|Posted: Sun Jan 15, 2006 10:01 pm Post subject: pencial marks
|[i]whenever i do this i always have pencial mark from erasing and ersaing is there anyway to help me figure out how to play so that i am able to have not as many pencial marks this way it will be easier to see the # that i have put in[/b]
Joined: 01 Aug 2005
Location: Bideford Devon EX39
|Posted: Mon Jan 16, 2006 2:51 am Post subject: Re: pencil marks
> I always have pencil marks.
> Is there anyway to help me figure out how to play so that I
> am able to have not as many pencil marks.
For Easy and Medium puzzles, it should be possible in most cases
to solve the puzzle without pencil marks - although some Medium
puzzles have thwarted me without marks!
A lot of the Hard and Very Hard puzzles can be progressed a long
way using the Mandatory Pairs marks. By their nature, these are
added and removed during the solution process and there will
never be as many of them as the marks for candidate profiles
if the latter are fully completed. However, there are quite a few
puzzles where resort to candidate profiles reaches the solution
much quicker than relying upon just Mandatory Pairs.
It mus be remembered that Mandatory Pairs is just a reasonably
efficient method of recording "information" gleaned from the
puzzle in a way that enables it to be used later - whereas using
Candidate Profiles is akin to simulating the work of a computer
and recognising patterns that will reveal the solution.
The Mandatory Pairs method (M/P) falls short when the puzzle
is based on pairs/triples etc which span more than one 3x3
region. Recognising this I find that more time needs to be given
to "Sole Position for Digit" searches if the simpler M/P techniques
fail to uncover the solution.
The standard technique "Counting" will reveal what numbers are
missing from any line (row/col) or region. There are then two
a) Sole Candidate: This applies when there is only one digit that
will fit into an empty cell. The method is to consider each empty
cell and use "counting" to determine which digits are eliminated
by being in rows or columns intersecting with that cell or in the
region that contains the cell. If it is possible to find EIGHT such
digits then the ninth MUST be the solution for that cell.
(Of course, there is also a useful variant whereby the technique
is applied to two cells in a line and the same two digits are found
to be the only candidates but this is "Hidden Pairs" - demonstrating
that Sole Candidate is but a simplified form of the Pair/Triple etc)
b) Sole Position: This technique considers each digit in turn and
looks at each empty cell in a line (of course one ignores digits
that have already been resolved within the line!) to determine
if it is possible to place the digit in each empty cell. If it is shewn
as possible in more than one cell one moves on to the next digit
to be considered but if only ONE cell in the line can contain the
digit under consideration then that cell is resolved. This can be
applied also a region in a similar way to a line.
Both these techniques are contained implicitly in the candidate
profile approach. The first occurs when there is only a single
candidate for a cell and the second when the profiles for a line
(or region!) contain a digit which appears only once. Of course
finding that involves a closer inspection than sole candidate!
With all of these techniques the REAL skill is based on
a) knowing which technique to use next
b) Selecting which line, region or digit to be the focus for the
next application of a technique.
One of the advantages of Mandatory Pairs is that it can 'root out'
a lot of the easier stuff and many of the "hidden pairs" in a far
more transparent manner than working through the candidate
profiles. This, in turn, reduces the number of occurrences with
which one is dealing in preparing the candidate profiles if it
becomes necessary to use the latter. Also some of the Candidate
techniques become redundant. For example the rule that "if the
only occurrences of a digit in a line are all in one region that digit
may be eliminated from the other two lines in the region" can be
difficult to spot. With M/P it becomes almost self-evident - certainly
obviating the need to scan profiles in the hope of spotting a pattern!
A similar situation arises with the rule about all occurrences of a
digit within a region being in a single row or column.
To return to the main question - pencil marks.
I never make "pencil" marks - as I always use a pen! However, if
I were to use a pen and eraser there would be definite advantages
in using Mandatory Pairs - the marks would be erased.
Two other tips:
1) When I have completed the puzzle as far as I can with M/P and
decide to progress to Candidate profiles, I change the colour of
my pen. This means that I have a simple "break-point" should I
make a mistake with the profiles. My experience is that mistakes
are MUCH more common with candidate profiles than with the
M/P part of the exercise. Applying a break point was a lesson
learned the hard way - although in most cases it is not necessary
to implement it!
2) With so many digits littering the page (and not using an eraser!)
I use the convention of circling the resolved digit (also written large
near to the centre of the cell) to distinguish it form the workings.
This may not be necessary if one is working in pencil and erasing
the digits and the alternative of using different colours for final
and working digits would involve frequent mistakes in which pen
I am aware that some commentators use the circling of numbers
to denote particular types of working - but I do not recall having
seen reference to this on THIS site. Those other people refer to
BIG numbers to distinguish the solution from the "tiny writing" as
one columnist referred to it in Spring 2005. My own view is that
"bigness" is not a adequately clear visual distinction - unless one
is a pedant for writing size, which I am not. However each to her
or his own when developing such conventions.
My personal convention is to put Candidate Profiles at the top left
of a cell and Mandatory Pair digits at bottom left - leaving the
bottom right for the "resolution sequence" number (this is just an
ascending sequential number incremented for each cell resolved
and which allows for tracking back). However, I am very prone to
errors with the these tracking numbers (more duplications than
omissions) as I pay heed to the resolutions rather than the next
number in the series and so the technique does not always prove
useful and does demand printing the LARGE version of the puzzles
as there is insufficient room for sequence numbers on the so-called
(PS: Why is "medium" the default for printing the grids? Only one
grid appears at a time and so have a smaller print does not save
paper. The default just means having to change it each time!!)
So, yes - there are ways to "manage" pencil marks.
One way is to get Sudoku San to print them with the grid - as
SamGJ has not yet acceded to the request to have a "sweep"
option included with the initial print facility in "Draw". As the
facility develops a solution in order to determine a grade for
each grid entered it MUST derive the initial profiles. All that
was requested was an option for them to be printed as
superscripts in a manner similar to the one used by Sudoku San.
Another way is to use Mandatory Pairs as the first resort if the
puzzle is clearly one not to be tacked in a "mark-less" way.
The "BIG" numbers could be distinguished by circles and key
points in the solution process could be marked by a change of
colour of the writing instrument used.
There are probably several more.
The challenge of Sudoku is to be creative!!!
Alan Rayner BS23 2QT
Joined: 07 Dec 2005
|Posted: Mon Jan 16, 2006 8:57 am Post subject: pencil marks
|See also the discussion here.
I reserve erasure for correcting (immediately recognised) mistakes.
|Posted: Fri Feb 17, 2006 5:38 pm Post subject: Re: pencial marks
|coolio wrote: |
|[i]whenever i do this i always have pencial mark from erasing and ersaing is there anyway to help me figure out how to play so that i am able to have not as many pencial marks this way it will be easier to see the # that i have put in[/b] |
When I find a need for pencil marks, I use tiny dots to indicate a cell's candidates, according to this pattern:
1 2 3
4 5 6
7 8 9
E.g., candidates 1, 2, 6, 9 would be marked like this in the cell:
When I've identified that a given number is constrained to one of two cells, I'll indicate that with a slightly heavier mark in those cells.
Then I need only erase tiny dots, and can enter a cell's number with a pen.
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