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Dec 9 Very Hard

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Dec 09, 2007 4:10 am Post subject: Dec 9 Very Hard

Marty, Thanks to e-mail, solved before midnight! A good example, I thought, of why one should be slow to fill in pencil marks. Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Dec 09, 2007 6:11 am Post subject: Re: Dec 9 Very Hard

keith wrote:

Marty,

Thanks to e-mail, solved before midnight! A good example, I thought, of why one should be slow to fill in pencil marks.

Keith

Well, I solved it after midnight. Of course, I fill in what I can when a number is given in two boxes in a band or stack. Then it's on to pencil marks. I do scan to see what's available before writing in the PMs, but I suspect you do a lot more than that.

But in this puzzle, I could see after the fact that some cells could've probably been solved without the marks had one spent more time looking.

I solve easier puzzles without PMs, like the Pappacoms that the local fish-wrapper carries.

andras

Joined: 31 Oct 2007
Posts: 56
Location: Mid Wales

Posted: Sun Dec 09, 2007 8:37 am Post subject: Re: Dec 9 Very Hard

keith wrote:

Marty,

Thanks to e-mail, solved before midnight! A good example, I thought, of why one should be slow to fill in pencil marks.

Keith

I'm not sure I get your point - I used PMs as usual, found an xy on 1,2,9, and the puzzle broke; but only after using pencil marks all over the shop.

Another nice puzzle!

John

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Dec 09, 2007 9:51 am Post subject: Re: Dec 9 Very Hard

andras wrote:

I'm not sure I get your point - I used PMs as usual, found an xy on 1,2,9, and the puzzle broke; but only after using pencil marks all over the shop.

Which is, I think, my point. After a few singles,

Code:

+-------------------+-------------------+-------------------+
| 7 1 259 | 4 269 3 | 2568 2689 589 |
| 369 56 2359 | 269 8 126 | 4 1269 7 |
| 8 4 29 | 7 1269 5 | 126 3 19 |
+-------------------+-------------------+-------------------+
| 5 2 134 | 369 13469 1468 | 7 18 138 |
| 134 7 6 | 235 12345 1248 | 9 128 1358 |
| 13 9 8 | 235 1235 7 | 1235 4 6 |
+-------------------+-------------------+-------------------+
| 1469 3 7 | 8 246 246 | 16 5 149 |
| 2 568 1459 | 356 7 46 | 1368 1689 13489 |
| 46 568 45 | 1 3456 9 | 368 7 2 |
+-------------------+-------------------+-------------------+

There is a hidden pair <19> in B7> and <35> in B8. Later, there is <69> in C4, <29> in B1, <129> in R2, <69> in C8, and <58> in B3.

Maybe it's just a question of style, but I find it much easier to enter only pm's for cells that have two candidates. The pairs show up much more easily than finding them as hidden in all the candidates. Translation: Much less erasing!

Keith

cgordon

Joined: 04 May 2007
Posts: 769
Location: ontario, canada

Posted: Sun Dec 09, 2007 5:01 pm Post subject:

I eventually found the <129> xy wing but the searching was starting to hurt. I really can't see any other solution.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Dec 09, 2007 8:19 pm Post subject:

xy-wing I am with cgordon, eyes hurting

alanr555

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

Posted: Sun Dec 09, 2007 8:20 pm Post subject: Re: Dec 9 Very Hard

wrote:

I do scan to see what's available before writing in the PMs, but I suspect you do a lot more than that.

It is possible to do a lot of preliminary work on this one.
Our old friend Mandatory Pairs enables
4 in row 2,
8 and 7 in row 3,
7 in row 5,
9 and 7 in row 6,
7 in row 7

Then it is down to pencil marks BUT the fact of having marked
the Mandatory Pairs tightens the PMs from those produced by
a "sweep".

In particular, there is a mandatory pair of 5 in r1c7 and r1c9
(because there must be a 5 in row 2 in c123)
This removes the 5 from r1c3 and gives a mutual reception
of 29 in r1c3 and r3c3.

That sets off a whole load more of Mandatory Pairs work and
enable solution of
9 in row 2, 6 and 9 in row 4, 9 in row 7 and 1 in row 8.

Careful inspection of the M/P marks enables some further
elimination of the profile marks and reveals the cells with
only two possibilities much more clearly.

In the top block there were
29 in r1c3,r3c3
12 in r2c6,r2c8
a triple 269 in row 1 (cols 3,5,8)
a quartet 1269 in row 4
(126 in r3c5,r3c7 and 19 in r3c9)

Clearly there is a possible link here.
Following the implications from the only values (2,9)
in r1c3 leads to a unique value for r2c8.

Having found that a test on the implications for r2c8
leads to a paradox - confirming the solution. After
that all cells resolved very easily.

+++
The challenge is to find the key cell that opens up an
implication chain. This is much easier when a lot of
cells have only two possibilities and the chains are
contained within a block - as today.

Using mandatory pairs as a preliminary does make it
much easier to refine the pencil marks.

I use a sequence of placing for pencil marks.

1) Mutual Receptions derived from the M/P process.
2) Rows and Columns with the maximum number of
cells already resolved.
3) Other rows/columns in sequence of descending
number of cells resolved.

In doing this I use process of writing the possibilities
remaining for a row/column outside the row/column.

eg col3 had (123459) at its head
When a pair/triple etc is discovered, the row/column
profile is amended to read say (29)(1345) which
indicates two subgroups in the row/column. In a few
cases I have known three sub-groups but usually one
is resolved almost immediately and so disappears.

Having written the PMs as above, the next stage is to
refine them from the Mandatory Pair information. As
the process continues, there may be additional M/P
information found and so the process is iterative.

The good news is that Mandatory Pairs will quite often
solve puzzles without resort to pencil marks giving
the profiles. Personally, I dislike the chore of deriving
the pencil marks and so I use Mandatory Pairs as much
as possible after getting stuck with "look and see". If
M/Pairs does not resolve, then the further good news
is (as above) its contribution to the refinement of the
profile pencil marks - reducing obfuscation!

Some readers of this post will not be aware of Mandatory
Pairs as a solution method. Use of the search index on
the Daily sudoku forum will reveal some historical posts
on the subject. It has been refined since the early days
but the essential principle remains - identification of the
ONLY two cells in a 3x3 box which could POSSIBLY
contain the specific digit. That digit is written (small!)
in the bottom left corner of the two cells to which it
relates. When information comes to light which means
that one of the two cells CANNOT hold that digit, the
binary principle means that it MUST be in the other cell.

This can lead to some rapid solving as resolving one cell
may eliminate one or more other values and those force
the resolution of other cells. That process is akin to the
binary chains discussed previously but, of course, not
all chains will be identified by M/Pairs - just a subset of
very useful ones!

+++

So, Mandatory Pairs will not win prizes for minimum solving times
but it does avoid the profile setting chore until much later in the
process and often enables it to be avoided altogether. Even on
more difficult puzzles, it can assist with identifying where to look
in terms of reducing the length of the PM profile elements without
the sometimes mind-boggling visual search for patterns. It is NOT
a method appropriate for computer solving but, in my view, it does
present a more human take on the solution challenge.

gtorborg77

Joined: 22 May 2007
Posts: 2

Posted: Thu Dec 13, 2007 8:53 pm Post subject: Dec 9 Very Hard

Hi...I haven't posted for a long while and I'm stumped. My puzzle didn't break down after finding the xy-wing mentioned earlier. In fact, I've found two other xy-wing patterns that result in no eliminations.

After basics, some naked pairs and at least one triple, an x-wing and the aforementioned xy-wing, I'm left with:

Code:

7 1 29 4 26 3 25 2689 589
36 56 35 9 8 12 4 12 7
8 4 29 7 126 5 16 3 19

5 2 34 6 9 148 7 18 138
134 7 6 23 154 148 9 128 1358
13 9 8 23 15 7 25 4 6

9 3 7 8 24 246 16 5 14
2 8 1 5 7 46 3 69 49
46 56 45 1 3 9 8 7 2

What am I missing?

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Dec 13, 2007 8:57 pm Post subject:

128 naked triple col 8

gtorborg77

Joined: 22 May 2007
Posts: 2

Posted: Thu Dec 13, 2007 9:07 pm Post subject: Dec 9 Very Hard

Thanks, that did it!

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Dec 13, 2007 9:13 pm Post subject: Re: Dec 9 Very Hard

gtorborg77 wrote:

Thanks, that did it!

You're welcome.

And welcome back ... Smile

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