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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Aug 19, 2006 9:08 am Post subject: DB Saturday Puzzle - August 19, 2006 |
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After finding a Unique Rectangle I am stuck for the moment.
Keith
| Code: | Puzzle: DB081906 ******
+-------+-------+-------+
| . . . | . . . | 3 7 . |
| . . . | 8 . 5 | 9 4 . |
| . . . | 2 . 7 | 8 . 5 |
+-------+-------+-------+
| 4 . 9 | . . . | . 5 . |
| . 5 . | . 8 . | . 3 . |
| . 7 . | . . . | 2 . 4 |
+-------+-------+-------+
| 2 . 5 | 3 . 4 | . . . |
| . 4 3 | 9 . 8 | . . . |
| . 1 6 | . . . | . . . |
+-------+-------+-------+ |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Aug 19, 2006 1:28 pm Post subject: |
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| Code: | *-----------------------------------------------------------*
| 5 89 48 | 16 49 A16 | 3 7 2 |
| 16 2 7 | 8 3 5 | 9 4 16 |
| 39 36 14 | 2 49 7 | 8 16 5 |
|-------------------+-------------------+-------------------|
| 4 36 9 | 7 2 136 | 16 5 8 |
| 16 5 2 | 4 8 A1-69 | 167 3 79 |
|B38 7 B18 |B16 5 A39 | 2 169 4 |
|-------------------+-------------------+-------------------|
| 2 89 5 | 3 16 4 | 167 1689 79 |
| 7 4 3 | 9 16 8 | 5 2 16 |
| 89 1 6 | 5 7 2 | 4 89 3 |
*-----------------------------------------------------------*
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With 3 strong links the 6 in r5c6 can be eliminated (r5c1-r2c1,r2c9-r3c8,r6c8-r6c4).
And there is an ALS, where the 3 is locked to r6c6 in A (1369) and to r6c1 in B (1368), when r4c6=6. But as always i first found a chain and then constructed the ALS. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 19, 2006 3:15 pm Post subject: |
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| Quote: | | And there is an ALS, |
What's that stand for, other than the dreaded disease? |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Sat Aug 19, 2006 3:20 pm Post subject: |
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Almost Locked Set. Not sure what the definition is.
Nice little puzzle, as usual. I tried like heck to make an XY-chain with all the (1,6) pairs but never could get a result. Finally realized it almost had to be an XY-wing, which took a while to find as there were many possibilities. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 19, 2006 5:17 pm Post subject: |
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| I also wanted to use the remote pairs technique with 16, but couldn't. I also couldn't find any X-Wings, XY-Wings, strong links, etc., so I had to rely on the old standby, the chain. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Aug 19, 2006 9:41 pm Post subject: |
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Hi Marty,
here is the original ALS link, but i am sure, you dont need it  |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sat Aug 19, 2006 11:58 pm Post subject: Finding the chain of remote pairs |
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| Marty R wrote: | | I also wanted to use the remote pairs technique with 16, but couldn't. |
Here's how I used the "double-implication chain" technique to extend the chain of remote pairs far enough to crack this puzzle.
| Code: | *-----------------------------------------------------------*
| 5 89 48 | 16 49 16 | 3 7 2 |
| 16+ 2 7 | 8 3 5 | 9 4 16- |
| 39 36 14 | 2 49 7 | 8 16+ 5 |
|-------------------+-------------------+-------------------|
| 4 36 9 | 7 2 136 | 16 5 8 |
| 16- 5 2 | 4 8 169 | 167 3 79 |
| 38 7 18 | 16 5 39 | 2 169 4 |
|-------------------+-------------------+-------------------|
| 2 89 5 | 3 16+ 4 | 167 1689* 79 |
| 7 4 3 | 9 16- 8 | 5 2 16+ |
| 89 1 6 | 5 7 2 | 4 89 3 |
*-----------------------------------------------------------* |
As indicated by the +/- signs above, there's already an extensive network of {1, 6} pairs spreading throughout the puzzle. Our "target" cell -- the one needed to make useful inferences from the pattern -- is r7c8, marked with an asterisk above.
We start the double-implication chain in r2c1.
A. r2c1 = 1 ==> r5c1 = 6 ==> r6c3 = 1 ==> r6c4 = 6 ==> r6c8 = 9 ==> r9c8 = 8 ==> {1, 6} at r7c8.
B1. r2c1 = 6 ==> r5c1 = 1 ==> r4c2 = 6 ==> r4c7 = 1
B2. r2c1 = 6 ==> r2c9 = 1 ==> r3c8 = 6
B3 (r4c7 = 1 & r3c8 = 6) ==> r6c8 = 9 ==> r9c8 = 8 ==> {1, 6} at r7c8.
So the double-implication chain reveals that neither "8" nor "9" can appear at r7c8, leaving the grid looking like this.
| Code: | *-----------------------------------------------------------*
| 5 89 48 | 16 49 16 | 3 7 2 |
| 16+ 2 7 | 8 3 5 | 9 4 16- |
| 39 36 14 | 2 49 7 | 8 16+ 5 |
|-------------------+-------------------+-------------------|
| 4 36 9 | 7 2 136 | 16 5 8 |
| 16- 5 2 | 4 8 169 | 167 3 79 |
| 38 7 18 | 16 5 39 | 2 169 4 |
|-------------------+-------------------+-------------------|
| 2 89 5 | 3 16+ 4 | 167 16- 79 |
| 7 4 3 | 9 16- 8 | 5 2 16+ |
| 89 1 6 | 5 7 2 | 4 89 3 |
*-----------------------------------------------------------* |
Now we see that r7c7 = 7, and that r6c8 = 9, after which we can extend the {1, 6} network a bit farther, and the entire puzzle falls to pieces. dcb |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Aug 20, 2006 10:40 am Post subject: Another (neat) solution |
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Here's what I did. After the usaul basic moves, and a Type 1 UR to remove <16> in R6C6:
| Code: | +----------------+----------------+----------------+
| 5 89 48 | 16 49 16 | 3 7 2 |
| 16 2 7 | 8 3 5 | 9 4 16 |
| 39 36B 14 | 2 49 7 | 8 16b 5 |
+----------------+----------------+----------------+
| 4 36b 9 | 7 2 136 | 16 5 8 |
| 16B 5 2 | 4 8 169c | 167 3 79 |
| 38 7 18 | 16a 5 39 | 2 169A 4 |
+----------------+----------------+----------------+
| 2 89 5 | 3 16 4 | 167 1689 79 |
| 7 4 3 | 9 16 8 | 5 2 16 |
| 89 1 6 | 5 7 2 | 4 89 3 |
+----------------+----------------+----------------+ |
Ravel also found this. I applied the logic of a fork or skyscraper:
If a is <6>, c is not <6>.
If a is not <6>, A is <6>, b is not <6>, B is <6>, and c is not <6>.
So, remove <6> from R5C6.
Now, a short chain:
R6C4 = <1> results in R5C6 = <9> and R6C6 = <3>.
R6C4 = <1> results in R5C3 = <8> and R6C1 = <3>.
So, R6C4 = <6>, which after some more basic moves brings us here:
| Code: | +----------------+----------------+----------------+
| 5 89 48 | 1 49 6 | 3 7 2 |
| 16 2 7 | 8 3 5 | 9 4 16 |
| 39 36 14 | 2 49 7 | 8 16 5 |
+----------------+----------------+----------------+
| 4 36 9 | 7 2 13 | 16 5 8 |
| 16 5 2 | 4 8 19 | 167 3 79 |
| 38 7 18 | 6 5 39 | 2 19 4 |
+----------------+----------------+----------------+
| 2 89 5 | 3 16 4 | 17 1689 79 |
| 7 4 3 | 9 16 8 | 5 2 16 |
| 89 1 6 | 5 7 2 | 4 89 3 |
+----------------+----------------+----------------+ |
There is an X-wing on <1> in R36(C38) which takes out <1> in R7C8.
There is an XY-wing on <361> in R45 which takes out <1> in R5C6.
There is an XY-wing on <391> in R6C6 which takes out <1> in R4C7.
Either of these XY-wings solves the puzzle.
Keith |
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