SERVING THE QUANTITATIVE FINANCE COMMUNITY

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: How long does it take to solve a jigsaw?

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: How long does it take to solve a jigsaw?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

Our town has a puzzle maker that specializes in puzzles with whimsy pieces such as these:

Paul
Topic Author
Posts: 10093
Joined: July 20th, 2001, 3:28 pm

### Re: How long does it take to solve a jigsaw?

Liberty Puzzles? I always think that calling things "Liberty This" and "Freedom That" as Americans are wont to do is virtually communist. It's the sort of thing the Russians and Chinese do.

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: How long does it take to solve a jigsaw?

Cool, does he have Escher tilings?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

There are no Eschers that I know of but there is a Pieter Bruegel (one of my favorite artists) puzzle of "Children's Games" in which many of the whimsey pieces are children playing which makes it hard to spot the painted bits of children playing.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

Liberty Puzzles? I always think that calling things "Liberty This" and "Freedom That" as Americans are wont to do is virtually communist. It's the sort of thing the Russians and Chinese do.
Yes, {Liberty, Freedom, Patriot} are magic incantations that if repeated often enough become true or at least they seems that way.

But aren't all countries forged from a combination of iron will and ironic slogans?

Paul
Topic Author
Posts: 10093
Joined: July 20th, 2001, 3:28 pm

### Re: How long does it take to solve a jigsaw?

And we used to use Imperial a lot! The default should be to name things after people, ideally me...something I practice!

Paul
Topic Author
Posts: 10093
Joined: July 20th, 2001, 3:28 pm

### Re: How long does it take to solve a jigsaw?

There are no Eschers that I know of but there is a Pieter Bruegel (one of my favorite artists) puzzle of "Children's Games" in which many of the whimsey pieces are children playing which makes it hard to spot the painted bits of children playing.
At those prices you aren't going to give up too soon!

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

There are no Eschers that I know of but there is a Pieter Bruegel (one of my favorite artists) puzzle of "Children's Games" in which many of the whimsey pieces are children playing which makes it hard to spot the painted bits of children playing.
At those prices you aren't going to give up too soon!
Indeed! Yet they are really nice puzzles made of laser-cut 1/4" wood.

And they are far cheaper on a $/hour basis than theatre tickets or Michelin-starred restaurants. outrun Posts: 4573 Joined: April 29th, 2016, 1:40 pm ### Re: How long does it take to solve a jigsaw?$125 laser cutter, your break even point is at 3/4 puzzles !

http://m.ebay.com/itm/281938936220

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: How long does it take to solve a jigsaw?

Here is a thought:
One possible puzzle is little rectangular tiles of various sizes that only fit in the square in one way (and its mirrors). This is probably equivalent to "bin packing" which is an NP-complete problem. Another classic NP-complete problem is 3SAT which is about finding boolean values for variables (x1=true, x2=true, x3=false) such that a sequence of clauses involving those variables are all true. This can likely be translated into puzzle shapes that have to match.

All these NP-complete problems are equivalently hard with no known polynomial time algorithm (only exponential). There will always be special cases that require exponential time'and If you can solve any NP-complete problem in polynomial time then you can solve *all* of then in polynomial time.

So IMO jigsaw is NP-complete and you won't be able to find a polynomial time algorithm.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

Standard jigsaws only become NP-complete if the solver cannot reject a prospective solution with bounded M<<N pieces. That is, the solver faces a non-zero chance of placing N-1 pieces in what seems like a valid configuration only to find that the last piece fails to fit.

For most jigsaw puzzles, however, the piece shape and color patterns across the boundary are so unique that it's virtually impossible to incorrectly put even two pieces together.

That said, I have seen puzzles with identically-shaped innie & outie tabs (and large expanses of uniform color) where one can get trapped and have to undo a set of pieces that seemed to go together.
Last edited by Traden4Alpha on January 11th, 2017, 10:33 pm, edited 1 time in total.

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: How long does it take to solve a jigsaw?

Yes, good insight, the common puzzles are incrementally solvable and way to easy, there is an opportunity here!

this fractal puzzle looks difficult, very confusing.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: How long does it take to solve a jigsaw?

Yes, good insight, the common puzzles are incrementally solvable and way to easy, there is an opportunity here!

this fractal puzzle looks difficult, very confusing.
Love that fractal puzzle!

One of the ancient versions of the Macintosh OS (maybe System 8. something?) came with a simple digital jigsaw puzzle that let one pick N. These days, with multi-finger touchscreen UIs and data logging systems, one could create an even better digital jigsaw puzzle system and gather empirical data on solver performance as a function of N.