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2/8/06 Daily Puzzle: What next?

 
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Paladin



Joined: 10 Feb 2006
Posts: 15

PostPosted: Fri Feb 10, 2006 10:35 pm    Post subject: 2/8/06 Daily Puzzle: What next? Reply with quote

Start Grid: 02/08/06 Sudocue.net Daily Puzzle

..1|.8.|.47
..3|... |...
6..|1..|...
---------------------
.1. |.7.|86.
... |...|...
.75|.4.|.1.
---------------------
... |..5|. 3
... |... |2..
18.|.2.|7..

After completing 26 cells, start grid reduces to*:

.51|.8.|647
8.3|...|12.
6.7|1..|.38
---------------------
31.|57.|864
468|.31|.7.
.75|.4.|31.
---------------------
7..|.15|4.3
53.|...|2.1
18.|.2.|756

*Reduction completed without application of XY Wings,
Turbot fish, unique rectangles, guardians, etc; no
X wings or swordfish or forcing chains located.
(Sorry about the sloppy appearance of the grids;
I just don't seem to be able to line this stuff up)

What must be done to solve this puzzle?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sat Feb 11, 2006 12:26 am    Post subject: Here's one way to solve it Reply with quote

Hi, Paladin! Welcome to the forum.

First, if you want to get grids to line up nicely you need to use the "Code" and "/Code" tags in your post. Here's an example of what you need to write.
Code:
[code]
1   2   3   4   .
5   6   7   8   .
.   .   .   .   .
[/code]

Try reading the "FAQ" about this ... it gives a fairly good explanation.

As to the puzzle, I've already posted a pretty complete explanation in this forum, right here. Oh -- there's some other stuff in that post ... the discussion of this puzzle starts about half-way down. Here's the short version of how this puzzle can be resolved.

At the point you illustrated the grid of possibilities looks like this.
Code:
 29     5     1    239    8    39     6     4     7
  8    49     3   4679   569   67     1     2    59
  6    24     7     1    59    24    59     3     8
  3     1    29     5     7    29     8     6     4
  4     6     8    29     3     1    59     7    259
 29     7     5    68     4    68     3     1    29
  7    29    269   689    1     5     4    89     3
  5     3    469  46789  69    678    2    89     1
  1     8    49    349    2    349    7     5     6


You can follow a "double-implication chain" from r7c2. Assume that r7c2 = 9. Then we get two chains of inference.

A. r7c2 = 9 ==> r9c3 = 4 ==> {3, 9} pair in r9c4 & r9c6
B. r7c2 = 9 & r9c3 = 4 ==> r8c3 = 6 ==>r8c5 = 9

And now it's easily seen that the bottom center 3x3 box cannot be completed, so we must have r7c2 = 2. dcb
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sat Feb 11, 2006 3:31 pm    Post subject: Reply with quote

In the situation given above by David, R1C1 and R4C6 are a remote pair <29>, so R1C6 cannot be <9>, it must be <3>.

Then you can complete the solution without forcing chains, but by finding an X-wing and an XY-wing.

Keith
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dejsmith



Joined: 23 Oct 2005
Posts: 40

PostPosted: Sun Feb 12, 2006 7:50 pm    Post subject: Please EXplain "Remote Pair" Concept Reply with quote

Keith, I also found an X Wing & XY Wing that helped me solve this puzzle; however I do not understand your "remote pair" concept. I "lightly" looked for an explanation online; but could not find any. My initial reaction is that I could not justify that this method is valid. Could you enlighten me as to when "remote pairs" can apply? Thanks in advance.

Dave
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Feb 12, 2006 8:30 pm    Post subject: Remote pairs Reply with quote

Hi, Dave! I haven't heard from you in a while.

A "remote pair" is related to "coloring" ... but instead of coloring for single digits, we mark only the cells that contain the same pair of possibilities (in this case, {2, 9}).
Code:
 29+    5     1    239    8    39     6     4     7
  8    49     3   4679   569   67     1     2    59
  6    24     7     1    59    24    59     3     8
  3     1    29+    5     7    29-    8     6     4
  4     6     8    29     3     1    59     7    259
 29-    7     5    68     4    68     3     1    29+
  7    29    269   689    1     5     4    89     3
  5     3    469  46789  69    678    2    89     1
  1     8    49    349    2    349    7     5     6

There are only two possible ways to fit the "2"s and "9"s into the cells marked with + and - signs in the grid -- either the + cells contain 2 and the - cells contain 9, or vice versa.

If r1c1 = 9 then r1c6 <> 9
If r1c1 = 2 then r4c6 = 9 and r1c6 <> 9

So there has to be a "3" at r1c6. dcb
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun Feb 12, 2006 9:53 pm    Post subject: Remote pairs Reply with quote

Dave,

Remote pairs are not very common, but they are very easy to spot. If the puzzle has a number of squares that have the same two possibilities, see if you can chain these squares together.

Here is a pair
Code:
 

AB  .  .  AB



No other square in the same row can have either the value A or the value B. Now suppose there are other squares which have the same possibilities. They might be laid out like this:

Code:
 

AB  .  .  AB
.   .  .  .
.   .  .  .
.   .  .  AB 
.   .  .  .   .
.   .  .  .   AB



where the lower two are in the same block. Now, number the nodes in the chain. Each odd-numbered square is a pair with each even-numbered square. (Or, label them + and - as David does.) If a pair is not in the same Row, Column, or Block, they are a "remote pair".

In this case, the top left and lower right squares are a remote pair. The square labelled "*" below cannot be A or B.

Code:


AB  .  .  AB
.   .  .  .
.   .  .  .
.   .  .  AB 
.   .  .  .   .
*   .  .  .   AB



I hope this helps,

Keith
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dejsmith



Joined: 23 Oct 2005
Posts: 40

PostPosted: Tue Feb 14, 2006 4:44 am    Post subject: Remote Pairs Reply with quote

Thanks guys. I'll have to print out your explanations & study them a bit. After those embarrassing, simple BUG puzzles I recently sent you, David, I decided to just work on getting better rather than bother you with additional puzzles.

Dave
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