dailysudoku.com :: View topic - Free Press 10 July, 2009 (Posted Aug 7)

dailysudoku.com
Discussion of Daily Sudoku puzzles

FAQ

Memberlist

Usergroups

Profile

Free Press 10 July, 2009 (Posted Aug 7)
Goto page 1, 2 Next

dailysudoku.com Forum Index -> Other puzzles

View previous topic :: View next topic

Author

Message

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Fri Aug 07, 2009 5:48 pm Post subject: Free Press 10 July, 2009 (Posted Aug 7)

I had not posted this one. Quite nice, a VH+ (at least).

Code:

Puzzle: FP071009
+-------+-------+-------+
| 3 8 7 | . . . | . . 4 |
| . . . | 7 . 1 | 3 . 9 |
| . . . | 8 . 6 | . . . |
+-------+-------+-------+
| . 6 . | 3 . . | . . . |
| . 3 4 | . . . | 6 9 . |
| . . . | . . 7 | . 1 . |
+-------+-------+-------+
| . . . | 6 . 5 | . . . |
| 9 . 5 | . . 3 | . . . |
| . . . | . . . | 9 7 . |
+-------+-------+-------+

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 12:41 am Post subject:

I ran this puzzle through my solver and it came up with a horrible solution. After basics, I decided to tackle it manually for a laugh (because I'm a terrible manual solver). Suddenly, I stopped laughing when I noticed ...

Code:

<25> UR pattern in [r26c12] -and-
<28> UR pattern in [r67c13]

I learned awhile back that this meant a potential <258> deadly pattern exists. So, what could I do?

Code:

[r6c23]=9 => [r4c3]<>9
[r7c1]=4 [r3c1]=1 [r3c3]=9 => [r4c3]<>9
+--------------------------------------------------------------+
| 3 8 7 | 259 25 29 | 1 6 4 |
| *25 *25 6 | 7 4 1 | 3 8 9 |
| 14 49 19 | 8 3 6 | 257 25 27 |
|--------------------+--------------------+--------------------|
| 1257 6 12-9 | 3 1258 49 | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| *258 *25+9 *28+9 | 49 6 7 | 245 1 3 |
|--------------------+--------------------+--------------------|
| *28+4 7 *28 | 6 9 5 | 24 3 1 |
| 9 124 5 | 124 7 3 | 8 24 6 |
| 6 124 3 | 124 128 248 | 9 7 5 |
+--------------------------------------------------------------+
# 66 eliminations remain

Singles, a <12> Naked Pair, and a <45+2> XY-Wing in [r4c8]/[r6c7]+[r8c8] complete the solution.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 1:43 am Post subject:

Danny,

You missed the daj double skyscraper??

It can also be seen as a half M-wing:

Code:

+----------------+----------------+----------------+
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| 14e 49# 19* | 8 3 6 | 257 25 27 |
+----------------+----------------+----------------+
| 1257 6 12-9 | 3 1258 49@ | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 259 289 | 49a 6 7 | 245b 1 3 |
+----------------+----------------+----------------+
| 248d 7 28 | 6 9 5 | 24c 3 1 |
| 9 124 5 | 124 7 3 | 8 24 6 |
| 6 124 3 | 124 128 248 | 9 7 5 |
+----------------+----------------+----------------+

If @ is <4>, so is # (via abcde). If @ is <4>, * is <9>. @* are pincers on <9> in R4C3.

The double skyscraper is here:

Code:

+----------------+----------------+----------------+
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| 14b 49B 19d | 8 3 6 | 257 25 27 |
+----------------+----------------+----------------+
| 1257 6 12-9 | 3 1258 49c | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 259 289 | 49A 6 7 | 245a 1 3 |
+----------------+----------------+----------------+
| 248B 7 28 | 6 9 5 | 24b 3 1 |
| 9 124 5 | 124 7 3 | 8 24 6 |
| 6 124 3 | 124 128 248 | 9 7 5 |
+----------------+----------------+----------------+

One of ab (in C7) is not <4>. One of AB is not <9>. One of cd is <9>.

Keith

Last edited by keith on Sat Aug 08, 2009 1:57 pm; edited 1 time in total

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sat Aug 08, 2009 3:49 am Post subject:

Code:

.------------------.------------------.------------------.
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| 14 49 19 | 8 3 6 | 257 25 27 |
:------------------+------------------+------------------:
| 1257 6 129 | 3 1258 *49 | 2457 *245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 259 289 |*49 6 7 | 245 1 3 |
:------------------+------------------+------------------:
| 248 7 28 | 6 9 5 | 24 3 1 |
| 9 124 5 |12-4 7 3 | 8 *24 6 |
| 6 124 3 | 124 128 248 | 9 7 5 |
'------------------'------------------'------------------'

multi-coloring 4
r6c4 = r4c6 - r4c8 = r8c8; r8c4 <> 4

Code:

.------------------.------------------.------------------.
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| 14 49 19 | 8 3 6 | 257 25 27 |
:------------------+------------------+------------------:
| 1257 6 129 | 3 1258 49 | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 259 289 | 49 6 7 | 245 1 3 |
:------------------+------------------+------------------:
| 248 7 28 | 6 9 5 | 24 3 1 |
| 9 U124 5 |U12 7 3 | 8 24 6 |
| 6 U12 3 |U124 128 248 | 9 7 5 |
'------------------'------------------'------------------'

(9=4)r3c2 - UR12[(4)r8c2 = (4)r9c4] - (4=9)r6c4 - (9)r4c6 = (9)r4c3; r3c3 <> 9

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 4:17 am Post subject:

Keith, an impressive find!

My solver found your half M-Wing with one exception ... the last cell. My solver doesn't flag M-Wings or variants directly, and I didn't (originally) search for it among the chains listed.

Code:

(9=4)r4c6 - r6c4 = r6c7 - r7c7 = r7c1 - r3c1 = (4-9)r3c2 = (9)r6c2 => r4c3,r6c4 <> 9
+--------------------------------------------------------------+
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| e14 49# 19 | 8 3 6 | 257 25 27 |
|--------------------+--------------------+--------------------|
| 1257 6 12-9 | 3 1258 49@ | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 259* 289 | a4-9 6 7 | b245 1 3 |
|--------------------+--------------------+--------------------|
| d248 7 28 | 6 9 5 | c24 3 1 |
| 9 124 5 | 124 7 3 | 8 24 6 |
| 6 124 3 | 124 128 248 | 9 7 5 |
+--------------------------------------------------------------+
# 66 eliminations remain

As for your Double Skyscraper, it's not a Skyscraper because A in [r6c4] and B in [r7c1] are not in the same chute.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 4:55 am Post subject:

Norm, an impressive find as well! Your UR chain can be shortened and used in my PM w/o first performing r8c4 <> 4.

Code:

(9=4)r3c2 - UR12[(4)r89c2 = (4)r89c4] - (4=9)r6c4; r6c2 <> 9
+--------------------------------------------------------------+
| 3 8 7 | 259 25 29 | 1 6 4 |
| 25 25 6 | 7 4 1 | 3 8 9 |
| 14 *49 19 | 8 3 6 | 257 25 27 |
|--------------------+--------------------+--------------------|
| 1257 6 129 | 3 1258 49 | 2457 245 278 |
| 1257 3 4 | 125 1258 28 | 6 9 278 |
| 258 25-9 289 | *49 6 7 | 245 1 3 |
|--------------------+--------------------+--------------------|
| 248 7 28 | 6 9 5 | 24 3 1 |
| 9 12+4 5 | 12+4 7 3 | 8 24 6 |
| 6 12+4 3 | 12+4 128 248 | 9 7 5 |
+--------------------------------------------------------------+
# 66 eliminations remain

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 2:06 pm Post subject:

daj95376 wrote:

As for your Double Skyscraper, it's not a Skyscraper because A in [r6c4] and B in [r7c1] are not in the same chute.

Why not?

Quote:

The double skyscraper is here:

Code:

One of ab (in C7) is not <4>. One of AB is not <9>. One of cd is <9>.

The floor of the first skyscraper on <4> is ab in C7. The towers are aA and bBbB, the last ending in R3C2. The second skyscraper on <9> is Ac in B5, and Bd in R3. The pincers are cd.

I don't see why there needs to be any constraint on the location of A and B.

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 2:59 pm Post subject:

keith wrote:

daj95376 wrote:

As for your Double Skyscraper, it's not a Skyscraper because A in [r6c4] and B in [r7c1] are not in the same chute.

Why not?

Quote:

The double skyscraper is here:

Code:

One of ab (in C7) is not <4>. One of AB is not <9>. One of cd is <9>.

I guess it's a matter of personal preference. To me, a Skyscraper is a specific elimination pattern. Your AabB skyscraper in [r6] & [r7] can't generate any eliminations. Extending it to AabBbB and calling the results a double skyscraper doesn't work for me. Your 8-cell (generalized?) M-Wing knocked my socks off Exclamation

Skyscraper:

Quote:

Code:

. . . | . . . | . . .
* * . | . d . | . . .
. . b | * | * | . . .
----|-----|----------
. . | | . | . | . . .
. . | | . | . | . . .
. . | | . | . | . . .
----|-----|----------
. . | | . | . | . . .
. . | | . | . | . . .
. . a | . c . | . . .

if ab and cd are two strong links (Conjugate Pairs), if a and c are on the same line (row or column) and b and d are within the same "box-area" (or the same "chute" I think it is called?), then all candidates with the same number as abcd on these: * spots can be eliminated.
As you can see, this definition fits well with an image of a skyscraper Smile

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 7:30 pm Post subject:

Danny,

OK. Maybe what I did was similar to Medusa multi-coloring. but it's not really Medusa, since some weak links (inferences?) are allowed.

Do you agree that a kite, a Turbot fish and a skyscraper are the same thing? If so, your rule about the chute does not apply.

Code:

. . . | . . . | . . .
. . . | . . . | . . .
. . b | . . . | . * .
----|----------------
. . | | . . . | . . .
. . | | . . . | . . .
. . | | . . . | . . .
----|----------------
c---+-------------d .
. . | | . . . | . . .
. . a | . . . | . . .

The requirement is that b and d have common buddies (they can both see at least one cell that possibly contains the candidate). (The cell marked + is a buddy of b and d, but cannot contain the candidate.)

The double skyscraper does not have even that requirement.

Code:

. . . | . . * | . . .
. . . | . . * | . . .
. . b---e . y | . x .
----|----------------
. . | | * . . | . . .
. . | | * . . | . . .
. . x | y . f-----d .
----|-------------|--
. . | | . . . | . | .
. . | | . . . | . | .
. . a | . . . | . c .

Suppose ab and cd are strong links in X, and be and df are strong links in Y. You can eliminate Y in the cells marked *. The cells marked x are irrelevant, since they cannot contain X. The cells marked y cannot contain Y.

In this diagram, b and d must contain X and Y, but they may contain other candidates as well.

It seems to me that if they contain only XY, Medusa multicoloring will find the eliminations. However if they do contain other candidates, the inference between X and Y in b and d becomes weak, and Medusa (as I understand it) stalls.

Best wishes,

Keith

Last edited by keith on Sat Aug 08, 2009 9:34 pm; edited 1 time in total

wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Sat Aug 08, 2009 8:12 pm Post subject:

keith wrote:

Do you agree that a kite, a Turbot fish and a skyscraper are the same thing?
Keith

Turbot covers "classic turbot" (the one with the fish shape), two-string kite and skyscraper.

A skyscraper is not an ER or a kite or a "classic" turbot.
A skyscraper is a sashimi x-wing, and some consider it a finned x-wing.

Daj, is Keith's 1st pattern a mutant sword with no elimination?

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 8:14 pm Post subject:

daj95376 wrote:

But, in the thread where you started this idea, you began with what you called an "unproductive skyscraper".

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=3794

I agree. If a skyscraper is made up of two strong links that are both in rows (or columns) eliminations may only be found if the chute rule is satisfied. But, so what? I would say eliminations will only be found if one of their common buddies contains the candidate.

I think that requiring the base skyscraper to satisfy the chute condition is unnecessary and will make your original idea much less useful.

Is this a skyscraper?

Code:

. . . | . . . | . . .
. . . | . . . | . . .
. . b | . . . | . . *
----|----------------
. . | | . . . | . . .
. . | | . . . | . . .
. . | | . . . | . . .
----|----------------
. . | | . . . | . . d
. . | | . . . | . / .
. . a | . . . | c . .

Keith

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 8:27 pm Post subject:

wapati wrote:

keith wrote:

Do you agree that a kite, a Turbot fish and a skyscraper are the same thing?
Keith

Wapati,

The way I see it, the logic for all these things is exactly the same. In the diagrams we have been using: One or both of a and c is false; one or both of b and d must be true. I think it is silly that they have different names based on the pattern they happen to present.

Danny's idea applies to Turbots, kites, and skyscrapers. If Turbot is the general pattern that includes the others, we should rename the double skyscraper as a Supra. (Twin turbo.)

Keith Laughing

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Aug 08, 2009 9:11 pm Post subject:

Here is a visual explanation of Danny's chute rule:

It applies only when both strong links are in two rows, or both are in two columns.

Code:

. . . | . . . | . . .
. . . | . . . | . . .
. . b | . . . | x . .
----|----------------
. . | | . . . | . . .
. . x | . . . | d . .
. . | | . . . | | . .
----|----------------
. . | | . . . | | . .
. . | | . . . | | . .
. . a | . . . | c . .

ab and cd are strong links in candidate X. One or both of a and c are not X; one or both of b and d must be X. b and d are pincers. Any of their common buddies cannot be X. Their common buddies are the cells marked x. But, they cannot possibly contain X or the strong links would not exist.

Consider this:

Code:

* * x | . . . | d . .
. . . | . . . | . . .
. . b | . . . | x * *
----|----------------
. . | | . . . | | . .
. . | | . . . | | . .
. . | | . . . | | . .
----|----------------
. . | | . . . | | . .
. . | | . . . | | . .
. . a | . . . | c . .

Again, the cells marked x are common buddies of b and d that cannot contain X. But, the cells marked * are common buddies where eliminations may be made.

So, for a skyscraper to make any eliminations, b and d must be in the same chute (in blocks 123, 456, or 789 if the strong links are in the columns, or in blocks 147, 258, or 369 if the strong links are in the rows.)

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 10:25 pm Post subject:

keith wrote:

Code:

Whoa, lots of discussion and I'm way behind. The answer to your question is Almost -- it all depends upon where you place the strong links in the Turbot Fish.

In the same link I provided for the Skyscraper is the definition of a 2-String Kite.

Havard wrote:

Code:

. . . | . . . | . . .
. . c-----------d . .
. a . | . . . | . . .
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. | . | . . . | . . .
--|------------------
. b . | . . . | * . .
. . . | . . . | . . .
. . . | . . . | . . .

if ab and cd are two strong links (Conjugate Pairs), and if a and c share the same box, then all candidates with the same number as abcd on this: * spot (where b and d meet) can be eliminated.
Here, the box that a and c shares is the "kite" and the two strong links are the "strings" Smile

In this thread, Havard acknowledges that the Skyscraper and 2-String Kite can be classified as Turbot Fish.

Nick70 wrote:

The new pattern instead uses 5 cells.

The 5 cells must be at the vertices of a 5-sided polygon; it's easy to see that for this to happen, two sides must be along a row, two sides along a column, and the fifth side must have the two vertices in the same box.
The possible layouts are therefore like these:

Code:

. . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .
. . . | *---------* . . . *-------------* . . . *-------------* .
. . . | | . . | . | . . . | | . . . | . | . . . | | . . . | . | .
---------|---------|--- -----|-------------|--- -----|-------------|---
. . . | *\. . | . | . . . | | . . . | . | . . . *-----------* | .
. . . | . \ . | . | . . . | | . . . | . | . . . . | . . . | .\| .
. . . | . .\*-----* . . . | | . . . | . | . . . . | . . . | . * .
----------------------- -----|-------------|--- -----------------------
. . . | . . . | . . . *\--|-------------* . . . . | . . . | . . .
. . . | . . . | . . . . \ | | . . . | . . . . . . | . . . | . . .
. . . | . . . | . . . . .\* | . . . | . . . . . . | . . . | . . .

Due to the second layout, I've called this pattern "Turbot Fish".

Depending on where you place strong links in the layouts, you have: a 2-String Kite, a Sashimi X-Wing, or an Empty Rectangle with only two candidate cells in "the box". Havard discovered that more eliminations were possible, and extended the Sashimi X-Wing variant into a Skyscraper. He also gave a name to the variant with strong links that we now know as a 2-String Kite.

Note: there is now a grouped 2-String Kite based on grouped strong links being used. I became entangled in a disagreement with Asellus on the traditional Empty Rectangle being a variant based on using grouped strong links as well. I won't reopen that Pandora's Box!

Wapati: Keith's 2-String Kite layout can also be described as either of two finned mutant X-Wings:

Code:

finned mutant X-Wing r7c3\r3b7 w/fin cell [r7c8] => [r3c8] <> X
finned mutant X-Wing r7c3\c8b7 w/fin cell [r3c3] => [r3c8] <> X

Regards, Danny

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 10:58 pm Post subject:

keith wrote:

The double skyscraper does not have even that requirement.

Code:

Here's your double skyscraper as an AIC. It matches what Norm already calls an Inverse W-Wing.

Code:

Dbl Sky: (Y)f = (Y-X)d = (X)c - (X)a = (X-Y)b = (Y)e

iW-Wing: (Y)s = (Y-X)a = (X)b - (X)c = (X-Y)d = (Y)t

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 11:20 pm Post subject:

keith wrote:

Code:

In my example, the Non-productive Skyscraper is in these cells, and the non-aligned cells are in the same chute -- [stack 2].

Code:

+-----------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| X / / | / / X | / / / |
|-------+-------+-------|
| . . . | . . . | . . . |
| X / / | X / / | / / / |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------+

Quote:

I agree. If a skyscraper is made up of two strong links that are both in rows (or columns) eliminations may only be found if the chute rule is satisfied. But, so what? I would say eliminations will only be found if one of their common buddies contains the candidate.

I think that requiring the base skyscraper to satisfy the chute condition is unnecessary and will make your original idea much less useful.

I think the so what? is important and that it's fundamental to calling a pattern a Skyscraper.

Your layout is not a Skyscraper because the non-aligned cells are not in the same chute. However, it is an Empty Rectangle with two cells in "the box". I've seen you call it a 2-String Kite. Many people call it a turbot fish.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 08, 2009 11:43 pm Post subject:

keith wrote:

wapati wrote:

keith wrote:

Do you agree that a kite, a Turbot fish and a skyscraper are the same thing?
Keith

The Turbot Fish pattern has five cells in a pentagon arrangement. In practice, four of the cells are connected by two strong links, but no cell is in more than one strong link. The fifth cell is unlinked and can be eliminated for the candidate value!

Names have been give to layouts with specific strong links to easily identify them. Havard named the Skyscraper and the 2-String Kite. I'll skip who named the Empty Rectangle.

Regards, Danny

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Aug 09, 2009 2:57 am Post subject:

Danny, Can we get this discussion to be about the double skyscraper and leave behind the discussions of the Turbot variants? By the way, the ER is not a subset of a Turbot, when the hinge pin cell contains the candidate. Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Aug 09, 2009 5:46 am Post subject:

Hmmm. I'd be glad to leave the Turbot variants behind, but you then added a remark about the ER not being a Turbot. I should leave it alone like I finally did with Asellus, but ...

Two identical 5-cell Turbot Fish patterns, but with different strong links used.

Code:

2-String Kite Empty Rectangle w/two candidates in [b7]
finned mutant X-Wing r8c2\r2b7 finned Franken X-Wing r2b7\c28
r2c2 = r9c2 - r8c1 = r8c8 => r2c8<>X r2c8 = r2c2 - r9c2 = r8c1 => r8c8<>X
+-----------------------------------+ +-----------------------------------+
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . X . | . . . | . * . | | / X / | / / / | / X / |
| . / . | . . . | . . . | | . . . | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . / . | . . . | . . . | | . . . | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . / . | . . . | . . . | | / / / | . . . | . . . |
| X / / | / / / | / X / | | X / / | . . . | . * . |
| . X . | . . . | . . . | | / X / | . . . | . . . |
+-----------------------------------+ +-----------------------------------+
____________________________________________________________________________________

Now, lets change [box 7] a bit in each example.

Code:

grouped 2-String Kite classic Empty Rectangle
finned mutant X-Wing r8c2\r2b7 finned Franken X-Wing r2b7\c28
r2c2 = r79c2 - r8c13 = r8c8 => r2c8<>X r2c8 = r2c2 - r789c2 = r8c13 => r8c8<>X
+-----------------------------------+ +-----------------------------------+
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . X . | . . . | . * . | | / X / | / / / | / X / |
| . / . | . . . | . . . | | . . . | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . / . | . . . | . . . | | . . . | . . . | . . . |
| . / . | . . . | . . . | | . . . | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| / X / | . . . | . . . | | / X / | . . . | . . . |
| X / X | / / / | / X / | | X X X | . . . | . * . |
| / X / | . . . | . . . | | / X / | . . . | . . . |
+-----------------------------------+ +-----------------------------------+
____________________________________________________________________________________

I don't see a problem with the hinge pin (ERI cell) being present in my second grouped example!

As for your double skyscraper, it's only a name. If that's how you see it, then use it. My original point stands. I didn't see it as a something I'd call a double skyscraper.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Aug 09, 2009 6:51 am Post subject:

It's all in a name. Maybe a naked single is a mutant franken sashimi hidden pair? Keith

Display posts from previous:

	dailysudoku.com Forum Index -> Other puzzles	All times are GMT Goto page 1, 2 Next
Page 1 of 2

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum