Published Hitori puzzles without unique solutions?
Angus Rodgers
I just want to check that I'm thinking straight, before posting
a critical review at Amazon, because I'm new to these [mainly]
Japanese logic puzzles.
Having done a couple of Hitori puzzles in /The Times Japanese
Logic Puzzles: Hashi, Hitori, Mosaic and Slitherlink/ (2006),
I turned to /The Daily Telegraph Japanese Puzzle Compendium/
(2008).
The latter gives as an example Hitori problem:
52543876
83654618
56342548
75263438
28885764
31726554
14538227
67412382
and as its solution:
52*43876
83654*1*
*63*2548
7526*43*
2*8*5764
31726*5*
145382*7
6741*382
You can see immediately that, although this solution is maximal
(in the sense that you can't unpaint any of its painted cells,
without breaking the rules of Hitori), it is not unique, because
it contains a 4x4 block of unpainted cells, several of which can
be painted, without breaking the rules, giving rise to several
alternative solutions.
A glance at the solutions at the end of the book seems to show
that every one of them suffers from the same flaw (if it is indeed
a flaw), e.g. the 7 at location (3, 3) in the first solution can
be painted out, without breaking the rules. (I haven't bothered
to check each solution in detail - in most of them, there are
obvious large unpainted rectangular blocks.)
I think that's probably bad enough (is it?), but what I actually
noticed first was that the given solution is not even the unique
maximal solution. Towards the end of solving the puzzle, I had
unpainted 5-cells at (row, column) coordinates (1, 1), (1, 3),
(3, 1), (3, 6), and (7, 3), and unpainted 6-cells at (2, 3) and
(2, 6). These can be painted in various ways, giving maximal
solutions differing from the solution shown in the book, e.g.:
*2543876
83*5461*
563*2*48
7526*43*
2*8*5764
31726*5*
14*382*7
6741*382
This is surely a serious blemish; so I don't trust the Hitori
puzzles in this book (/The Daily Telegraph Japanese Puzzle
Compendium/). However, I haven't found anything wrong with the
other kinds of puzzle in the book (which indeed I have been
enjoying a lot). Am I thinking straight about the apparent
flaw in the Hitori puzzles?
--
Angus Rodgers
Kevin Stone
>
> 52543876
> 83654618
> 56342548
> 75263438
> 28885764
> 31726554
> 14538227
> 67412382
As far as I can tell this has no unique solution.
In addition the Hitori solver at http://homepage.uibk.ac.at/~csae1761/
agrees with me...
For all your hitori needs you know where to go...
--
Kev
www.brainbashers.com/you_know_where_to_go_for_hitori
Mike Terry
news:8dr0m3...@mid.individual.net...
> > The latter gives as an example Hitori problem:
> >
> > 52543876
> > 83654618
> > 56342548
> > 75263438
> > 28885764
> > 31726554
> > 14538227
> > 67412382
>
> As far as I can tell this has no unique solution.
>
> In addition the Hitori solver at http://homepage.uibk.ac.at/~csae1761/
> agrees with me...
Well given that Angus exhibited two different solutions in his post, that's
hardly surprising :-)
All the Hitori puzzles I've ever done have had unique solutions, but I don't
think I've ever done any from the Daily Telegraph. I think it's generally
expected that solutions for all these logic puzzles should be unique, and
some sources make this clear, while for others it comes into the category of
"secret rules" (which I strongly disapprove of). I suspect the Telegraph is
pretty clueless about these logic puzzles in general - I remember reading
their "difficult sudoku" puzzle book where it was explained that all the
difficult puzzles would require "backtracking" (and then there were several
pages showing the user how to guess answers in pencil and rub them out if
they were later found to be wrong, as though their audience couldn't work
out this technique without their help!)
I wonder - is there an "official" (e.g. trademarked?) definition of what
constitutes these puzzles? If not, then it would be hard to claim the
puzzle is invalid, assuming the Telegraph do not claim their solutions to be
unique. (Just avoid this source if you expect uniqueness.)
Mike.
Kevin Stone
> Well given that Angus exhibited two different solutions in his post,
> that's
> hardly surprising :-)
Indeed, but it's always nice for someone to actually read your post and
agree with your logic!
--
Kev