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Paladin
Joined: 10 Feb 2006
Posts: 15
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 Posted: Fri Feb 10, 2006 10:35 pm Post subject: 2/8/06 Daily Puzzle: What next? |
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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
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| Posted: Sat Feb 11, 2006 12:26 am Post subject: Here's one way to solve it |
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Feb 11, 2006 3:31 pm Post subject: |
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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: 42
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| Posted: Sun Feb 12, 2006 7:50 pm Post subject: Please EXplain "Remote Pair" Concept |
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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
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| Posted: Sun Feb 12, 2006 8:30 pm Post subject: Remote pairs |
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Feb 12, 2006 9:53 pm Post subject: Remote pairs |
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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
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
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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
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I hope this helps,
Keith |
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dejsmith
Joined: 23 Oct 2005
Posts: 42
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| Posted: Tue Feb 14, 2006 4:44 am Post subject: Remote Pairs |
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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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