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November 19th - Very Hard

 
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alanr555



Joined: 01 Aug 2005
Posts: 193
Location: Bideford Devon EX39

PostPosted: Sat Nov 19, 2005 2:27 pm    Post subject: November 19th - Very Hard Reply with quote

Code:

This is yet another example of where the grading system CANNOT
adequately match the human exprience if it is based (as it is) on a
set of computer algorithms.

The algorithm sets "Very Hard", I believe, if it needs to use one of the
"advanced" techniques more than once during its solution. This is not
how the human solver operates.

Clearly it would be impractical to conduct a "focus group" test on each
puzzle before releasing it - so that real people supply the grading. I am
NOT complaining - just advising that we need to take the gradings with
a pinch of salt!

+++
That said, this puzzle was relatively straightforward for solution using
the Mandatory Pairs method. I did need to start documenting the
"missing" profiles (this is not always necessary) but after doing some
work on column 8 the puzzle resolved fairly easily and so I did not
need to complete any more profiling after cols 1-8 already done.

In fact, this is probably a good starter for anyone wishing to explore
the Mandatory Pairs approach having learned the basics. So far as I
recall there were no tricky techniques to use and it fell out in about
half an hour of relatively leisurely attention.

Alan Rayner  BS23 2QT
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samgj
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Joined: 17 Jul 2005
Posts: 106
Location: Cambridge

PostPosted: Sun Nov 20, 2005 12:29 am    Post subject: Re: November 19th - Very Hard Reply with quote

alanr555 wrote:

The algorithm sets "Very Hard", I believe, if it needs to use one of the
"advanced" techniques more than once during its solution. This is not
how the human solver operates.


I don't understand what you mean by "not how the human etc". Very hard currently needs 3 or more "hard" logic steps, which means that the puzzle (by this measure) has 3 choke points. Some people will not notice these points because they are fully familiar and conversant with the logic involved, but these points exist for every human (and indeed computer) solver. The problem with the grading is that some "hard" logic steps are clearly easier than others. Differentiation between them will (eventually) improve the gradings.

Sam
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alanr555



Joined: 01 Aug 2005
Posts: 193
Location: Bideford Devon EX39

PostPosted: Sun Nov 20, 2005 2:11 am    Post subject: Re: November 19th - Very Hard Reply with quote

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> Very hard currently needs 3 or more "hard" logic steps, which
> means that the puzzle (by this measure) has 3 choke points.
>  Some people will not notice these points because they are fully
> familiar and conversant with the logic involved, but these points
> exist for every human (and indeed computer) solver.

My point with this is that the computer solver depends in all cases on
recognising patterns within the candidate profiles. The human solver
will encounter the same "choke" points if solving using candidate
profiles - but may not using other methods.

My use of Mandatory Pairs involves a "different" way of looking at the
relationships in the grid and reasonably often means that a pattern
requiring "advanced" techniques using candidate profiles is a "simple"
technique using M/Pairs.

Thus I have the paradoxical situation whereby "Very Hard" according
to the Candidate Profile method often turn out to be simpler in practice
than the puzzles graded hard - all because the preponderance of what
are "choke" points in C/Profile are much simpler in M/Pairs. Conversely
the ONE choke point of a "hard" puzzle may be such as to cause great
difficulty in the M/Pair scenario.

I am NOT criticising the grading system. It does its job tolerably well.
A few months ago it was a mystery to many of us - but once it had
been explained I suspect that we can all live with it. In fact, anyone
attempting to develop a gradings system deserves praise for being
willing to take on a certain loser. One will NEVER be able to satisfy
the end user with a consistent set of grades agreed by everyone.
There will always be differences of opinion on specific puzzles.

> The problem with the grading is that some "hard" logic steps are
> clearly easier than others.  Differentiation between them will
> (eventually) improve the gradings.

This is true!
However there is another aspect which affects the human solver but
which is NOT a factor for the computer. That is the time spent
searching for the patterns. Modern computing techniques (especially
using vector arrays etc) can resolve a resolvable puzzle in little more
than a few microseconds. The human solver may take several minutes
before she/he finds the same pattern. This affects the PERCEPTION of
the puzzle as hard, v.hard etc - even if the human solver is fully
conversant with how to handle an XY-wing etc once it has been located.

Thus there are two differences between the human and the computer.

a) The methodology employed may well be different and what is "hard"
    in one method may be "simple" in another.

b) Time to locate patterns is not a factor with a computer but is a major
    part of the human experience and will influence the *perception*
    of the hardness or otherwise of a puzzle.

I trust that this clarifies the point.
Meanwhile, I am sure that we would all wish to thank SamGJ for the
enduring magnificent work he does in providing us with this site and
the opportunity to interact with others interested in this pastime.

Alan Rayner  BS23 2QT

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samgj
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Joined: 17 Jul 2005
Posts: 106
Location: Cambridge

PostPosted: Sun Nov 20, 2005 11:52 am    Post subject: Re: November 19th - Very Hard Reply with quote

alanr555 wrote:

My use of Mandatory Pairs involves a "different" way of looking at the
relationships in the grid and reasonably often means that a pattern
requiring "advanced" techniques using candidate profiles is a "simple"
technique using M/Pairs.


OK -- thanks. I need to take some time to understand this better. Ultimately the judgement of what is "hard" logic is subjective. You may spot steps quickly that it takes me ages to see.

alan wrote:

One will NEVER be able to satisfy
the end user with a consistent set of grades agreed by everyone.
There will always be differences of opinion on specific puzzles.


Indeed not, but I do realise that I can do better than I currently do! I'm holding out for 30 hour days!

Sam
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sun Nov 20, 2005 12:05 pm    Post subject: Reply with quote

Sam,

If the 30 hours a day, from 24, are not enough,
use some night hours!

;-)
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alanr555



Joined: 01 Aug 2005
Posts: 193
Location: Bideford Devon EX39

PostPosted: Mon Nov 28, 2005 4:10 am    Post subject: Reply with quote

Code:

> I read your essay about mandantory pairs with many interest, but
> sorry it is not understandable for me.
> I didn't understand how to go on to find the pairs. When I solve the
> puzzle I look at each cell for the candidate list and fortunately
> sometimes I get a naked pair or even a hidden pair and then I know
> that in the column or in the box or in the row the members of this pairs > could't exist anymore. But what do you mean with mandantory pairs
> and how do you get them.

Mandatory Pairs is primarily a method of recording information gleaned
during the solving process so that it is easily accessible when building
further logic upon such a foundation.

The Pairs are found using all the normal "logic" rules - apart from those
which involve looking for patterns among the candidate lists!

I will have a go at the Nov 19th Puzzle to demonstrate how this works.
Please have a copy of that puzzle printed - from the archive - so that
it is possible to follow the logic of Mandatory Pairs.

NB: I have NOT followed the strict sequencing logic of the standard
method and so the sequence of the steps may seem to be jumping
about a bit at times. The intention was to shew the techniques in
practice (warts and all) rather than to give a text book presentation.

1) set r2c3 to 7
2) set r8c4 to 7
3) set r3c4 to 6
Nothing so far is special to M/P - just ordinary logic.
4) Mark r7c6 and r8c6 as a M/P value 6
    (This means that the 6 in region 8 must go in one of those two cells)
5) Set r2c5 to 1
6) Mark r1c5 and r3c5 as a M/P value 8
    (only two possible places in region 2 for value 8)
7) Mark r4c6 and r5c6 as a M/P value 8
    (This is possible because the M/P at step 6 "closes" col 5 for value 8
     and the 8 in r7c4 has closed col 4. Thus only col 6 remains for the
    8 needed in region 5. It has only two blank cells and so these two
    cells form a M/P).
8) Mark r1c5 and r3c5 as a M/P - value 9
9) Note that r1c5 and r3c5 are in Mutual Reception.
    (This means that two cells share the SAME pair of M/P values - so
    that the two together MUST hold them both.
10) Notice that region 2 has seven "allocated" cells.
     Apply "counting" to determine that only 2 and 4 are not allocated.
11) Mark r2c4 and r2c6 as M/P - values 2 and 4
    (These form a mutual reception pair and can be allocated because
     only two values remained for two unallocated cells).
12) Set r4c6 to 3
     (Only place in region 5 remaining open to value 3)
13) Notice that r4c6 has value 8 in its subscript (from  step 7)
     (However this cell is now set to 3 and so 8 is NOW impossible)
14) Set r5c6 to 8
     (Resolved because its partner is impossible)
15) Remove the subscripts from BOTH cells (r4c6 and r5c6)
     NB: Step 14 is the first tangible benefit of Mandatory Pairs.
     If one had not been recording them, one would have to hold
     a lot of logic in one's head to remember that the 8 in column 5
     must be in region 2 so that the 8 in region 5 must be in column 6.
     By recording the M/Ps one avoids having to re-do that logic!
16) Set r5c4 to 5
17) Notice that region 5 now has seven values resolved.
18) Use counting to find that region 5 has 2 and 4 missing.
19) Mark r5c5 and r6c4 as M/Ps - values 2 and 4.
20) Set r7c2 as 1
21) Mark r6c8 and r6c9 as a M/P - value 7
22) Mark r1c8 and r1c9 as a M/P - value 7
23) Notice that value 7 has seven resolutions and two M/Ps.
      (This may be marked as a dot next to the 7 in the string outside
      the grid - as a reminder not to look for any more 7s. From now
      on the 7 will be involved only in confirmation or negation)
24) Mark r3c2 and r3c3 as a M/P - value 3
25) Mark r3c2 and r3c3 as a M/P - value 5
26) Notice that r3c2 and r3c3 are in Mutual Reception.
     (and remember that M/R counts as two allocations when "counting"!)
27) Notice that region 1 now has seven allocations
     (and so the remaining two cells must be in Mutual reception with
      the two 'missing' values)
28) Apply 'counting' to region 1 and find 49 to be missing.
29) Mark r1c1 and r1c2 as M/P - values 4 and 9.
30) Notice that line 1 now contains THREE entries for 9 and that two of
     them are in mutual reception. The one that is not in M/R clearly is
     impossible to be correct.
31) Set r3c5 to 9
     (This is because its partner - in r1c5 - is now impossible)
     NB: This MUST be done in this order as else one is liable to get
     confused. It is WRONG to set r1c5 first - the temptation if one is
     used to dealing with candidate profiles.
32) Remove subscript 9 from both r1c5 and r3c5.
33) Notice that r3c5 has 8 in its subscript but that this value is now
     impossible as the cell has been set to 9.
34) Set r1c5 to 8
35) Remove subscript 8 from both r1c5 and r3c5
36) Mark r2c7 and r2c9 as a M/P - value 3
     (Value 3 in region 3 must be in line 2 as the M/R of 3 in r3c2, r3c3
      "closes" line 3 within this region. The '3' in r5c8 closes column 2
     and so only two cells remain as possibles.
37) Mark r2c7 and r2c9 as a M/P - value 5.
     (logic almost identical to preceding step)
38) Notice that line 2 now has eight cells allocated and apply 'counting'
     to find that '9' is missing.
     (There are TWO mutual receptions on this line - which contribute
      four to the cell count. Add the four resolved and one has eight!)
39) Set r2c8 to 9.
40) Notice that line 3 now has seven allocations (5 resolved + 2 M/R)
41) Use counting to find 4 and 8 missing from line 3
42) Mark r3c7 and r3c8 as M/Ps - values 4 and 8 (also in M/R!)
43) Mark r7c7 and r8c7 as a M/P - value 9.
44) Mark r5c9 and r6c9 as a M/P - value 9
45) Mark r6c1 and r6c3 as a M/P - value 3
46) Mark r4c7 and r4c9 as a M/P - value 6
47) Set r4c1 to 1
48) Notice that all NINE values of '1' have been found and cross
     off that value from the external string.
49) Mark r9c1 and r9c3 as a M/P - value 8
50) Notice that r3c2 contains subscript 5 when there is already a
     resolved 5 in that column.
     (This should have been noticed earlier!!!)
51) Declare r3c2 as impossible for 5 and promote r3c3.
     NB: From here on the tedious repetition on the stages of setting
     mutual reception pairs will be omitted - on the assumption that
     the procedure became obvious earlier. This includes the removal
     of both pairs of subscripts.
52) Set r3c3 to 5
53) Set r3c2 to 3
54) Mark r8c1 and r9c1 as a M/P - value 5.
55) Mark r8c2 and r9c2 as a M/P - value 6.

At this point a scan of the grid does not shew any obvious next steps
and so it is time to move on to "Stage Two" of the technique. This is
the recording at the right of each row and the top of each column
the "Missing" profile for the line involved. "Stage Three" is the writing
of candidate profiles for each cell - but this is delayed for as long as
possible!

The "Missing" profiles for each line are written in such as way as to
highlight the existence of any embedded pairs/triplets etc as the
profile for lines 1 and 2 below will demonstrate.

Profiles are set as
Row 1: (49) and (267)
Row 2: (24) and (35)
Row 3: (48)
Row 4: (2468)
Row 5: (249)
Row 6: (234789)
Row 7: (23569)
Row 8: (234569)
Row 9: (234568)

Col 1: (34589)
Col 2: (2469)
Col 3: (23489)
Col 4: (24)
Col 5: (2345)
Col 6: (246)
Col 7: (2345689)
Col 8: (24678)
Col 9: (235679)

During this process it sometimes becomes clear that there is only
one number possible for a particular cell or that a digit must be placed
in one of only two cells.

The interim position is:

001/385/000
687/010/090
235/697/001

100/973/050
076/508/130
050/061/000

710/800/004
000/700/018
000/109/700

56) Here it is apparent that the pair (35) can be excluded from
     most of the cells in column 9
     35 in r1c4,r1c6 excludes r1c9
     35 in r5c8,r4c8 excludes all region 6

    Thus 35 in column 9 must be in r2c9 or r9c9 so that the
    missing profile for col 9 becomes (35)(2679)

Looking at my original solution of this puzzle, I find that I had some
other M/Ps marked but at this time of the morning, I cannot see why
they have been marked. Thus, I will need to return to this one.

The M/Ps marked are

62 in r1c7 and r1c9
46 in r4c7 and r4c9
9 in r6c1 and r6c3
8 in r6c7 and r6c8
2 in r7c6 and r8c6
26 in r7c8 and r9c8

Because M/Ps can be added at any time (and removed when the cell
or its partner is resolved), I cannot tell the sequence in which these
pairs were identified. It is clear that if those values were genuinely
derived, the solution is fairly easy. At present I do not know if I
was deluding myself and had a "lucky break" to get the right answers.

The solution CAN be obtained by moving to Candidate Profiles at
this point to reduce Column 7.

r1c7,r3c7,r4c7,r6c7 reduce to a quadruple with 2468
(values 26,48,2468,248 respectively)
which leaves a triple in r2c7,r7c7,r8c7 of 359 (35,359,359).

Then, using 'counting' on box 9 gives

1478 resolved
359 in a triple
26 remaining
These last two become a mutual reception in r7c8 and r9c8

57) Mark r7c8  and r9c8 as a M/P values 2,6.
58) Mark r1c7 and r1c9 as a M/P - value 6.
     (The '6's at r7c8 and r9c8 close that column and
      those at r2c1 and r4c4 close rows 2,3 leaving only row 1)
59) Mark r1c7 and r1c9 as a M/P - value 2.
     (Logic almost the same as for preceding step)
60) Notice that r1c7 has 26 and r1c9 has 267 as subscript.
     
      Here there is a rule of Mandatory Pairs. If two cells share the
      same two values as Mandatory Pairs (and thus are in Mutual
      Reception) no third value is allowable.

      Here this means that 7 in r1c9 is impossible.

61) Set r1c8 to 7
62) Set r6c9 to 7 (because r6c8 cannot be 7)
63) Set r5c9 to 9 (because r6c9 cannot be 9)

These last two steps shew the ease with which cells can be resolved
when their partners are proved to be impossible.

64) Mark r6c1 and r6c3 as M/P - value 9
65) Notice that all nine '7's have been resolved.
66) Set r4c3 to 8
     (Value 8 in region 4 cannot be in row 6 as there is a mutual
     reception which precludes any other value)
67) Set r9c1 to 8 (because partner in r9c3 cannot be 8)
68) Set r8c1 to 5 (because partner in r9c1 cannot be 5)
69) Notice that Box 4 has seven cells allocated.
     Counting reveals missing values to be 2 and 4.
     Normally r5c1 and r4c2 would be set as mutual reception (24)
     but r3c1 is already set as 2 and so we can skip the M/R.
70) Set r4c2 to 2
71) Set r5c1 to 4
72) Notice that r1c1 cannot be 1 and set r1c2 to 4
73) Set r1c1 to 9 consequent on previous step
74) Notice that r6c1 cannot be 9 and set r6c3 to 9
75) Set r6c1 to 3 consequent on preceding.
76) Notice that col 2 has 7 cells allocated.
     (then usual count check - not always noted from here onwards)
77) Set r8c2 to 9
78) Set r9c2 to 6 consequent on preceding.
79) Notice that row 4 has seven allocated.
80) Set r4c7 to 4
81) Set r4c9 to 6
82) set r3c7 to 8
83) Set r3c8 to 4
84) Set r5c5 to 2
85) Set r6c4 to 4
86) Set r6c8 to 8
87) Set r6c7 to 2
88) Set r1c9 to 2 (as r1c7 cannot be 2)
89) Set r1c7 to 6
90) Set r8c7 to 3
     (column 7 is missing 359 and 59 exist in row 8)
91) Set r7c7 to 9 (as r8c7 cannot be 9)
92) Set r2c9 to 3 and r2c7 to 5
93) Set r9c9 to 5
94) Set r7c8 to 6 (as r9c8 cannot be 6)
95) Set r9c8 to 2
96) Set r7c6 to 2
     (col 6 lacks 246 and 46 exist in row 7)
97) Set r8c6 to 6 and then r2c6 to 4 and r2c4 to 2.
98) Set r7c3 to 3 and r7c5 to 7
99) The remaining four cells resolve easily.

++++

The crunch point after step 55 is clearly what gained this one a
'very hard' grade. Apart from that point, the whole thing was
solvable using Mandatory Pairs as the only pencil marks.

When I first did the puzzle, I appear to have solved it using only
Mandaory Pairs and just eight of the "Missing " profiles - having
stopped recording them after column 8. Thus it may be that it was
not necessary to resort to candidate profiles.

> I would be very pleased to hear from you, especially I'm stucked with
> puzzle from Nov 19 and I want to apply your interesting method. Thx a
> lot for your efforts in advance.

+++
Hopefully those who worked through much of the puzzle (and in
practice it takes less time to solve than it does to document!) will
find some of the techniques useful.

a) Medium puzzles can usually be solved without any other techniques
b) Difficult puzzles can uually be solved in the same way but sometimes
    can prove to be a bit trickier.
c) Even where Mandatory pairs does not take one all the way to a solution
    it can be very useful in terms of getting a major way along the road
    before having to clutter up the grid with candidate profiles and having
    to embark on the associated pattern discernment process. I find that
    many 'hidden pairs' are not so hidden in many cases (although the
    Nov 19th example shews that hidden triplets can still obscure smooth
    progress!
d) My recommendation would be to try the techniques on a 'Medium'
    puzzle and compare the ease of solution with 'no pencil marks'.
e) As can be seen from the solution commentary, the emphasis in
    the M/P work is on spotting the logic rather than scanning profiles
    for patterns. In theory, this give a more satisfying experience.
    Only by trying the method can one discover whether this is so.

+++
Thanks to all those who have managed to read this far!

Alan Rayner  BS23 2QT
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