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lando45
Joined: 10 Feb 2006
Posts: 1
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 Posted: Fri Feb 10, 2006 1:43 pm Post subject: This is killing me... |
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Can anyone help me with this?
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Fri Feb 10, 2006 3:34 pm Post subject: This is killing me... |
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It is certainly quite a neat puzzle.
As for the next step, I suggest 6 in r6c5. This is the only place for 6 in the central box bearing in mind that two cells are taken up by the pairs (49) in the fourth row and (47) in the fifth.
Back to you.
Steve |
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george woods1
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| Posted: Tue Mar 28, 2006 5:32 pm Post subject: |
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This is one of the puzzles that comes to a crunch point, where it is either impossible or difficult to find the next move. so given one cell that can be either this or that it is often quicker to try "this" and when it fails try "that"
So on this one one reaches the crunch point( for me) via
e6,f25,e2,c5 At this point cell a in block d can either be a 6 or a 7. Tried 7 fialed and then a 6 and it works
i use the convention
abc
def
ghi
to identify blocks So e6 means put a 6 in block e (the central one) hopefully the position will be fairly obvious! etc..
For what it is worth the solution I got was
e6(pos a as a guess),f76,c9c62,a6d9,f49,e974,h9,i4,g7,d17,g49,i59,a8,b2,a14,h8,b8,b57,c317 etc... |
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George Wooods1
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| Posted: Tue Mar 28, 2006 5:34 pm Post subject: |
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| Misprint Sorry my guess at the crunch point was d6 (position a) |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Wed Mar 29, 2006 2:06 pm Post subject: |
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George Woods1,
| Quote: | | ...so given one cell that can be either this or that it is often quicker to try "this" and when it fails try "that". |
This is guessing, which is not necessary to solve a puzzle which only has one solution, such as this one. Most people are interested in logic techniques, not just the fastest way to find the solution. |
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George Woods1
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| Posted: Thu Mar 30, 2006 1:55 pm Post subject: |
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I agree that the real interest is the logical solution BUT has anyone proved that there is always a logical solution, and indeed the precise differnce between logic and trail and error may be somewhat blurred!
for instance I have met this type of situation twice so it seems like logic now, but first time felt like trial and error
12 14 where the "connections" go round the "square"
12 24
so if first the 12 is 1 then second 12 becomes 1 (via 14 and 24) so it is wrong
so it becomes
2 14
1 24
So is this logic or trial and error? ! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Mar 30, 2006 2:59 pm Post subject: XY-wing |
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The given pattern:
| Code: |
12 ... 14
. .
. .
12 ... 24
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is an XY wing on <1>, rooted in the lower right square <24>. The elimination of the possibility <1> in the top left square is clearly not a guess, nor is it trial and error.
Keith |
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Mon Apr 03, 2006 12:28 am Post subject: xy wings |
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Keith
Haven't found a definition of xy Wings. Is this one?- came across it today at the crunch point of a puzzle - and it did the trick!
15
145 245
__________
157 47
where the line shows the "box line"
so if 4 is chosen from 245 the lower box has two 7's allowing this 4 to be eliminated |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Mon Apr 03, 2006 1:05 am Post subject: |
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George,
An xy-wing is composed of three bivalue cells in the pattern (a,b), (b,c) & (c,a), where the (b,c) cell (sometimes called the 'stem' or 'pilot' cell) shares a group (row, box or column) with both of the other cells (sometimes called the 'wing' cells). Any cell that contains the (a) value and sees both the 'wing' cells can't be (a).
| Code: |
col 1 col 2
---------------------
(a,b)
<-BOX 1
---------------------
(b,c)
<-BOX 2
(c,a)
---------------------
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In this (poor) example, (a,b) shares a column with (b,c). (b,c) shares a box with (c,a). Any cell in column 2 in box 1 can't be (a) and so can be excluded. If any of those cells was an (a) then (b,c) would have no candidates. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Tue Apr 04, 2006 9:57 am Post subject: |
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It sems as if "Trial & Error" is a verboten term for sudoku theorists. When all else fails, Trial and Error chases the "error" path- finding the quickest way to demonstrate failure, and calls this sequence a "forcing function"! - So whats in a name?
In the context of XY wings, I found what might be a variant of XY wings that should be fairly easy to spot, but was called a forcing function by one author!
consider
XZ XZ
----------------
YZ YZ
where the left XZ is connected to the right XZ which is connected to the right YZ which is connected to the other YZ. Z is barred to any "buddy" of the left XZ and left YZ. ie it's as if the right XZ and YZ act as an XY connected to both of the elementson the left to give a classic XY wing
The point about this one is that it is not uncommon to find a pair of XZ in one "row" and a pair of YZ in another, and if a couple line up we have this variant of an XY wing!
These discussions suggest that yesterday's forcing function may be tomorrow's documented "soup ladle" or whatever else it is christened |
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Tue Apr 04, 2006 10:01 am Post subject: |
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In my previous the formatting after "submit" obscured my point. so using dots I will try again
XZ................XZ
-----------------------------
....YZ.............YZ
. |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Tue Apr 04, 2006 1:09 pm Post subject: What's in a name? |
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| George Woods wrote: | | ... yesterday's forcing function may be tomorrow's documented "soup ladle" or whatever else it is christened. |
That's an astute observation, George. The thing to keep in mind when considering the nomenclature for "methods" is that virtually all of it was coined during 2005. People were inventing new terms left and right. Some of them stuck. Others didn't. dcb |
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alanr555
Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39
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| Posted: Fri Apr 07, 2006 10:52 pm Post subject: |
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| Code: |
> I have met this type of situation twice so it seems like
> logic now, but first time felt like trial and error
> 12 14 where the "connections" go round the "square"
> 12 24
> so if first the 12 is 1 then second 12 becomes 1 (via
> 14 and 24) so it is wrong
> so it becomes
> 2 14
> 1 24
> So is this logic or trial and error?
+++ Response:
If one starts from the {12} cell it IS trial and error.
However, if one starts from the {14} cell it is an example
of an implicational chain.
> 12 14
> 12 24
If one assumes '1' in 14
=> '2' in upper left
If one assumes '4' in 14
=> '2' in 24
=> '1' in lower left
=> '2' in upper left
Thus it is proven that irrespective of the value chosen
for the {14} cell the top left MUST take value '2'.
This is LOGIC.
+++
Clearly there is a thin line - but it is a thin line not a void.
In the original a chain is tried, it fails and so the opposite is
taken as true - trial and error!
Using the second method two chains are found - which together
exhaust the possibilities for a 'start' cell. Each cahin leads to the
same result. Thus it is logic.
The key is to find the 'start' square from which to apply the
logic - not always easy! However, those with a "spatial"
mind will spot these patterns visually and will declare them
as logic just knowing the theory - without working it out
each time as has been demonstrated here.
Alan Rayner BS23 2QT
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minnseoelite
Joined: 14 Apr 2006
Posts: 5
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| Posted: Fri Apr 14, 2006 8:22 pm Post subject: |
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| Is it just me or is the guy posting before me using auto posting software sorry looks computer generated to me. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Apr 14, 2006 9:00 pm Post subject: |
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No,
I think it's just his style.
If you hit the "Code" button, the subsequent text is in a fixed xx (typewriter) font. Columns line up.
I presume Alan prefers not to xx back and forth between Code and regular, as some others do.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Apr 15, 2006 4:54 pm Post subject: |
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| Quote: | If one starts from the {12} cell it IS trial and error.
However, if one starts from the {14} cell it is an example
of an implicational chain. |
I continue to be confused about where the line is drawn between logic and trial and error. I have two questions:
1) Is there something I should know that tells me that the 14 cell is the "proper" starting point?
2) If I start with the 12 cell, I learn that the "1" leads to duplicates; therefore, this cell must have the value of "2." Why is this not logic?
In the one case, we forced the value of another cell, in the other we forced the value of the starting cell. I'm just unable to see the distinction.  |
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alanr555
Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39
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| Posted: Sun Apr 16, 2006 8:49 am Post subject: |
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| Code: |
>> If one starts from the {12} cell it IS trial and error.
>> However, if one starts from the {14} cell it is an example
>> of an implicational chain.
> I continue to be confused about where the line is drawn
> between logic and trial and error.
... as have been many before you, and will be many behind you ...
> I have two questions:
> 1) Is there something I should know that tells me that the 14
> cell is the "proper" starting point?
No - other than that it leads to an implicational chain whereas
the other cell does not.
> 2) If I start with the 12 cell, I learn that the "1" leads to duplicates;
> therefore, this cell must have the value of "2." Why is this not logic?
This is "logic" but a subset of logic variously known as "reductio ad
absurdum" or "trial and error" (of which Ariadne's thread is perhaps
the most logical).
+++
> In the one case, we forced the value of another cell, in the
> other we forced the value of the starting cell. I'm just unable
> to see the distinction. :?:
One of the (unwritten?) conventions of solving Sudoku is that
one never alters a resolved value. It is FIXED - unless one has
made an error in which case - "start again time" has arrived!!
Thus the two strands of logic CAN be distinguished.
A) One sets the value of a cell arbitrarily and continues until one
reaches a contradiction. When it does not work, one has to
backtrack and ERASE previously set cells.
That is why it is called "trial and error"!!
B) One demonstrates that the digit in a particular cell MUST be
a specific value for EVERY possibility of the value in another
cell. This is a 'deterministic' approach.
Note: In this second case, one is NOT setting any cells - except
the final one, which is proven to have a unique value.
+++
Again, an "unwritten" approach is that Sudoku is about gaining
information about unresolved cells from what is already known.
It is not about making assumptions and disproving them. The
Ariadne's Thread approach is to assume that everything is
possible then to eliminate possibilities by testing them in turn.
The latter is the computer approach to solution. It postulates
that every cell (except the initial givens!) can hold ANY of the
digits 123456789. It then goes about disproving particular
values as possibilities for cells until only one remains per cell.
The human solver works in a different way. Quite often it will
take the form of
If A cannot be X then B must be Y
This leads to a POSITIVE setting for cell B, rather than the negative
approach of eliminating all except Y as possible values.
+++
Those who use "Candidate Profiles" as their sole or primary method
of solving Sudoku are emulating a machine method. This is fine as
a method of learning about Sudoku but, I would suggest, ultimately
unsatisfactory if one is thereby declining to use one's human traits.
Those who are "deeply" into Sudoku crave more and more difficult
examples as they are exploring the subtle patterns of the puzzle
(much as astronomers explore the universe and postulate methods
of learning more about it). This IS using their human creativity - and
then they often seek to get computers to emulate them!
One of the virtues of the "Mandatory Pairs" approach is that it is
designed to lead to positive resolutions - albeit by demonstrating
that a particular digit is impossible in another cell. However, it
does not in any way SET values until they have been proven to
be UNIQUE for the cell concerned. Certainly, cells are marked with
possibilities but they are neither JUST possibilities nor a set of ALL
possibilities. The markings are symptoms of RELATIONSHIP between
different cells (Mutual Reception being the strongest) rather than
each cell being considered on its own.
I have no doubt that Mandatory Pairs is only a step on the path to
a more comprehensive understanding of the HUMAN approach to
the resolution of Sudoku puzzles. If it can highlight the need for
consideration of "relationship" rather than consideration of each
cell in isolation, then it will have been of service.
There is elsewhere a posting on the concept of "Strong Links" and
this has a very exciting potential - because it draws attention to
the power of relationships. My personal circumstances at present
(recent death of my mother and partner in a hospice) do not allow
me to devote time to developing methods in the way that I did
with Mandatory Pairs last October but I am sure that there is scope
for such development - we are not MERELY machines!
Alan Rayner BS23 2QT
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