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Jan 20 Puzzle

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PostPosted: Tue Jan 24, 2006 1:27 am    Post subject: Jan 20 Puzzle Reply with quote

Been doing these puzzles for a couple months now and am totally addicted. I was wondering if there are two solutions to this one or did I do something wrong.

My second row is 6-9-5 8-4-2 1-7-3
Their second row is 6-5-9 8-4-2 1-7-3

My sixth row is 5-6-9 4-2-8 3-1-7
Their sixth row is 5-9-6 4-2-8 3-1-7
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Steve R

Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Tue Jan 24, 2006 4:00 am    Post subject: Jan 20 Puzzle Reply with quote

I am afraid you have fallen into error. The puzzle has a unique solution.
There is not sufficient information to identify the slip. Why not try the drawer? If it brings out a difficulty, I and others will do our best to resolve it.

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Posts: 198
Location: Bideford Devon EX39

PostPosted: Tue Jan 24, 2006 10:56 pm    Post subject: Reply with quote

This puzzle is solvable using Mandatory Pairs - without any
need to resort to Candidate Profiles.

Alan Rayner BS23 2QT
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PostPosted: Wed Jan 25, 2006 3:49 am    Post subject: Reply with quote

Thank you for the responses. One more question: what is a mandatory pair?
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Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Jan 26, 2006 1:42 am    Post subject: Reply with quote


>  One more question:  What is a mandatory pair?

Mandatory Pairs is a system of recording information about a
puzzle as such information is discovered - as opposed to the
"Candidate Profiles" which seek to determine which values
are still possible for each cell.

Essentially a "Mandatory Pair" is a condition that a particular
digit MUST be in one of just TWO positions within one of the
3x3 regions.

The method is an aid to HUMAN solvers and saves clogging up
the short term memory.

There is an early explanation of the method at

[url=http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=187&highlight=mandatory+pairs] October 13th.[/url]

Link Here.


The usefulness of Mandatory Pairs is enhanced by their binary
property. If it can be shewn that one of the pair is impossible
then the other member of the pair MUST be true.

The discussion quoted contains much of the material but some
other aspects have been developed since.

One of the challenges is to solve "Medium" graded puzzles without
ANY pencil marks and to solve Hard/V.Hard puzzles using only the
Mandatory pair marks. The latter can be difficult in many cases as
the solution may depend upon subtle patterns within the Candidate
Profiles but using Mandatory Pairs can take one a good way along
the road to solution and reduce the work involved in derivation of
the Candidate Profiles IF (!) one needs to xx to that method
after exhausting the Mandatory Pairs.

Using M/P often brings out much more clearly patterns relating
to pairs which might take a lot of hunting using the C/P method.
Its deficiency is that it does not record REMOTE pairs and so these
have to be found and stored in short-term memory. However, the
method does reduce the load on such memory considerably.

A recent posting in the "Daily Puzzles" category of the forum gave
a worked example of using M/P for the November 5th puzzle. This
one involved xx to Candidate Profiles but demonstrated some
of the ideas involved and how the M/P marks can assist the C/P
part of the exercise.

With some of the puzzles I have posted a note to the effect that
they can be solved entirely using Mandatory Pairs. Those puzzles
would prove interesting exercises and useful practice in the method.
M/P still uses logic as its generator rather than relying on the
accuracy of candidate derivation (prone to error if done manually)
and scanning of digit strings for patterns. Of course, the latter is
necessary for the more complex/hidden cases but preliminary use
of M/P eases the task by allowing one to concentrate on the
"breaking point" of the puzzle rather than having to wade through
the "mush" of profiles existing on a fresh puzzle.

From time to time one resorts to C/P and then discovers afterwards
that one missed something in M/P so that it was not really necessary
to make the transition to C/P. That can be personally maddening
but points the way to a learning process.

There are four steps to solving a 'hard or v.hard' sudoku puzzle.

a) Apply logic to the puzzle and record information gleaned
    using the Mandatory pairs protocols.

b) Derive the "Missing" profiles for each row/column and record
   them at the end of the row/column - taking especial note of
   any "subsets" discovered in the process as a result of
   recording Pairs in "Mutual Reception". These profiles can be
   used for spotting "Sole Candidate" and "Sole Position" solutions.

c) Move on to full Candidate Profiles.
   By convention the C/P information is recorded at the top left
   of each cell whereas the M/P information is recorded at the
   bottom left of each cell. Care must be taken to distinguish
   them as the treatment accorded to each category is different.
   (M/P implies binary characteristics but C/P does not. On the
   other hand absence in C/P means impossible but not in M/P)
   There is scope for changing to a different colour pen when
   making the transition to C/P.

d) If the puzzle is still not solved, advanced techniques may be
   needed. These include such things as Implicational Chains -
   following through "paths" between two cells in such a way
   that the value derived by logic for the destination cell of the
   path is the same whichever value is selected for the origin
   cell. However, puzzles requiring these types of solution tend
   to be in the "Other" section rather than the "Daily Puzzles" one.


Thus I encourage those who have not used Mandatory pairs to
give it a fair go - for a different experience of Sudoku solving.

M/P often enables a solution without resort to the chore of the
'tiny writing' and provides a method of building on what one
has learned earlier about a particular puzzle by making very
simple marks on a "mark as you go" basis - with corresponding
expunction of marks as their usefulness has expired by the
setting of resolved cells based on the information so recorded.

Alan Rayner  BS23 2QT

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