Mechanical puzzles
Mechanical puzzles have been around for centuries. What makes a
great mechanical puzzle is that it looks simple but is difficult
to solve. A good example is the classic puzzle consisting of two
twisted linked nails which one must unlink.
On first glance one expects to solve it in seconds. But many
people find it much more difficult than it appears. Such puzzles
are simple and complex at the same time.
Computer assisted design
Quzzle is not an ordinary puzzle. Quzzle takes the idea of
making a complex simple puzzle a step further by using a
computer to assist in its design. Inventor Jim Lewis, set a goal
of creating the most difficult simple sliding block puzzle in
the world*.
Just $19.95
Programming the solution
After more than a month of programming and running his programs,
Mr. Lewis arrived at a puzzle that is more difficult to solve
than any other of its type. Yet it has just nine pieces. Mr.
Lewis knows his puzzle is the world's hardest of its type as
his computer considered every possible puzzle among ten's of
thousands, each having an often long sequence of moves.
(Puzzle enthusiast's Henderson and Dogon discovered a small bug in the
program that created Quzzle, resulting in a slightly different starting
position that adds a few moves. See if you can discover it after solving
the classic Quzzle.)
* Types of puzzles considered
Mr. Lewis considered puzzles consisting of blocks one by one,
one by two, and two by two in frames up to four by five; where
the objective is to move the largest piece from one specific corner to
another specific corner. Analyzing small frames of size 3x4 and 4x4 he found
even the hardest configurations nearly trivial to solve. He also
concluded that frames larger than 4x5 are too hard to solve and
take too much computer time to analyze, due to a problem called
combinatorial explosion. He also found blocks with a dimension
larger than two grid lock puzzles of such sizes.
Theory of sliding block puzzles
For those interested in some of the computer theory of sliding
block puzzles, it has been shown that sliding block puzzles are
in a class of problems that are the most difficult even for a
computer to solve. These types of problems are called PSPACE-complete.
In fact sliding block puzzles can themselves form an unusual
type of computer. What does this mean? For example, one could
devise a sliding block puzzle that "computes" whether a certain
number is a prime number, by having a solution if the number is
prime and not having a solution if the number is not prime. It is
a rather bizarre diversion in the world of computer science. |
Programming language
Mr. Lewis wrote the Computer Assisted Puzzle Analyzer (CAPA)
software in Haskell, a so called "Functional" programming
language. He went through numerous revisions of the program to
allow computation of a solution in an acceptable amount of time.
The first version would have taken years of computer time to
complete. Subsequent versions progressively reduced the needed
computer time by making the program more and more efficient.
Solvability
It is common for puzzle goers to reach a point where they are
certain there is no solution. In fact Mr. Lewis tried to solve
the final puzzle generated by his program and at first concluded
the puzzle was unsolvable. He thought there was a bug in the
program. He had an assistant go through the computer solution to
verify that the puzzle really was solvable. Sure enough, the
puzzle was indeed solvable.
Dad's puzzle
The general type of sliding block puzzle that motivated the
Quzzle is a puzzle known as "Dad's" puzzle. Dad's puzzle is
shown below:
The objective is the move the large piece from one specific
corner to another specific corner (a different corner than
Quzzle and a different configuration of pieces). Dad's puzzle can be tried using Quzzle, making for two
puzzles in one. Dad's puzzle is not easy but it is much easier
than Quzzle. The name "Dad's" puzzle supposedly reflects the
task of the head of the family rearranging pieces of furniture.
The large block represents a grand piano, to be moved to a
specific corner of the room. No doubt Dad's puzzle was
invented by a mechanical tinkerer who tried many combinations
randomly, stopping when he found a "rather" difficult
combination. Little could he imagine that a century later every
possible puzzle of the type would be scrutinized by a high speed
electronic brain - work that could take years to do manually.
Tips
The Quzzle puzzle comes with instructions leading you to a web
page with a progression of
tips. For example you might want to know how many moves it takes
to solve, or whether the first move is up or down. You can
reveal tips gradually if you get stuck, or just look at the
solution if you want to spoil the fun.
About the Inventor
Mr. Lewis is a puzzle lover that collects mechanical puzzles -
many of which were given to him as presents by those who know
his passion. Read the press See what the world famous
Economist wrote about Quzzle
here.
See what Science Magazine wrote
here. Check the Family Review Organization
here. Quzzle and Quirkle
Quzzle fits into the Quirkle line in that it re-engineers a
classic toy, taking it to the next level. There is simply no
sliding block puzzle of its type in the world that is
simultaneously as simple and complex. |