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25th February - V.Hard Classic

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

PostPosted: Sun Feb 26, 2006 10:41 am    Post subject: 25th February - V.Hard Classic Reply with quote


This was an excellent example of a puzzle that can be solved
using Mandatory Pairs - with recourse to several of the M/Pairs
techniques. It took me about 20/25 minutes - a delightful
journey of revelation as logical point followed logical point.

Among the techniques used the most important was recognition
of mutual reception. From this base it was possible to use the
"eliminate the interloper" technique (a) and also the "counting"
technique (b) - in one instance with two mutual receptions in the
same region. Another useful one was that of a "Mutual Pair closes
the line" (c).

a) If three cells are involved in Mandatory Pairs as eg
     34,3,4 and it transpires that digit 5 is restricted to the first
    two cells the involvements become 345,35,4. The first two
    are now in mutual reception with (35) and the '4' in the
    first cell is an 'interloper'. Thus the '4' can be eliminated
    and the '4' in the third cell is promoted to being resolved
    (irrespective of whatever else is happening! If the third cell
    were to be 46 say then the resolution of that 4 would lead
    on to resolve the partner of the '6' as well!)

b) If two cells are in Mutual Reception they count towards the
    fulfilment of the row, column or region in which they are
    situated - FOR the purposes of 'counting'.

   eg A 'line' has 1234 resolved and Mutual receptions of (58) in
   two cells plus (69) in two others. Immediately the unmarked
   cell can be resolved with value '7' as the M/R values must be
   discounted in determining the "Missing" profile for the line.

   Further if the line has only 123 (rather than 1234 above)
   resolved. One can then set the remaining TWO cells as being
   in mutual reception with values (47).

c) If a mutual reception occurs in a true line (row/col rather
    than askew in a region) they are very likely to provide an
    additional constraint on the placement of other values in the
    region - wonderful!

    This is an extension of the general situation that a Mandatory
    Pair "closes" a line to any further occurrence of that digit in
    the same line - even in a different region and despite the
    fact that no cell has been resolved. A mutual reception also
   closes the CELLS involved to any other possibility.
    It is important to recognise these as they have the potential
    to restrict quite significantly the possibilities for other digits
    in the same region or for the same digit in other regions. If
    such restriction does reduce the possibilities to a single cell
    - another one is resolved!


Anyway, this puzzle (25-Feb) is an excellent example of the M/Pairs
techniques in action. I commend the method (for this puzzle!) as
being more enjoyable than using Candidate Profiles (probably a
long slog if the grading of V.Hard is correct!).

Alan Rayner  BS23 2QT
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