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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Fri Aug 19, 2011 1:41 pm Post subject: Free Press August 19, 2011 |
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Not yet done. Looks to be on the difficult side.
| Code: | Puzzle: FP081911
+-------+-------+-------+
| . . 3 | . . . | 4 . . |
| 6 . . | 9 4 1 | . . . |
| 1 4 . | . . . | . 5 . |
+-------+-------+-------+
| . . . | . 6 . | 1 . . |
| 3 . . | . 1 5 | . . 7 |
| . . 2 | . 8 . | . . . |
+-------+-------+-------+
| . 3 . | . . . | . 4 1 |
| . . . | 2 9 6 | . . 8 |
| . . 8 | . . . | 9 . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 20, 2011 12:19 am Post subject: |
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I doubt that this will win any awards for elegance.
Finned X-Wing, r25; r4c8<>8
Hidden UR (37); r2c8<>3
Skyscraper; r4c2, r9c1<>5
W-Wing (57), SL 5 in c7; r4c2, r9c1<>7 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 20, 2011 3:23 pm Post subject: |
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After basics: | Code: | +----------------+----------------+----------------+
| 289 289 3 | 568 57 78 | 4 1 26 |
| 6 28 5 | 9 4 1 | 37 2378 23 |
| 1 4 7 | 68 2 3 | 68 5 9 |
+----------------+----------------+----------------+
| 5789 5789 4 | 37 6 2 | 1 89 35 |
| 3 689 69 | 4 1 5 | 28 289 7 |
| 57 1 2 | 37 8 9 | 35 6 4 |
+----------------+----------------+----------------+
| 29 3 69 | 58 57 78 | 26 4 1 |
| 4 57 1 | 2 9 6 | 357 37 8 |
| 257 2567 8 | 1 3 4 | 9 27 256 |
+----------------+----------------+----------------+ |
I believe 578 in R17C456 are a deadly pattern. R1C4 must be 6, and the puzzle is solved.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 20, 2011 3:34 pm Post subject: |
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Nice. Apparently sitting there staring me in the face is not enough.  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 20, 2011 4:15 pm Post subject: |
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Marty,
Your W-wing is present in the "After Basics" grid, and it is actually a Remote Pair, or you can see it as a skyscraper on 5. In any event -5-7 in R4C2, R9C1 is a one-stepper.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Aug 20, 2011 4:56 pm Post subject: |
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Not as impressive as Keith's DP, but still interesting. BTW, Marty found half of it.
| Code: | HoDoKu 2.0.1: Hidden Rectangles exist for r2c7<>3=7 and r8c8<>7=3
That's sufficient to force r8c7<>37=5, which cracks the puzzle
+--------------------------------------------------------------+
| 289 289 3 | 568 57 78 | 4 1 26 |
| 6 28 5 | 9 4 1 | *37 *37+28 23 |
| 1 4 7 | 68 2 3 | 68 5 9 |
|--------------------+--------------------+--------------------|
| 5789 5789 4 | 37 6 2 | 1 89 35 |
| 3 689 69 | 4 1 5 | 28 289 7 |
| 57 1 2 | 37 8 9 | 35 6 4 |
|--------------------+--------------------+--------------------|
| 29 3 69 | 58 57 78 | 26 4 1 |
| 4 57 1 | 2 9 6 | *37+5 *37 8 |
| 257 2567 8 | 1 3 4 | 9 27 256 |
+--------------------------------------------------------------+
# 53 eliminations remain
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Alternate perspective using external UR constraints:
| Code: | <37> UR r28c78 => r2c9=3 and/or r9c8=7
after r2c9=3 and UR cells resolved
*-----------------------------------------------------------*
| 289 289 3 | 568 57 78 | 4 1 26 |
| 6 28 5 | 9 4 1 | 7 28 3 |
| 1 4 7 | 68 2 3 | 68 5 9 |
|-------------------+-------------------+-------------------|
| 5789 5789 4 | 37 6 2 | 1 89 5 |
| 3 689 69 | 4 1 5 | 28 289 7 |
| 57 1 2 | 37 8 9 | 3 6 4 |
|-------------------+-------------------+-------------------|
| 29 3 69 | 58 57 78 | 26 4 1 |
| 4 7 1 | 2 9 6 | 5 3 8 |
| 257 2567 8 | 1 3 4 | 9 27 26 |
*-----------------------------------------------------------*
after r9c8=7 and UR cells resolved
*-----------------------------------------------------------*
| 289 289 3 | 568 57 78 | 4 1 26 |
| 6 28 5 | 9 4 1 | 7 28 23 |
| 1 4 7 | 68 2 3 | 68 5 9 |
|-------------------+-------------------+-------------------|
| 5789 5789 4 | 37 6 2 | 1 89 35 |
| 3 689 69 | 4 1 5 | 28 289 7 |
| 57 1 2 | 37 8 9 | 3 6 4 |
|-------------------+-------------------+-------------------|
| 29 3 69 | 58 57 78 | 26 4 1 |
| 4 7 1 | 2 9 6 | 5 3 8 |
| 25 256 8 | 1 3 4 | 9 7 26 |
*-----------------------------------------------------------*
UR cell r8c7<>37=5 cracks puzzle.
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Tue Aug 23, 2011 6:49 am Post subject: |
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| daj95376 wrote: | | Not as impressive as Keith's DP, but still interesting. |
Very interesting! I have all bit given up on hidden rectangles as I have yet to find one that helps the solution.
Here is one that actually cracks a puzzle! |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Aug 23, 2011 1:54 pm Post subject: |
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| Peter: It actually took two Hidden Rectangles working together on the same UR. Individually, I don't recall them being very effective. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Tue Aug 23, 2011 9:32 pm Post subject: |
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| daj95376 wrote: | | Code: | HoDoKu 2.0.1: Hidden Rectangles exist for r2c7<>3=7 and r8c8<>7=3
...
+--------------------------------------------------------------+
| 289 289 3 | 568 57 78 | 4 1 26 |
| 6 28 5 | 9 4 1 | *37 *37+28 23 |
| 1 4 7 | 68 2 3 | 68 5 9 |
|--------------------+--------------------+--------------------|
| 5789 5789 4 | 37 6 2 | 1 89 35 |
| 3 689 69 | 4 1 5 | 28 289 7 |
| 57 1 2 | 37 8 9 | 35 6 4 |
|--------------------+--------------------+--------------------|
| 29 3 69 | 58 57 78 | 26 4 1 |
| 4 57 1 | 2 9 6 | *37+5 *37 8 |
| 257 2567 8 | 1 3 4 | 9 27 256 |
+--------------------------------------------------------------+
# 53 eliminations remain
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If one writes out the AICs for those so-called "hidden rectangles", one sees that r2c8<>7 and r8c7<>3 are the most appropriate exclusions. Anything else lengthens the AICs.
| Code: | AUR(37)r28c78:[(28)r2c9 = (5-7)r8c7] = (7)r2c7 ==> r2c8<>7
AUR(37)r28c78:[(5)r8c7 = (28-3)r2c8] = (3)r8c8 ==> r8c7<>3
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It's obvious that a "hidden rectangle exclusion" requires only one strong link, not two as shown on sudopedia. Since there are four SLs, there are two more exclusions.
| Code: | AUR(37)r28c78:[(28)r2c9 = (5-3)r8c7] = (3)r8c8 ==> r2c8<>3
AUR(37)r28c78:[(5)r8c7 = (28-7)r2c8] = (7)r2c7 ==> r8c7<>7
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These last two are superfluous, however, since the first two exclusions above cause hidden singles that do the same thing. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Aug 23, 2011 11:45 pm Post subject: |
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| ronk wrote: | | daj95376 wrote: | | HoDoKu 2.0.1: Hidden Rectangles exist for r2c7<>3=7 and r8c8<>7=3 |
If one writes out the AICs for those so-called "hidden rectangles", one sees that r2c8<>7 and r8c7<>3 are the most appropriate exclusions. Anything else lengthens the AICs.
| Code: | AUR(37)r28c78:[(28)r2c9 = (5-7)r8c7] = (7)r2c7 ==> r2c8<>7
AUR(37)r28c78:[(5)r8c7 = (28-3)r2c8] = (3)r8c8 ==> r8c7<>3
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It's obvious that a "hidden rectangle exclusion" requires only one strong link, not two as shown on sudopedia. Since there are four SLs, there are two more exclusions.
| Code: | AUR(37)r28c78:[(28)r2c9 = (5-3)r8c7] = (3)r8c8 ==> r2c8<>3
AUR(37)r28c78:[(5)r8c7 = (28-7)r2c8] = (7)r2c7 ==> r8c7<>7
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These last two are superfluous, however, since the first two exclusions above cause hidden singles that do the same thing.
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According to my notes on a Hidden Rectangle, it's a network and not an AIC. Maybe that's why you failed to obtain the Hidden Rectangle eliminations r2c7<>3 and r8c8<>7 in your AIC conclusions.
What you're relying upon is another strong link -- (7)r2c8 = (7)r2c7 => r2c7<>3 -- to produce the first HR elimination. Likewise on the second HR elimination -- (3)r8c7 = (3)r8c8 => r8c8<>7. The final outcome is the use of 2x strong links on <7> and <3>, no matter the approach.
From my notes:
| Code: | ===== ===== ===== ===== Hidden Unique Rectangle
(*) bivalue w/ 2x strong links in an "L" pattern
+--------------+
| . . . |
| 12X . 1Y-2 |< strong link on <1>
| . . . |
+--------------+
| . . . |
|*12 . 12Z |
| . . . |
+--------------+
^ strong link on <1>
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Note: the presence of "Y" is optional. This leads to the interpretation that a Unique Rectangle Type 6 can be viewed as two concurrent Hidden Rectangles where the X-Wing presents 4x strong links on one value, and eliminations occur for the other value in the bivalue cells.
Concurrent HR version from my notes:
| Code: | ===== ===== ===== ===== Unique Rectangle Type 6 (UR + X-Wing in <1>)
(diagonal variant of Type 4)
4x strong links on <1>
+---------------+
| . . . |
| 1-2 . 12X |
| . . . |
+---------------+
| . . . |
| 12Y . 1-2 |
| . . . |
+---------------+
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Wed Aug 24, 2011 1:26 am Post subject: |
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| daj95376 wrote: | | What you're relying upon is another strong link -- (7)r2c8 = (7)r2c7 => r2c7<>3 -- to produce the first HR elimination [ronk edit: r2c8<>7]. |
Exactly, that's a hidden single move and it's the point of my post. How many other techniques can you name that embed a hidden single move within the technique? |
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