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alanr555
Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39
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 Posted: Sun Feb 26, 2006 10:41 am Post subject: 25th February - V.Hard Classic |
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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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