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September 12 Very hard
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TPM



Joined: 13 Jun 2006
Posts: 4
Location: Gauteng, South Africa

PostPosted: Tue Sep 12, 2006 4:02 pm    Post subject: September 12 Very hard Reply with quote

Just when I thougt I'm getting the feel for this thing, pops one out of hell(if there is such a place).
Did the basic elimination until I got and X-wing on 5's in rows 3&7 cols 2 & 7. So, far I have the following:

7 {2369} {569} {238} {245} {248} {345} 1 {46}
4 {23} {15} {1237} {257} 6 {35} 9 8
{136} {356} 8 {13} 9 {14} 7 {3456} 2
5 {78} 3 6 1 {27} {248} {248} 9
{69} {6789} {679} 4 {27} 3 1 {28} 5
2 1 4 9 8 5 6 7 3
8 {57} 2 {17} 3 {147} 9 {456} {46}
{1369} {369} {169} 5 {246} {2489} {2348} {2348} 7
{369} 4 {57} {278} {267} {2789} {2358} {238} 1

Asking for a hint gives me a 4 in r3c6. can't see why. Am I missing something?
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blackwood



Joined: 12 Sep 2006
Posts: 4
Location: Lehi, Utah, USA

PostPosted: Tue Sep 12, 2006 5:51 pm    Post subject: Reply with quote

There is a hidden set {5,6} in R3C8 and R7C8. This then leaves the 4 in R3C6 as the only 4 for R3. (A pinned square)

Blackwood
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Tue Sep 12, 2006 9:29 pm    Post subject: Reply with quote

Just to say the same thing as Blackwood did, except a little differently. In rows 4, 5, 8 and 9 in col. 8 there is a naked quad of 2348. When you make the eliminations from this quad, the 56 goes from a hidden to naked set.

I personally do not have the eye to spot hidden sets, but can generally spot the complementary naked sets.
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George Woods



Joined: 28 Mar 2006
Posts: 234
Location: Dorset UK

PostPosted: Tue Sep 12, 2006 11:24 pm    Post subject: Reply with quote

I solved this one by what seems to be like an XY wing. r7c6 cannot hold 4 'cos the 4 propagated by the 46 in col9 would make for a 4 in r3c6 which is of course a no no- so there is now a 17 pair in row 7 allowing progress- and a solution to be obtained.

Trying to understand the analysis above. I found a diificulty with the original contents of r8c8 and r9c8 (given as 2348 and 238) I make these two 23468 and 23568 so where have I missed the obvious?
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Wed Sep 13, 2006 4:55 am    Post subject: Reply with quote

Just to give yet one more illustration of how many different ways there are to solve many puzzles, on this one there were two Finned X-Wings, an X-Wing and then strong links (aka fork, aka skyscraper) on "4" opened it up.
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TPM



Joined: 13 Jun 2006
Posts: 4
Location: Gauteng, South Africa

PostPosted: Wed Sep 13, 2006 5:23 am    Post subject: Reply with quote

Okay ta everybody. I should have seen the hidden 56 in 8. Just had one of those bad days. However, I've learned now about a quad. I have never used it before as I did not understand it.

George, you cannot have a 6 in r8c8 as the 6 in r7 can only be in col 8 or col 9, hence eliminating any other 6's in the last box. alternatively, looking at the bottom 3 boxes, you can see that the 6 in the first 2 boxes is in rows 8 & 9 hence forcing the 6 in the last box to be in row 7 only.

The 5 is eliminated by the X-wing on the 5's in rows 3&7 cols 2&8. Hope this helps.
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George Woods



Joined: 28 Mar 2006
Posts: 234
Location: Dorset UK

PostPosted: Wed Sep 13, 2006 7:56 am    Post subject: Reply with quote

Marty R. wrote:
Just to give yet one more illustration of how many different ways there are to solve many puzzles, on this one there were two Finned X-Wings, an X-Wing and then strong links (aka fork, aka skyscraper) on "4" opened it up.


So how do you describe my method? (I spotted the "strong" link between r7c6 to r7c9 to r1c9 to r3c6 with the last one in my terminology a negative one i.e normally a 4 in one cell denies the 4 in the "strongly" linked cell but here a 4 in r1c9 forces the 4 in r3c6 - so in my terminology we have a chain but with one negative which makes for a nonsense) what I can't do (ignorance) is classify it a s a skyscraper or finned Xwing - never having taken a course in sudoku solving!

And whats more this leads to a solution directly - never putting more than a "double" candiate for a cell! and no need for the XWing
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Wed Sep 13, 2006 3:50 pm    Post subject: Reply with quote

Quote:
So how do you describe my method?


I don't have an answer; maybe one of the more creative types can describe it. But whatever, if it's based on logic, that's the name of the game.

Quote:
what I can't do (ignorance) is classify it a s a skyscraper or finned Xwing - never having taken a course in sudoku solving!


I've taken that course. It consisted of scouring web sites for basic and advanced techniques and printing them out to build up a reference base. Also on this forum, when someone used a technique that wasn't familiar to me, I asked about it and printed out the answer for my reference files.

I've now been into this nonsense long enough that I don't have to refer to that material very often, but it was a great aid in learning. The technique I mentioned above--Finned X-Wing--was one I didn't see on the web sites and learned from this forum. I suspect with my questions that I may have been considered a pest at times, but asking is the way I learn.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Sep 13, 2006 10:09 pm    Post subject: Reply with quote

George Woods wrote:
So how do you describe my method?


It's known either as a 'turbot fish' or more generally as multi-colouring.

The grid probably looks something like this:
Code:
 
 *--------------------------------------------------------------------*
 | 7      23569  569    | 238    245    248    | 3458   1      46B    |
 | 4      235    15     | 12378  257    6      | 358    9      58     |
 | 136    356    8      | 13     9      14a    | 7      3456A  2      |
 |----------------------+----------------------+----------------------|
 | 5      78     3      | 6      1      27     | 248    248    9      |
 | 69     6789   679    | 4      27     3      | 1      258    58     |
 | 2      1      4      | 9      8      5      | 6      7      3      |
 |----------------------+----------------------+----------------------|
 | 8      567    2      | 17     3      147    | 9      456    46b    |
 | 1369   369    169    | 5      246    12489  | 2348   23468  7      |
 | 369    4      5679   | 278    267    2789   | 2358   23568  1      |
 *--------------------------------------------------------------------*


The cells in row 3 are conjugate (strong links). The cells in column 9 are also. The cells with capitals both can't be 4 so one or both of the small lettered cells must be. Any cell that 'sees' both of a and b can't be a 4.


Last edited by TKiel on Thu Sep 14, 2006 12:10 am; edited 1 time in total
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CT Yankee



Joined: 17 Jul 2006
Posts: 11
Location: New England

PostPosted: Wed Sep 13, 2006 10:59 pm    Post subject: Reply with quote

I solved this one using basic techniques, and then a Swordfish on the 5s. This is the very first time I have ever had to use a Swordfish! I've been aware of the technique for a long time, and I always look for it, but this is the very first time it ever really stood out as a way forward when I couldn't spot anything else. Most of the time I suspect I've been using other methods that supercede fishing expeditions - that's the only explanation I have for why I never seem to need a technique that everyone else considers indispensable.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Sep 14, 2006 12:59 am    Post subject: Reply with quote

CT Yankee,

The X-wing and the Swordfish are complementary and basically make the same exclusions. Many fish are accompanied by other fish. It makes sense when you think about it. If there are 5 rows & columns not solved for a particular number and 2 of those row & columns form an X-wing, the other cells must form a Swordfish.

As to why you've never had to use a Swordfish before I don't have an answer. Maybe you need to start doing easier puzzles. Smile
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riderdude



Joined: 04 Jun 2006
Posts: 9
Location: Mass

PostPosted: Fri Sep 15, 2006 3:07 am    Post subject: Reply with quote

TPM wrote:
George, you cannot have a 6 in r8c8 as the 6 in r7 can only be in col 8 or col 9


sorry, i'm with George. why can't there be a 6 in r2c7?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Sep 15, 2006 10:38 am    Post subject: Reply with quote

riderdude wrote:
sorry, i'm with George. why can't there be a 6 in r2c7?


Not sure if the cell location is just a misprint, but r2c6 is a 6.
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riderdude



Joined: 04 Jun 2006
Posts: 9
Location: Mass

PostPosted: Fri Sep 15, 2006 1:14 pm    Post subject: Reply with quote

TKiel wrote:
Not sure if the cell location is just a misprint, but r2c6 is a 6.


doh

yes, typo. i meant r7c2. if i can get rid of the 6 there, i can get rid of other 6s in box 9. then the 4 in r3c8 is apparent. i was at pretty much the same place as TPM when i got stuck, too.

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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Sep 15, 2006 6:35 pm    Post subject: Catching swordfish Reply with quote

CTYankee wrote:
This is the very first time I have ever had to use a Swordfish! ...

There's a very cute example of a swordfish in the archives over at Ruud's excellent web site.

Oh -- it's on the "8"s, in columns. And it's a real swordfish -- the complement is a "jellyfish". There's also a "finned swordfish" (on a different digit) after you find the straightforward one. Better yet, finding those two finny friends doesn't solve the puzzle -- there's still a lot of work to do after you've reeled in your catch! dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Fri Sep 15, 2006 9:00 pm    Post subject: Reply with quote

Quote:
And it's a real swordfish -- the complement is a "jellyfish".


David, could you elaborate? I was under the impression that complementary fish added up to nine, whereas a swordfish + jellyfish = seven. Question
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Sep 15, 2006 9:27 pm    Post subject: Fish & complements Reply with quote

Marty R wrote:
was under the impression that complementary fish added up to nine ...

Hi, Marty!

The formula you need is

order(fish) + order(fishy complement) + # of digits "x" already resolved = 9

So if no "5"s (for instance) have yet been placed in the puzzle, and there's a "swordfish" on the "5"s, then the complementary fish will be of order 6. (It's a little more complicated than that ... for instance, the set of 9 columns and rows might be broken up into 3 distinct swordfish. Or there might be the one swordfish, one jellyfish, and one X-Wing. Or one swordfish and 3 X-Wings, etc.) But if 2 "5"s have already been placed in the puzzle, then the complement of the swordfish will be of order 4 (ie, a jellyfish) because 3 + 4 + 2 = 9.

In the "Nightmare" puzzle I was talking about two "8"s have been given as initial clues. So there are only 7 columns & rows that need an "8", and those 7 break up into a swordfish (on columns) and a jellyfish (on rows). Does that make sense? dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Sat Sep 16, 2006 5:03 am    Post subject: Reply with quote

Quote:
Does that make sense?


Yes, up to a point. I understand why I was wrong about the complements adding up to nine, but I'll have to read this a few more times to digest it fully.

Thanks David.
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George Woods



Joined: 28 Mar 2006
Posts: 234
Location: Dorset UK

PostPosted: Sat Sep 16, 2006 11:28 am    Post subject: Reply with quote

riderdude wrote:
TKiel wrote:
Not sure if the cell location is just a misprint, but r2c6 is a 6.


doh

yes, typo. i meant r7c2. if i can get rid of the 6 there, i can get rid of other 6s in box 9. then the 4 in r3c8 is apparent. i was at pretty much the same place as TPM when i got stuck, too.



Look at the 57 attacks on box 7 -- your cell has to be 57 hence no 6!
I suppose this is described a s a "hidden pair" 57 in box 7
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keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Sat Sep 16, 2006 8:15 pm    Post subject: Missing a fish? Reply with quote

David wrote:

Quote:
order(fish) + order(fishy complement) + # of digits "x" already resolved = 9

Except, in this case
Code:
+-------------------+-------------------+-------------------+
| 7     23569 569   | 238   245   248   | 3458  1     46    |
| 4     235   15    | 12378 257   6     | 358   9     58    |
| 136   356   8     | 13    9     14    | 7     3456  2     |
+-------------------+-------------------+-------------------+
| 5     78    3     | 6     1     27    | 248   248   9     |
| 69    6789  679   | 4     27    3     | 1     258   58    |
| 2     1     4     | 9     8     5     | 6     7     3     |
+-------------------+-------------------+-------------------+
| 8     57    2     | 17    3     147   | 9     456   46    |
| 1369  369   169   | 5     246   2489  | 2348  2348  7     |
| 369   4     57    | 278   267   2789  | 2358  2358  1     |
+-------------------+-------------------+-------------------+

Three (3) of the 5's are solved, and there is supposedly an X-wing (2) and a complementary swordfish (3). Adds up to 8.

Even more fishy, the eliminations of the swordfish and the X-wing are not the same.

Here is the X-wing:


Here is the Swordfish:



In fact, the X-wing is part of a second Swordfish. Here it is:



Keith
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