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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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 Posted: Sat Dec 15, 2007 7:58 am Post subject: daily telegraph - 12/14 |
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| Code: | . . . | 1 . . | . . 7
6 1 . | . . . | . 2 .
. . 4 | 9 . . | 1 . .
------+-------+------
8 . . | . 1 . | . . 4
. 4 2 | . . . | 8 1 .
9 . . | . 4 . | . . 6
------+-------+------
. . 8 | . . 9 | 6 . .
. 2 . | . . . | . 9 3
5 . . | . . 7 | . . . |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Dec 15, 2007 8:23 am Post subject: |
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| Code: | 23 8 9 | 1 256 2356 | 35 4 7
6 1 57 | 358 578 4 | 35 2 9
237 35 4 | 9 257 235 | 1 6 8
---------------------+----------------------+-------------------
8 6 57 | 2357 1 235 | 9 37 4
37 4 2 | 367 9 36 | 8 1 5
9 35 1 | 357 4 8 | 2 37 6
---------------------+----------------------+-------------------
1 7 8 | 4 3 9 | 6 5 2
4 2 6 | 58 58 1 | 7 9 3
5 9 3 | 26 26 7 | 4 8 1
after basics
xy-wing on {3,5,7} first in boxes 4 and 6 takes out 3 in r6c8
then DP??? on {5,8} in col 4 and 5??
Norm |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Sat Dec 15, 2007 12:53 pm Post subject: |
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The potential [58] DP in R28C45 takes out both <5>'s in R2C4 and R2C5, then i found two ER's in Box 1 eliminating <3>*(*= strong link on <3> in R5) and <5>@(@= strong link on <5> in R4) in R3C6.
ER <3> :
| Code: |
+--------------------------+--------------------------+--------------------------+
| 23 8 er 9 er | 1 256 2356 | 35 4 7 |
| 6 1 er 57er | 38 78 4 | 35 2 9 |
| 237 eri 35 4 | 9 257 2-[3]5| 1 6 8 |
+--------------------------+--------------------------+--------------------------+
| 8 6 57 | 27 1 25 | 9 3 4 |
|*37 4 2 | 67 9 *36 | 8 1 5 |
| 9 35 1 | 35 4 8 | 2 7 6 |
+--------------------------+--------------------------+--------------------------+
| 1 7 8 | 4 3 9 | 6 5 2 |
| 4 2 6 | 58 58 1 | 7 9 3 |
| 5 9 3 | 26 26 7 | 4 8 1 |
+--------------------------+--------------------------+--------------------------+
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ER <5> :
| Code: |
+--------------------------+--------------------------+--------------------------+
| 23 er 8 er 9 | 1 256 2356 | 35 4 7 |
| 6 er 1 er 57 | 38 78 4 | 35 2 9 |
| 237 35 4 eri| 9 257 2-[5] | 1 6 8 |
+--------------------------+--------------------------+--------------------------+
| 8 6 @57 | 27 1 @25 | 9 3 4 |
| 37 4 2 | 67 9 36 | 8 1 5 |
| 9 35 1 | 35 4 8 | 2 7 6 |
+--------------------------+--------------------------+--------------------------+
| 1 7 8 | 4 3 9 | 6 5 2 |
| 4 2 6 | 58 58 1 | 7 9 3 |
| 5 9 3 | 26 26 7 | 4 8 1 |
+--------------------------+--------------------------+--------------------------+
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Dec 15, 2007 3:11 pm Post subject: |
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Johan's <3> elimination in r3 can also be seen as a Skyscraper. And, the <5> elimination can be seen as a Kite that pivots in Box 4.
There is a very interesting coloring in this puzzle with those <5>s and it can be done without invoking that UR to remove the <5>s in R2c45. The approach would work even if there were no potential UR. First, however, notice the conjugate <5> pair in r8. I label them "A" and "B" below. Each of them is involved in an XYZ Wing-like ALS structure in r2, labeled "a" and "b" for the cells in which "A" and "B" are involved, respectively.
| Code: | +--------------------+---------------------+-----------+
| 23 8 9 | 1 256 2356 | 35 4 7 |
| 6 1 a5G7 |b358 a758 4 |b35 2 9 |
| 237 35R 4 | 9 257 235 | 1 6 8 |
+--------------------+---------------------+-----------+
| 8 6 5R7 | 27 1 25G | 9 3 4 |
| 37 4 2 | 67 9 36 | 8 1 5 |
| 9 35G 1 | 35R 4 8 | 2 7 6 |
+--------------------+---------------------+-----------+
| 1 7 8 | 4 3 9 | 6 5 2 |
| 4 2 6 |B58 A58 1 | 7 9 3 |
| 5 9 3 | 26 26 7 | 4 8 1 |
+--------------------+---------------------+-----------+ |
I have used R and G to color the <5>s partially. I will use A, B, a, b to refer to the <5>s in those cells, as well as to the cells themselves.
Note that if A is true, then B is false and one of the "b" cells must be true. This would make r2c3 false, so the Red <5>s would be true, including r6c4. Thus, the only "b" cell that could be true is r2c7 AND it must be Red. We can now eliminate the <5>s in r2c45 and continue the <5> coloring to completion. This will eliminate the <5>s in r1c5 and r3c6 as well.
You might be skeptical. (I was at first.) Well then, let's check the other alternative. If B is true, than A is false and one of the "a" cells must be true. But, if B is true, then Red is false and the Green <5> in r2c3 is true and is thus the only cell in r2 that can satisfy the requirement.
Either way, r2c45 cannot be true (and it has nothing to do with the UR).
(After this, a {235} XY Wing with pivot r4c6 removes <3>s from r5c6 and r2c4 and solves the puzzle. But, the point was to show the interesting coloring, not to recommend a solution path.) |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Dec 15, 2007 7:05 pm Post subject: |
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asellus,
I see it, that was nice !! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Dec 15, 2007 9:13 pm Post subject: |
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Edited 12/16/17, 6:11 EST - Keith
Asellus,
You stopped too soon! Coloring solves the puzzle!
In a trick I learned from Marty:
If you think you have a coloring opportunity, make a quick grid of two vertical lines and two horizontal lines (with pencil and paper). Then put dots where the candidates exist. In this puzzle, for the candidate <5> we get:
| Code: |
| oo|o
o|oo |o
o | oo|
___|___|___
o| o|
| |
o |o |
___|___|___
| |
|oo |
| |
|
The strong links (conjugate pairs) are pretty obvious. Draw lines to connect the dots for the strong links. If necessary, label the cells a A, etc. to show their polarity. Coloring eliminations are now easy to spot.
| Code: |
+----------------+----------------+----------------+
| 23 8 9 | 1 256 2356 | 35c 4 7 |
| 6 1 57a | 358 578 4 | 35C 2 9 |
| 237 35A 4 | 9 257 235 | 1 6 8 |
+----------------+----------------+----------------+
| 8 6 57A | 27 1 25a | 9 3 4 |
| 37 4 2 | 67 9 36 | 8 1 5 |
| 9 35a 1 | 35A 4 8 | 2 7 6 |
+----------------+----------------+----------------+
| 1 7 8 | 4 3 9 | 6 5 2 |
| 4 2 6 | 58B 58b 1 | 7 9 3 |
| 5 9 3 | 26 26 7 | 4 8 1 |
+----------------+----------------+----------------+
|
There are three sets of strong links, shown as solid lines. You can color across the weak links, dotted lines, to connect these three sets, using the same logic as a skyscraper. For example, if b R8C5 is not true (is not <5>), then a R6C2 is true. If c is not true, A is true.
We end up with the following: Any cell that sees both
1. a and A [R3C6, R2C4]
2. a and b [R2C5]
3. A and c
4. b and c [R1C5]
cannot be <5>.
Then, coloring on <3>, starting in R1C7 and ending in R5C1, solves R1C1 as <2>, and the puzzle.
Keith
Last edited by keith on Sun Dec 16, 2007 11:15 am; edited 1 time in total |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Dec 16, 2007 2:32 am Post subject: |
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A reconsideration:
I realize I wasn't quite correct when I said that it has nothing to do with the UR. The existence of the two XYZ Wing-like structures means that a UR necessarily exists since r2c45 must each contain {58}, plus another digit. However, the logic is independent of that. Only one of those XYZ Wink-like structures (either Aa or Bb) is necessary to perform the complete coloring eliminations, in which case there would be no UR. Also, either or both could be XY Wings, with a <5> or <8> removed from each of r2c45, and it would also work (and again, no UR). But, these are fine points for those who are sticklers. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Dec 16, 2007 12:00 pm Post subject: |
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Keith,
Yes, it seems that my fancy XYZ Wing-like structures weren't essential: conventional multi-coloring ("color wings") does the trick... though it eliminates exactly the same four <5>s. (No surprise there.) Still, it is interesting that one can approach the same thing from (at least somewhat) different conceptual points of view.
Next, you used <3> coloring and I used an XY Wing to produce the same result. In either case, it's the same number of steps. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Dec 16, 2007 12:57 pm Post subject: |
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| I cant see a possible elimination of 5 in r3c6 with coloring. [Edit:]Ah, you started with a more advanced grid, i still have a 5 in r4c4 (the other eliminations are already possible here). So an xy-wing is needed anyway. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 16, 2007 2:53 pm Post subject: |
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| ravel wrote: | | ... you started with a more advanced grid ... |
Yes, the grid I posted is after an XY-wing that solves C8, that leads to a triple in C4 ...
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 16, 2007 3:04 pm Post subject: |
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| Asellus wrote: | Keith,
Yes, it seems that my fancy XYZ Wing-like structures weren't essential: conventional multi-coloring ("color wings") does the trick... though it eliminates exactly the same four <5>s. (No surprise there.) Still, it is interesting that one can approach the same thing from (at least somewhat) different conceptual points of view.
Next, you used <3> coloring and I used an XY Wing to produce the same result. In either case, it's the same number of steps. |
Asellus,
Please note that I have no intent to suggest that anything is not "essential", or that one point of view is better than another.
But, if you are counting (advanced) steps, you can skip the coloring on <5> entirely. Coloring on <3> to solve R1C1 as <2>, then another XY-wing (which takes out <2> in R3C5) are enough to put this one to bed.
Best wishes
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Dec 17, 2007 3:11 am Post subject: |
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| keith wrote: | | But, if you are counting (advanced) steps, you can skip the coloring on <5> entirely. |
My interest was solely in exploring the potentials within the array of <5>s, not in solution paths for the puzzle as a whole.
| keith wrote: | | Please note that I have no intent to suggest that anything is not "essential" |
I didn't believe you had such an intent. I had thought that maybe those wing structures provided some special "key" to unlocking those <5>s. But, the multi-coloring shows that that isn't so. (I tend to ignore multi-coloring situations involving more than two color clusters, a resistance I should perhaps overcome.)
That there was an alternate to my "key" isn't surprising, actually. I have noticed that almost every solving technique based on "complex patterns" has one or more complementary alternate routes to the same result. Sometimes, those alternate routes are so complex (long intricate chains, for instance) as to be "non-existent" for practical purposes. Other times, they are quite obvious (an ER elimination that can also be accomplish with a finned fish or a kite, for instance). In this case, the alternate route was somewhere in between: not an obvious method, but not hopelessly complex. Instead, it was an unusual but interesting pattern.
Or, at least that's how my current thinking runs on such matters. |
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