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dec 28 Hard

 
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George Woods



Joined: 28 Mar 2006
Posts: 303
Location: Dorset UK

PostPosted: Fri Dec 28, 2007 2:58 pm    Post subject: dec 28 Hard Reply with quote

This one presented me with a DR, (declined) later an X wing (again declined). Knowing that a "Hard" doesn't need "advanced" techniques I solved it in the fashion that I suppose could be described as "intended" BUT this is OK with puzzles from this site. What about puzzles from elsewhere? Presumably one could decline an X Wing (or whatever) and then waste hours searching for something else!

Maybe like "religion" I should stick to one source!
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froycard



Joined: 29 Dec 2007
Posts: 1

PostPosted: Sat Dec 29, 2007 5:52 pm    Post subject: and it has several solutions Reply with quote

Besides, the Dec 28īs sudoku has at least three different solutions that I already checked out. I don't like this kind of sudoku since you need guessing to find a solution. That's not my type.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Dec 29, 2007 6:11 pm    Post subject: Reply with quote

froycard,

A program I use says it only has one solution and Sam's puzzles usually only have one solution. Is it possible you made an error someplace?
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Sun Dec 30, 2007 12:52 am    Post subject: Reply with quote

TKiel wrote:

A program I use says it only has one solution and Sam's puzzles usually only have one solution. Is it possible you made an error someplace?


This should perhaps read:
"Sam's puzzles ALWAYS have only one solution"!

I solved this one using the regular Mandatory Pairs techniques in a
relatively short time. As I recall, it was missing a "Sole Position" for
the '9' in column six that delayed me slightly but I found it before
resorting to deriving the candidate profiles. It is that latter process
which can be a chore and so I aim to delay doing it until I have
exhausted the M/Pair techniques.

+++
I have found that the following approach reduces (normally to zero!)
the number of errors arising in the setting of the candidate profiles.
It is particularly useful when Mandatory Pairs have been used but
the guiding principle of how to sequence the cells selected for the
derivation of the options would apply generally.

The clue seems to be to derive the options NOT in an order
determined by the grid layout but by identifying:

Firstly all cells that have mutual reception, remote pairs, closed
triples etc as the M/Pairs become the profile marks.

Secondly any regions that are "fully defined" (ie all nine digits are
either resolved or present as M/Pairs data). Again, the M/Pairs
become the profile marks.

Thirdly those rows or columns with the least number of "undefined"
cells. For this purpose a cell is "defined" it is resolved OR contains
an element of a pair or closed triple/quartet in the row or column
being considered.

The technique is to identify the digits that must be distributed among
the undefined cells - and to write these adjacent to the row/column
just outside the grid along with any pairs/triples/quartets in the line.
eg (23)(567) would indicate that 1,4,8 and 9 are resolved and that
the unresolved cells contain a pair and a triple. Quite often, this
process of documentation will reveal a pair/triple not previously
recognised - with relevant eliminations as a bonus!

Lastly the latter process continues by identifying always the columns
or rows with the least number of undefined cells. When it comes to
those lines with six or seven undefined cells, it will be found that most
of the cells in the line already have profiles and so the work of
deriving them is minimised. It is also easier to check the work and
the error rate is much lower as one is usually dealing with fewer
digits in each cell.

Having set all the profiles, the next step is a quick scan of each
region to check for "congruence" and to ensure that any strong links
revealed by the M/Pair marks are reflected in the profiles (although
quite often such links will be spotted when setting the profiles!).

Congruence is the rule that the number of distinct digits used in the
profiles of a row, column or region MUST be exactly equal to the
number of unresolved cells in the same row, column or region.

My practice is to check congruence for rows and columns when
setting the profiles and then to check the overall work by looking
at region congruence after the profiles have been set.

This methodology has the advantage of focussing on one dimension
at a time - row or column or region - and therefore reduces the
likelihood of error.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Dec 30, 2007 12:34 pm    Post subject: Reply with quote

Quote:
"Sam's puzzles ALWAYS have only one solution"!


I was allowing for the possibility of an error when I said 'usually only have one solution". What I should have said is "intended to have one solution".
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