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November 18th - Medium

 
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Fri Nov 18, 2005 4:59 pm    Post subject: November 18th - Medium Reply with quote

Code:

It always seems aesthetically more pleasing when a solved Sudoku
grid contains just 81 digits - and NO "pencil marks". Of course, one
can erase the latter, but that is not the point!

Although the hard and very hard offer challenges at the boundaries
for solution techniques, the "medium" puzzles offer the challenge of
solving them without "pencil marks" or similar aides.

The November 18th is an excellent example of this challenge. I found
about half a dozen resolved cells at the start and then got "stuck". My
first thought was then to start marking up the "Pairs" (of which I had
noticed several) but instead of that I perservered without making any
marks - except resolved cells. I was glad that I did because the task
presented a number of challenges and the need to widen my thought
process to encompass logic that usually I would have by-passed by
making 'intermediate' pencil marks. In well under an hour I had a
solved grid with just the 81 digits.

Thus, my message is: Please do not dismiss the medium puzzles as
not having the allure of hard or very hard. They have their own purpose
and can provide a satisfying challenge - just keep them simple!

Alan Rayner BS23 2QT
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Louise56



Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA

PostPosted: Fri Nov 18, 2005 8:50 pm    Post subject: Reply with quote

That's quite a challenge Alan. How did you do the puzzle without making any marks? I just looked at it and the 7's are obvious, but I wouldn't know how to do it without writing in candidates. I can do this with the easy puzzles and I do them with a pen, but not this one. Take me through your thought process. I don't think I have enough brain cells.
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sat Nov 19, 2005 4:42 am    Post subject: Reply with quote

Code:

> How did you do the puzzle without making any marks? I just
> looked at it and the 7's are obvious, but I wouldn't know how
> to do it without writing in candidates.  I can do this with the
> easy puzzles and I do them with a pen, but not this one.
> Take me through your thought process.

Thank you for your interest in this one. I had to re-do the puzzle
and was apprehensive as to whether I would solve it again! However,
this time I marked each cell with a sequence number as I solved it.

Here is the sequence of my resolutions.

r6c6, r9c7, r7c9, r5c9, r4c9,
r9c9, r4c7, r8c6, r6c3, r4c3,

r5c6, r6c1, r4c2, r8c3, r5c8,
r8c8, r8c7, r8c2, r6c4, r4c4,

r4c6, r9c4, r9c5, r7c3, r7c5,
r7c6, r1c6, r5c5, r1c5, r3c5,

r5c4, r3c4, r2c4, r2c8, r2c2,
r2c7, r2c3, r7c7, r7c8,r9c3,

r9c2, r5c1, r5c2, r3c2, r1c3,
r3c3, r1c7, r1c8, r6c8, r6c7,

r3c7, r3c1, r1c1.

I do not claim that this is the most logical sequence of cells as at
times I just spotted something rather than working logically through
the grid. The sequence may have been different first time round.

I have not included what values I set in each cell. This allows for
the puzzle to be reworked - knowing where to look next but not
knowing exactly what to find! Of course, it would be possible to
check the solution anyway to find the value for each cell resolved.

The following points occurred to me as possibly being a little
bit more "difficult"  and so I will give some hints.

3) The '6' in box 3 must be in column 8 (as col 9 is full for box 3)
    Thus the 6 in box 9 must be in col 9
    Row 9 already has a 6 and so r7c9 is the only place.

9) The '1' in box 5 must be in row 5
    (because 1 is in r4c9 and r8c4 and r6c5 and r6c6 are filled)
    Thus the '1' in box 4 must be in row 6

11) The '2' in box 2 must be in row 3 (r3c4 or r3c5)
      The '2' in box 9 must be in row 7
      (row 9 is full and row 8 has a '2' already)
      The '2' in box 8 must be in row 9
      (row 8 has one already and box 9 has the row 7 one)
      The '2' in row 9 must be in r9c4 or r9c5

      Now comes a rule learned from Mandatory Pairs work!

      "If a digit is constrained to TWO columns out of the three in a
      'broad' column in TWO of the three regions in the same broad
      column, that digit in the third region MUST be in the third column."

      The same applies for rows of course. A "broad" column is defined
      as the set of three regions such as r1c1 to r9c3 or r1c4 to r9c6
      or r1c7 to r9c9.

      Here the broad column is r1c4 to r9c6.
      There is a 2 in either r3c4 or r3c5.
      There is a 2 in either r9c4 or r9c5.
      Thus the '2' in TWO regions is constrained to TWO columns (4 and 5).
      This means that the '2' in the third region (r4c4 to r6c6) MUST be
      in the third column (here col 6).

      This restricts the '2' to r5c6 as a '2' has just been placed in r4c3
      and r6c6 is occupied by a '7'.

      NB) Users of candidate profiles may have applied this rule under a
      different name. It has some affinity to the X-wing perhaps but I
      leave that point to be explored by others.

+++
Very probably the eleventh placement was the most tricky. There may
well have been easier ways to solve the puzzle but we each draw on
our previous experience and my speciality has centred on Mandatory
Pairs. With that method, binary constraints (it must be A or B and cannot
be anything else) are both important and powerful. Thus I am used to
recognising them (and usually recording them on the grid!).

+++
The general approach of 'manual' methods is to get all three cells in
a line within a region resolved. This means that any other digits as
yet unresolved can go in only one of TWO lines rather than three.
This constraint can be used to assist with a third region - even if one
does not know exactly where in a 'line' the digit should go.

The other technique that I used was "counting". I did not note it above
but at placement 34, I had four values missing from row 2 - 1349
(which I counted rather than recording!). I noticed that col 8 at that
point already contained digits 3,4,9. Thus r2c8 must be '1' - leaving
only 349 to be found in row 2. Col 2 already had 3 and 4 and so
r2c2 must be 9. Now row 2 still needed 34 but col 7 already had a '3'
and so r2c7 must be '4' and  then r2c3 is the only one left and must
take value 3. The whole row was cleared with five consecutive
placements - just by counting and comparing the intersecting lines.
It does not happen very often - but is sweet when it does!

Hopefully this gives some ideas as to usable techniques. When I first
encountered Sudoku I generated candidate profiles for everything but
it became very tedious (and I am error-prone when things get tedious!).
Thus I sought another way which would maintain the interest but omit
the tedium. Thus were "Mandatory Pairs" born - whilst spending some
time on a wind-swept beach in the south of France. However even that
has its limits and so I noticed particularly a comment by SamGJ that
many human solvers use more powerful techniques than are necessary
in order to solve medium puzzles. The comment inspired me - and now
the challenge is on to solve medium puzzles without pencil marks. We
all know that they CAN be solved with candidate profiles and we can use
then to improve our timings - but they can have another use, one that I
believe is equally as satisfying if not more so.

Alan Rayner  BS23 2QT

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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sat Nov 19, 2005 9:35 am    Post subject: Reply with quote

Hi,

I am amazed what nice complicate (for me!!!) rules you have developed and your skills in applying them without paper and pencil. Bravo!

I am sticking to the simple techniques, well known by everybody:
- Sole Candidate
- Unique Horizontal
- Unique Vertical
- Unique in 3x3 block

Using ONLY this ones, I got by putting in the following order:

r9c9 r4c9 r5c9 r7c9 r6c6 r8c6 r9c7 r6c3 r6c1 r4c3
r4c7 r4c2 r8c3 r8c2 r1c6 r4c6 r1c5 r4c4 r2c3 r5c5
r5c4 r7c3 r9c4 r2c7 r9c5 r1c3 r3c4 r3c1 r1c8 r2c4
r2c2 r3c5 r9c3 r2c8 r3c2 r7c7 r9c2 r3c7 r5c1 r6c8
r7c8 r1c7 r1c1 r3c3 r5c6 r5c2 r6c7 r7c5 r7c6 r8c8
r5c8 r6c4 r8c7

the digits into the cells - to the solution.

My mother, age 84, is using them also. Successfully.
I enjoy also climbing the mountains, without alpinist equipment.
And it must not be all the time a 4000 m one.

You are right, Alan. It's fun!

see u,
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sat Nov 19, 2005 10:39 am    Post subject: Reply with quote

Code:

> I am sticking to the simple techniques, well known by everybody:
> - Sole Candidate
> - Unique Horizontal
> - Unique Vertical
> - Unique in 3x3 block

> Using ONLY this ones, I got by putting in the following order:

> r9c9 ......

This had me lost on the very first cell!!

I had a '3' in r9c9 - but not until the sixth placement. I fail to see
how it can be placed as the first item - especially using JUST the
four techniques quoted. There must be a lot of intermediate thought!

Taking the bottom right region

3 in r7c1 eliminates row 7
3 in r3c8 eliminates column 8

This leaves r8c7, r9c7, r9c9 as possibilities for digit '3'
How does one know which of those is correct?

Taking row 9 on its own

3 in r7c1 eliminates columns 2 and 3
6 in r9c6 eliminates column 6

This leaves r9c4, r9c5, r9c9 as possibilities for digit '3'
How does one know which of those is correct?

NB: These possibilities do not overlap with the earlier ones and
so must be treated as independent.

Similarly column 9 has three possibilities (r4c9, r5c9 and r9c9)
and I do not see how to discern which is correct.

+++
This, perhaps, exemplifies, the "different" way that our friends in
Munchen and Colorado "see" the puzzles. They seem to be able to
bypass some stages in the logic and reach a result where many
other people would need to record something on the way. There
are, of course, different ideas as to what should be recorded!

In this case the "obvious" resolutions of the '7' digits is put to one side
and what, to me, seems an obscure choice is placed. I am perplexed!
How is it done - using just the four techniques?????

Alan Rayner BS23 2QT
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sat Nov 19, 2005 12:19 pm    Post subject: Reply with quote

Hi Alan,

Hi Alan,



Let's start from the beginning.
Here is my initial position (hope I have it correct, as yours):

Code:
  - 2 - 7 - - - - 9
  7 - - - 8 5 - - 2
  - - - - - 4 - 3 7
  9 - - - 4 - - 7 -
  - - 7 - - - 6 - -
  - 3 - - 6 - - - 5
  3 7 - 4 - - - - -
  2 - - 1 7 - - - 8
  1 - - - - 6 - 4 -


Now taking a look at the 9-th row and at the 9-th column, I can deduce
number 3 as the "Sole Candidate" for r9c9.

Quote:
This had me lost on the very first cell!!

I had a '3' in r9c9 - but not until the sixth placement. I fail to see
how it can be placed as the first item - especially using JUST the
four techniques quoted.


Is this what you was looking for?

see u, Alan
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sat Nov 19, 2005 2:15 pm    Post subject: Reply with quote

Code:

  - 2 - 7 - - - - 9
  7 - - - 8 5 - - 2
  - - - - - 4 - 3 7
  9 - - - 4 - - 7 -
  - - 7 - - - 6 - -
  - 3 - - 6 - - - 5
  3 7 - 4 - - - - -
  2 - - 1 7 - - - 8
  1 - - - - 6 - 4 -

> Taking a look at the 9-th row and at the 9-th column, I can deduce
> number 3 as the "Sole Candidate" for r9c9.
> Is this what you were looking for?

Not quite!
The phrase "Taking a look" does not supply any logic to my mind.
It is as if the phrase were addressed to a blind person. I just can NOT
"see" that '3' is the sole candidate from the data presented. Can any
assistance be given with the "I can deduce" bit. That implies that a
process of logic with intermediate setps may have occurred.

I acknowledge that there is a problem here. The challenge is akin to
a sighted person attempting to convey the essence of the colour red
to a blind person. Reference to its vibrational frequency would not be
sufficient to convey its innate qualities. We could ask ourselves how
we, individually, came to know what the colour red is. The answer
from an artist may well be different from that of a communist! The
concept defies total definition but we all get near enough to a common
understanding to be able to communicate about it - except for those
who are blind and have never "seen" it.

So it is with this Sudoku puzzle, I just cannot "see" that r9c9 must be '9'.
Is this the basic dilemma of Sudoku - that we need some form of
"Pauline" conversion to be able to see what is in front of our eyes?

Are there two types of people, those who can "see" Sudoku patterns
and those who are temperamentally unfit to do so - or is this a skill
that can be acquired by directed training (just as a blind person can
be assisted to an enhanced sense of touch or hearing)?

It MIGHT help if the "seers" could explain what processes they believe
occur in their brains/minds when the 'see' such a result - but I recognise
that this request may be impossible to fulfil. Red is just red and no
amount of bluster can adequately describe it!

Alan Rayner  BS23 2QT
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Jim



Joined: 03 Nov 2005
Posts: 3
Location: Austin, TX

PostPosted: Sat Nov 19, 2005 3:26 pm    Post subject: Reply with quote

By golly I think the Bavarian is right! I am pretty new to this. I always look to intersections of rows but that corner is uniquely a 3. Good tip.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sat Nov 19, 2005 7:30 pm    Post subject: I'll try to describe "Red"! Reply with quote

AlanR555 wrote:
It MIGHT help if the "seers" could explain what processes they believe
occur in their brains/minds when they 'see' such a result - but I recognise
that this request may be impossible to fulfil. Red is just red and no
amount of bluster can adequately describe it!

In this particular case the request is not impossible to fulfil.

Row 9 already contains {1, 4, 6} Column 9 already contains {2, 5, 7, 8, 9}. That's eight -- count them, 8 -- distinct values. Therefore r9c9 must contain the ninth value, or "3". dcb Smile
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sun Nov 20, 2005 1:42 am    Post subject: Re: I'll try to describe "Red"! Reply with quote

Code:

> Row 9 already contains {1, 4, 6}
> Column 9 already contains {2, 5, 7, 8, 9}. That's eight -- count them,
> -- distinct values. Therefore r9c9 must contain the ninth value, or "3"

Thank you.
Very simple - for those that have eyes to see!
I have always seen this "intersect" as being the finding of the "missing"
values on the intersecting line (eg finding 1346 missing from col 9 and
spotting 146 in row 9 or finding 235789 missing from row 9 and then
spotting 25789 in column 9). The concept of regarding the intersecting
lines as a whole has not been part of my repertoire - probably because
I tend to limit the range of my viewing (rarely beyond a "broad column"
so that the dimensional sum (row width plus column height within the
view) does not usually exceed 12. This technique calls for 18 (9+9=max).

I will aim to include it at an earlier stage in the solution but I suspect
that spotting it will not be easy for one as myopic as myself.

Alan Rayner  BS23 2QT
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PostPosted: Sun Nov 20, 2005 4:25 am    Post subject: Re: I'll try to describe "Red"! Reply with quote

alanr555 wrote:
Code:

> Row 9 already contains {1, 4, 6}
> Column 9 already contains {2, 5, 7, 8, 9}. That's eight -- count them,
> -- distinct values. Therefore r9c9 must contain the ninth value, or "3"

Thank you.
Very simple - for those that have eyes to see!
I have always seen this "intersect" as being the finding of the "missing"
values on the intersecting line (eg finding 1346 missing from col 9 and
spotting 146 in row 9 or finding 235789 missing from row 9 and then
spotting 25789 in column 9). The concept of regarding the intersecting
lines as a whole has not been part of my repertoire - probably because
I tend to limit the range of my viewing (rarely beyond a "broad column"
so that the dimensional sum (row width plus column height within the
view) does not usually exceed 12. This technique calls for 18 (9+9=max).

I will aim to include it at an earlier stage in the solution but I suspect
that spotting it will not be easy for one as myopic as myself.

Alan Rayner  BS23 2QT


I'm not quite sure what he said but I think he meant - "Woops, you're absolutely right. I missed it."
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Nov 20, 2005 1:26 pm    Post subject: Re: I'll try to describe "Red" Reply with quote

AlanR555 wrote:
... I suspect that spotting it will not be easy for one as myopic as myself.

Don't sell yourself short, Alan. We can all learn new tricks. Think of it as getting glasses! :)

For what it's worth, I overlook this sort of pattern more often than I'd like. In this particular case it was easy to spot because the row and column involved lie on the edges of the puzzle. I have more trouble seeng this pattern when the intersecting row and column lie in the interior region. dcb
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Louise56



Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA

PostPosted: Mon Nov 21, 2005 5:38 pm    Post subject: Reply with quote

alanr555 wrote:
Code:


Here is the sequence of my resolutions.

r6c6, r9c7, r7c9, r5c9, r4c9,
r9c9, r4c7, r8c6, r6c3, r4c3,

r5c6, r6c1, r4c2, r8c3, r5c8,
r8c8, r8c7, r8c2, r6c4, r4c4,

r4c6, r9c4, r9c5, r7c3, r7c5,
r7c6, r1c6, r5c5, r1c5, r3c5,

r5c4, r3c4, r2c4, r2c8, r2c2,
r2c7, r2c3, r7c7, r7c8,r9c3,

r9c2, r5c1, r5c2, r3c2, r1c3,
r3c3, r1c7, r1c8, r6c8, r6c7,

r3c7, r3c1, r1c1.


Alan,

Thanks for explaining how you solved this without any pencil marks. I tried it as well and was surprised to find I could do it! In looking at how you did it though, I could not see how you got r5c6 = 2, and r6c1 = 4. Thanks again for presenting this.
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alanr555



Joined: 01 Aug 2005
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Location: Bideford Devon EX39

PostPosted: Wed Nov 23, 2005 2:57 am    Post subject: Reply with quote

Code:

> Thanks for explaining how you solved this without any pencil marks.
> I tried it as well and was surprised to find I could do it!  In looking at
> how you did it though, I could not see how you got r5c6 = 2, and r6c1
> = 4.  Thanks again for presenting this.

r5c6 was the 11th placement - derived as follows:
It was, perhaps, the most tricky of all the placements for this puzzle.

11) The '2' in box 2 must be in row 3 (r3c4 or r3c5)
      The '2' in box 9 must be in row 7
      (row 9 is full and row 8 has a '2' already)
      The '2' in box 8 must be in row 9
      (row 8 has one already and box 9 has the row 7 one)
      The '2' in row 9 must be in r9c4 or r9c5

      Now comes a rule learned from Mandatory Pairs work!

      "If a digit is constrained to TWO columns out of the three in a
      'broad' column in TWO of the three regions in the same broad
      column, that digit in the third region MUST be in the third column."

      The same applies for rows of course. A "broad" column is defined
      as the set of three regions such as r1c1 to r9c3 or r1c4 to r9c6
      or r1c7 to r9c9.

      Here the broad column is r1c4 to r9c6.
      There is a 2 in either r3c4 or r3c5.
      There is a 2 in either r9c4 or r9c5.
      Thus the '2' in TWO regions is constrained to TWO columns (4 and 5).
      This means that the '2' in the third region (r4c4 to r6c6) MUST be
      in the third column (here col 6).

      This restricts the '2' to r5c6 as a '2' has just been placed in r4c3
      and r6c6 is occupied by a '7'.

      NB) Users of candidate profiles may have applied this rule under a
      different name. It has some affinity to the X-wing perhaps but I
      leave that point to be explored by others.

+++

r6c1=4 was the 12th placement
BY then there is a '4' in row 4 and in row 5 and so the '4' in row 6 is
relatively easy to find - it must be in box 4!
r6c2 has clue '3' and r6c3 has a '1' from placement 9.
Thus r6c1 is the only place remaining for the third '4' in the "broad row"
that occupies rows 4,5,6.

+++

Congratulations to those who solved it without pencil marks.
The challenge is different to working on the advanced techniques
discussed with many of the puzzles - but still a satisfying one.
As with so many things, the acceptance of the challenge can draw
on that old phrase - where there is a will, there is way (and as long as
the way is not 'trial and error', I would commend that way!)

Alan Rayner  BS23 2QT
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Louise56



Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA

PostPosted: Wed Nov 23, 2005 11:20 pm    Post subject: Reply with quote

alanr555 wrote:
Code:

Congratulations to those who solved it without pencil marks.
The challenge is different to working on the advanced techniques
discussed with many of the puzzles - but still a satisfying one.
As with so many things, the acceptance of the challenge can draw
on that old phrase - where there is a will, there is way (and as long as
the way is not 'trial and error', I would commend that way!)

Alan Rayner  BS23 2QT


Thanks Alan for your responce!
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Wed Nov 23, 2005 11:39 pm    Post subject: Re: I'll try to describe "Red" Reply with quote

David Bryant wrote:
AlanR555 wrote:
... I suspect that spotting it will not be easy for one as myopic as myself.

Don't sell yourself short, Alan. We can all learn new tricks. Think of it as getting glasses! Smile

Alan

I don't consider that "seeing." That is simply solving for a cell by identifying candidates using only the row and the column. That is one method of solving for a cell, and you discover it as soon as you look for it (and it doesn't require pencil marks). It's when do you look for it that I am curious about. I do not start doing this until after I have tried solving box-by-box using rows and columns as they intersect on box.

So I would not have started there, but I certainly would have gotten there. And that is just a method or technique. I have been hoping to generate some discussion in the general forum about just this -- where do you start, what progressions do you take? Not much to date.
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alanr555



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PostPosted: Thu Nov 24, 2005 3:31 am    Post subject: Re: I'll try to describe "Red" Reply with quote

Code:

> That is one method of solving for a cell, and you discover it as soon
> as you look for it (and it doesn't require pencil marks).

Indeed. The cell in question was completed as the SIXTH when I did
the puzzle manually. I doubt that I was wrong to give attention to
five other "solvable" cells first.

> It is WHEN do you look for it that I am curious about.

I agree that this "When?" question is crucial to discussion about how to
solve these puzzles in an effective manner. Whilst efficiency is not the
prime objective, there needs to be a modicum of it if one is not to
spend all day just 'faffing around" with a puzzle.

> I do not start doing this until after I have tried solving box-by-box
> using rows and columns as they intersect on box.

I have tended recently to proceed in the following sequence.

a) Broad columns (ie a stack of three regions)

For each broad column, I will look for two occurrences of any digit
and investigate what can be gleaned from such occurrences.

b) Broad Rows (ie a block of three regions across the grid)

Same procedure as for Broad Columns

c) Consideration of each digit in turn

For each digit 1,2, ... 8,9 I inspect (in greated detail than in a/b above)
each broad column and then the broad rows.

d) During the processing of 'c', I aim to notice when a row, column or
region builds up to six resolved cells. Then I derive the "missing" profile
and look for an intersecting line to any of the blank cells where such
line contains two digits from the "missing" profile and the target cell
can then be resolved as the third member of the 'missing' profile. Of
course it is even better if seven cells are already resolved!

e) Step (d) is essentially an interruption of step (c) but on completion
 of (c), attention is turned more directedly to the "counting" of lines
and regions - generally addressing first those with the larger number
of resolved cells. The procedure is the same - identify the 'missing'
profile and then look at each blank cell to ascertain if the missing digits
occur in a line at right angles or in the target cell's region.

f) Having done that, I sometimes return then to re-do step 'c' - if I sense
that sufficient cells have been filled in step (e) to warrant such further
attention (eg completing a line of three within a region is a powerful aid
to solution as it can restrict the placement of a digit within another region
in the same broad row/column to one specific row/column).

g) The next step depends upon what method is being used.
A manual method with no pencil marks will then continue to look for
cluses to solution working mainly on 'missing' profiles but working those
in with the effects derived elsewhere in the puzzle.
With Mandatory Pairs, a detailed inspection in conjunction with the
repertoire of M/P techniques may well resolve a few cells.

h) However, in a number of cases, I have to decide to set up the candidate
profiles. These are much easier to do if the 'missing' profiles have already
been prepared - as the candidate profiles have to be "congruent" with
the 'missing' profile. This is also the point to find the 'hidden pairs'
which lurk in the 'missing profile'. I write this profile at the end of the
row/column (but do not record it for regions) but separate out the writing
if hidden pairs are involved (eg {12345} may be written as {25}{134}
if the line resolves into a pair and a triplet)

i) Usually, one of the rows/columns/regions will be "incongruent" (ie
the number of unresolved cells may not be equal to the number of
distinct digits involved in the candidate profiles for the row/column/region
in context. As that row/column/region is made congruent it is normal
for some other row/column/region to become incongruent and so the
process continues.

j) If it transpires that ALL the rows/columns/regions are congruent
(after meticulous checking!) then one has to consider some form of
"tie-breaking". For this I generally write out the candidate profiles on
a separate sheet - using hyphens for resolved cells and cells that
are not relevant for the particular technique/implementation. This
gives emphasis to the cells that will assist the resolution - without the
"noise" of all the other pencil marks on the grid.

These advance techniques often involve some form of binary chain
and so the 're-written' (selected) profiles can be used for plotting such.
If new information is gained, this can then be used on the original grid
to progress it towards solution.

+++
The above gives an indication of how the solution is approached. I
doubt that it is efficient! My impression is that  visual "seeing" of a
pattern can shorten the solution times significantly but we do not
yet seem to have developed any training for that - either we have it
or (like myself) we do not!

Perhaps one of the participants in this forum has some experience of
a significant improvement in solving times once the method of seeking
or of 'spotting' had changed. This would be useful as most of the time
human beings tend to pursue the same path as yesterday and only
rarely choose a new path - despite the fact that human creativity and
inventiveness can have truly amazing effects. If we can capture the
moments of transition in our learning/understanding we have the
potential to serve the wider Sudoku-playing community.

There is some material being posted around at present which refers
to the mindset of the player and the importance of geting this right
at the outset and through the process of play. A lot of this is likely to
be over-emphasised for the sake of the profits of the promoters but
there is a genuine point below it all. The question will then be whether
those who acquire both the tranquility and the determination of the right
mindset find that their play improves and whether they can glean
some techniques suitable to be shared with the rest of us mere mortals.
Should we all take up meditation, or would that be a waste of time?

> So I would not have started there, but I certainly would have gotten
> there.
As even I did by the sixth placement!

> I have been hoping to generate some discussion in the general forum
> about just this -- where do you start, what progressions do you take?

I agree that this is a worthwhile aspect to tackle in discussion.

Alan Rayner  BS23 2QT
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RogerC



Joined: 08 Oct 2005
Posts: 14
Location: High Wycombe, Bucks, England

PostPosted: Thu Nov 24, 2005 7:12 am    Post subject: Night owls Reply with quote


    I take my hat off to you, Alan! Anyone who can write such a lengthy and erudite tract on Su-Dokus at 3:30 in the morning must be a genius.

    I thought I got up early at 5a.m.!

    Roger.
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Thu Nov 24, 2005 8:17 am    Post subject: Reply with quote

Hi,

I suspect that Alan is quoting a lot from this own work and uses cut and pastle Wink
At least this is what I would do, to get to the status of a genius ... ;-)

see u,
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