image on the box is not (but is related to) the image on the puzzle.
Not a grid-pattern or rectangular would be good and tricky.
-- neutrinos_shadow, Mar 05 2012


Have the pieces non-interlocking, and with tiny solar-powered wigglers on the bottom so they slowly wander across the table when you're not looking.
-- pocmloc, Mar 05 2012


Cockroach jigsaw puzzle: if you don't finish it in one sitting, all of the loose pieces crawl away and hide under the fridge. At night, they come out and assemble themselves on the kitchen floor, but they scatter when you turn on the light.
-- Alterother, Mar 05 2012


An M.C. Escher puzzle with pieces shaped like one of his metamorphosis drawings would be cool.
-- RayfordSteele, Mar 05 2012


//no edge pieces...// One way to guarantee that you never finish the puzzle - every month you receive, in the mail, an envelope containing a few more pieces which expand the puzzle just a bit.
-- lurch, Mar 05 2012


Of course, you are describing a jigsaw *puzzle*. A maximum difficulty jigsaw could have a blade made of silly putty, etc.
-- spidermother, Mar 05 2012



random, halfbakery