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garytorborg
Joined: 19 Jan 2011
Posts: 28
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 Posted: Tue Mar 15, 2011 8:55 pm Post subject: A puzzle "too hard" |
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The Draw/Play generator rated this as "too hard". It's rated as "fiendish" on my smartphone software, but the last 5 puzzles from there that I have "drawn" on this site all came up as either "hard" or "very hard" and I was able to solve them without outside help.
Not this time.
| Code: |
+--------------+--------------+--------------+
| 46 1246 9 | 7 14 5 | 8 24 3 |
| 47 147 3 | 8 149 2 | 59 45 6 |
| 5 24 8 | 49 3 6 | 7 1 249 |
+--------------+--------------+--------------+
| 278 378 4 | 1259 59 19 | 56 3567 57 |
| 1 9 5 | 6 7 34 | 2 34 8 |
| 27 37 6 | 25 8 34 | 1 9 457 |
+--------------+--------------+--------------+
| 4689 4568 17 | 3 2 19 | 4 5678 579 |
| 4689 4568 12 | 1459 4569 7 | 3 2568 259 |
| 3 456 27 | 459 4569 8 | 569 2567 1 |
+--------------+--------------+--------------+
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Play this puzzle online at the Daily Sudoku site.
The puzzle has already so far included two naked pairs, a naked triple, and a naked quad, one xy-wing (resulting in only one elimination), and one x-wing (which nicely took out 3 candidates from cells), but I'm still left with the above mess, particularly boxes 7, 8, and 9.
Any ideas, anyone? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Mar 15, 2011 9:54 pm Post subject: |
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Interesting. If I load your grid into my solver or HoDoKu, then they report multiple solutions exist. If I load your grid into Simple Sudoku, then it's perfectly happy and solves the puzzle. The only distinction is that Simple Sudoku treats r7c7=4 as a Naked Single and auto-eliminates r7c12<>4 during loading of the puzzle. Neither my solver nor HoDoKu seem to load the puzzle properly with the extra candidates.
First Step: Solve r7c7=4 as a Naked Single.
Second Step: Hidden Pair <27> in [row 9].
Third Step: Look for a 2-String Kite in <9>.
Fourth Step: X-Wing in <9>.
Puzzle now solves with Singles. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Mar 15, 2011 11:28 pm Post subject: |
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The possibilities for R7C1, 4689, are incorrect. They should be 6789.
The correct puzzle can be solved by an XY-wing -247, then a skyscraper on 9 and an X-wing on 9.
The XY-wing is not needed.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 12:36 am Post subject: |
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| keith wrote: | The possibilities for R7C1, 4689, are incorrect. They should be 6789.
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The Naked Triple in [c3] prevents <7> from being in r7c1. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 12:51 am Post subject: |
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| daj95376 wrote: | | keith wrote: | The possibilities for R7C1, 4689, are incorrect. They should be 6789.
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The Naked Triple in [c3] prevents <7> from being in r7c1. |
Danny,
I meant if you generate the possibilities from only the solved cells (no basics) they include 7 and not 4. Same thing (not 4) goes for R7C2.
Maybe you should get your solver to check for incorrect candidates in unsolved cells.
I think a statement like: "The value in a solved cell cannot be a candidate in any of its peers (buddies)" is kind of self-evident. I am unwilling to accept that an invalid candidate in an unsolved cell invalidates the puzzle. The candidates are not part of the puzzle statement.
(And, by invalid I mean that a valid candidate is missing, or an invalid candidate is present.)
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 1:09 am Post subject: |
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| keith wrote: | Danny,
I meant if you generate the possibilities from only the solved cells (no basics) they include 7 and not 4. Same thing (not 4) goes for R7C2.
Maybe you should get your solver to check for incorrect candidates in unsolved cells.
I think a statement like: "The value in a solved cell cannot be a candidate in any of its peers (buddies)" is kind of self-evident. I am unwilling to accept that an invalid candidate in an unsolved cell invalidates the puzzle. The candidates are not part of the puzzle statement.
(And, by invalid I mean that a valid candidate is missing, or an invalid candidate is present.)
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There are various trains of thought on what constitutes a "clue/given cell" vs. a "solved cell" in a grid w/o the original puzzle.
Since the original grid contains <4> in r7c12, there are those who would say that cell r7c7 is simply a partially solved cell and not a clue/given cell. Run this puzzle through whichever solver you want and tell me how many solutions you encounter.
| Code: | +-----------------------+
| . . 9 | 7 . 5 | 8 . 3 |
| . . 3 | 8 . 2 | . . 6 |
| 5 . 8 | . 3 6 | 7 1 . |
|-------+-------+-------|
| . . 4 | . . . | . . . |
| 1 9 5 | 6 7 . | 2 . 8 |
| . . 6 | . 8 . | 1 9 . |
|-------+-------+-------|
| . . . | 3 2 . | . . . |
| . . . | . . 7 | 3 . . |
| 3 . . | . . 8 | . . 1 |
+-----------------------+
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| Code: | you'll get bogged down at this point
*-----------------------------------------*
| 6 1 9 | 7 4 5 | 8 2 3 |
| 4 7 3 | 8 1 2 | 9 5 6 |
| 5 2 8 | 9 3 6 | 7 1 4 |
|-------------+-------------+-------------|
| 2 8 4 | 1 5 9 | 6 3 7 |
| 1 9 5 | 6 7 3 | 2 4 8 |
| 7 3 6 | 2 8 4 | 1 9 5 |
|-------------+-------------+-------------|
| 8 45 7 | 3 2 1 | 45 6 9 |
| 9 45 1 | 45 6 7 | 3 8 2 |
| 3 6 2 | 45 9 8 | 45 7 1 |
*-----------------------------------------*
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Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 1:41 am Post subject: |
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| Quote: | | Run this puzzle through whichever solver you want and tell me how many solutions you encounter. |
Two.
How do you conclude R7C7 <>4? I can delete single-candidate cells in any puzzle to make it invalid.
A single-candidate cell is not a solved cell?
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 2:00 am Post subject: |
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Danny,
Give me a break!
What does your solver do with this one?
| Code: | +-----------------------------------------------------------------------------------------------+
| 123456789 123456789 9 | 7 123456789 5 | 8 123456789 3 |
| 123456789 123456789 3 | 8 123456789 2 | 123456789 123456789 6 |
| 5 123456789 8 | 123456789 3 6 | 7 1 123456789 |
|-------------------------------+-------------------------------+-------------------------------|
| 123456789 123456789 4 | 123456789 123456789 123456789 | 123456789 123456789 123456789 |
| 1 9 5 | 6 7 123456789 | 2 123456789 8 |
| 123456789 123456789 6 | 123456789 8 123456789 | 1 9 123456789 |
|-------------------------------+-------------------------------+-------------------------------|
| 123456789 123456789 123456789 | 3 2 123456789 | 4 123456789 123456789 |
| 123456789 123456789 123456789 | 123456789 123456789 7 | 3 123456789 123456789 |
| 3 123456789 123456789 | 123456789 123456789 8 | 123456789 123456789 1 |
+-----------------------------------------------------------------------------------------------+ |
Is this not the starting point of every puzzle? All candidates are possible in all cells that do not have a single candidate?
I see absolutely no logical difference between the puzzle above and this one:
| Code: | +-----------------------+
| . . 9 | 7 . 5 | 8 . 3 |
| . . 3 | 8 . 2 | . . 6 |
| 5 . 8 | . 3 6 | 7 1 . |
|-------+-------+-------|
| . . 4 | . . . | . . . |
| 1 9 5 | 6 7 . | 2 . 8 |
| . . 6 | . 8 . | 1 9 . |
|-------+-------+-------|
| . . . | 3 2 . | 4 . . |
| . . . | . . 7 | 3 . . |
| 3 . . | . . 8 | . . 1 |
+-----------------------+ |
Except, the first will make your solver croak.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 2:16 am Post subject: |
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| keith wrote: | | Quote: | | Run this puzzle through whichever solver you want and tell me how many solutions you encounter. |
Two.
How do you conclude R7C7 <>4? I can delete single-candidate cells in any puzzle to make it invalid.
A single-candidate cell is not a solved cell?
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Here's where thing get into a grey area. There are two avenues through which we can proceed.
1) Treat r7c7 as a Naked Single; i.e., solved cell ... and continue solving the puzzle. This is what Simple Sudoku does.
2) Do what you can to verify that a valid grid exists and that the original puzzle had a unique solution.
In the second alternative, we now encounter a problem. Since r7c7=4 is not acceptable as a clue/given cell because of the presence of <4> in r7c12, we can at most hope that the remaining single-values cells would still force a unique solution IF they were treated as clue/given cells. However, you've already confirmed that this is not the case.
We're left with an inconsistent puzzle/grid state because the presence of <4> in r7c12 prevents us from deriving r7c7=4 as a solved cell ... and the presence of r7c7 as a clue/given cell prevents r7c12 from containing <4> as a candidate.
Regards, Danny |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 2:36 am Post subject: |
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| keith wrote: | Give me a break!
What does your solver do with this one?
| Code: | +-----------------------------------------------------------------------------------------------+
| 123456789 123456789 9 | 7 123456789 5 | 8 123456789 3 |
| 123456789 123456789 3 | 8 123456789 2 | 123456789 123456789 6 |
| 5 123456789 8 | 123456789 3 6 | 7 1 123456789 |
|-------------------------------+-------------------------------+-------------------------------|
| 123456789 123456789 4 | 123456789 123456789 123456789 | 123456789 123456789 123456789 |
| 1 9 5 | 6 7 123456789 | 2 123456789 8 |
| 123456789 123456789 6 | 123456789 8 123456789 | 1 9 123456789 |
|-------------------------------+-------------------------------+-------------------------------|
| 123456789 123456789 123456789 | 3 2 123456789 | 4 123456789 123456789 |
| 123456789 123456789 123456789 | 123456789 123456789 7 | 3 123456789 123456789 |
| 3 123456789 123456789 | 123456789 123456789 8 | 123456789 123456789 1 |
+-----------------------------------------------------------------------------------------------+
__________________________________________________________________________________________________
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Is this not the starting point of every puzzle? All candidates are possible in all cells that do not have a single candidate?
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No!!! Assuming the following is your intended initial puzzle, then here's the initial state in my solver.
| Code: | +-----------------------+
| . . 9 | 7 . 5 | 8 . 3 |
| . . 3 | 8 . 2 | . . 6 |
| 5 . 8 | . 3 6 | 7 1 . |
|-------+-------+-------|
| . . 4 | . . . | . . . |
| 1 9 5 | 6 7 . | 2 . 8 |
| . . 6 | . 8 . | 1 9 . |
|-------+-------+-------|
| . . . | 3 2 . | 4 . . |
| . . . | . . 7 | 3 . . |
| 3 . . | . . 8 | . . 1 |
+-----------------------+
+--------------------------------------------------------------------------------+
| 246 1246 9 | 7 14 5 | 8 24 3 |
| 47 147 3 | 8 149 2 | 59 45 6 |
| 5 24 8 | 49 3 6 | 7 1 249 |
|--------------------------+--------------------------+--------------------------|
| 278 2378 4 | 1259 159 139 | 56 3567 57 |
| 1 9 5 | 6 7 34 | 2 34 8 |
| 27 237 6 | 245 8 34 | 1 9 457 |
|--------------------------+--------------------------+--------------------------|
| 6789 15678 17 | 3 2 19 | 4 5678 579 |
| 24689 124568 12 | 1459 14569 7 | 3 2568 259 |
| 3 24567 27 | 459 4569 8 | 569 2567 1 |
+--------------------------------------------------------------------------------+
# 96 eliminations remain
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For each clue/given cell value, that value is eliminated in the peer cells.
You'll notice that <4> does not exist in r7c12 of my grid.
Load your puzzle into any solver and see if it gives your grid or my grid.
Regards, Danny
Last edited by daj95376 on Wed Mar 16, 2011 2:47 am; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 2:44 am Post subject: |
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| daj95376 wrote: | | keith wrote: | | Quote: | | Run this puzzle through whichever solver you want and tell me how many solutions you encounter. |
Two.
How do you conclude R7C7 <>4? I can delete single-candidate cells in any puzzle to make it invalid.
A single-candidate cell is not a solved cell?
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Here's where thing get into a grey area. There are two avenues through which we can proceed.
1) Treat r7c7 as a Naked Single; i.e., solved cell ... and continue solving the puzzle. This is what Simple Sudoku does.
2) Do what you can to verify that a valid grid exists and that the original puzzle had a unique solution.
In the second alternative, we now encounter a problem. Since r7c7=4 is not acceptable as a clue/given cell because of the presence of <4> in r7c12, we can at most hope that the remaining single-values cells would still force a unique solution IF they were treated as clue/given cells. However, you've already confirmed that this is not the case.
We're left with an inconsistent puzzle/grid state because the presence of <4> in r7c12 prevents us from deriving r7c7=4 as a solved cell ... and the presence of r7c7 as a clue/given cell prevents r7c12 from containing <4> as a candidate.
Regards, Danny |
The original posting:
| Code: | +----------------+----------------+----------------+
| 46 1246 9 | 7 14 5 | 8 24 3 |
| 47 147 3 | 8 149 2 | 59 45 6 |
| 5 24 8 | 49 3 6 | 7 1 249 |
+----------------+----------------+----------------+
| 278 378 4 | 1259 59 19 | 56 3567 57 |
| 1 9 5 | 6 7 34 | 2 34 8 |
| 27 37 6 | 25 8 34 | 1 9 457 |
+----------------+----------------+----------------+
| 4689 4568 17 | 3 2 19 | 4 5678 579 |
| 4689 4568 12 | 1459 4569 7 | 3 2568 259 |
| 3 456 27 | 459 4569 8 | 569 2567 1 |
+----------------+----------------+----------------+ |
Danny,
Come on!
By exactly the same logic you cannot use the quad in R9 to eliminate 56 in R9C8. The quad cannot be valid because R9C8 contains 56.
R7C7 is given as 4. R7C12 cannot be 4. Maybe the zeroth basics are not complete, but the fact that your solver fails when presented with unremoved or extraneous candidates is not a problem in Sudoku theory.
If this is a valid puzzle, R7C7 <4> must be an initial clue.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 3:04 am Post subject: |
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Keith,
Bottom Line for Me: I've see so many invalid/typo grids over the years that I'm tired of trying to diagnose what's correct and what's incorrect in them.
The original puzzle was not included and the grid was inconsistent for r7c7=4 as a clue/given. I should have quit there!!!
My apologies for getting involved in this protracted discussion.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 3:27 am Post subject: |
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| daj95376 wrote: | Keith,
Bottom Line for Me: I've see so many invalid/typo grids over the years that I'm tired of trying to diagnose what's correct and what's incorrect in them.
The original puzzle was not included and the grid was inconsistent for r7c7=4 as a clue/given. I should have quit there!!!
My apologies for getting involved in this protracted discussion.
Regards, Danny |
Danny,
I don't think so. In a partially solved puzzle, I would take the single-candidate cells as given. Is the puzzle valid, considering only these cells?
If so, check the candidates in the unsolved cells. Are the candidates valid? If not, assume the (presumably human) solver has made a mistake.
And, if you do not know the original puzzle, exclude any uniqueness arguments.
But, if the puzzle is ambiguous, it is ... ambiguous.
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Wed Mar 16, 2011 12:46 pm Post subject: |
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| keith wrote: | In a partially solved puzzle, I would take the single-candidate cells as given. Is the puzzle valid, considering only these cells?
If so, check the candidates in the unsolved cells. Are the candidates valid? If not, assume the (presumably human) solver has made a mistake.
And, if you do not know the original puzzle, exclude any uniqueness arguments. |
If clues plus placements make a valid puzzle, why is it necessary to "exclude uniqueness arguments?" |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 12:54 pm Post subject: |
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| Quote: | | If clues plus placements make a valid puzzle, why is it necessary to "exclude uniqueness arguments?" |
Because you cannot accurately identify Deadly Patterns if you don't know the initial clues.
Keith |
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garytorborg
Joined: 19 Jan 2011
Posts: 28
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| Posted: Wed Mar 16, 2011 1:48 pm Post subject: |
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| Thanks everyone. The first response helped me solve the puzzle. I was confused by the talk of R7C7 being a naked single when it was not only already a solved cell but was one of the "original" cells of the puzzle. Then I noticed the 4s as candidates in R7C12 and realized I must have typed some things in incorrectly. My apologies. At any rate, the hidden pair <27>, the 2-string kite, and the x-wing busted it open the rest of the way. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Wed Mar 16, 2011 3:29 pm Post subject: |
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| keith wrote: | | ronk wrote: | | If clues plus placements make a valid puzzle, why is it necessary to "exclude uniqueness arguments?" |
Because you cannot accurately identify Deadly Patterns if you don't know the initial clues. |
When the initial clues are still there, that makes no sense to me. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 4:46 pm Post subject: |
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Maybe it's semantics. Here's what I mean.
Using Danny's example from above:
| Code: | +-------+-------+-------+
| 6 1 9 | 7 4 5 | 8 2 3 |
| 4 7 3 | 8 1 2 | 9 5 6 |
| 5 2 8 | 9 3 6 | 7 1 4 |
+-------+-------+-------+
| 2 8 4 | 1 5 9 | 6 3 7 |
| 1 9 5 | 6 7 3 | 2 4 8 |
| 7 3 6 | 2 8 4 | 1 9 5 |
+-------+-------+-------+
| 8 5 7 | 3 2 1 | 4 6 9 |
| 9 4 1 | 5 6 7 | 3 8 2 |
| 3 6 2 | 4 9 8 | 5 7 1 |
+-------+-------+-------+ |
Is this a solution of a valid puzzle? It depends.
Note the deadly patterns of 45 in B789 and of 17 in B78. (There are probably others.) If at least one cell in each of these DPs is not an initial clue, the original puzzle is invalid.
I suppose you could say that if the original puzzle is valid, then a correctly solved cell is no different than an initial cell. I'd have to concede that.
But, I don't like that equation. As Danny noted, posted partially complete puzzles often have mistakes (like this one?) which you cannot unravel if you do not know the initial clues.
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Wed Mar 16, 2011 5:59 pm Post subject: |
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| keith wrote: | | I suppose you could say that if the original puzzle is valid, then a correctly solved cell is no different than an initial cell. I'd have to concede that. |
Thought that's what you wrote earlier as ...
| keith wrote: | | In a partially solved puzzle, I would take the single-candidate cells as given. Is the puzzle valid, considering only these cells? If so ... |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Mar 16, 2011 6:34 pm Post subject: |
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| ronk wrote: | | keith wrote: | | I suppose you could say that if the original puzzle is valid, then a correctly solved cell is no different than an initial cell. I'd have to concede that. |
Thought that's what you wrote earlier as ...
| keith wrote: | | In a partially solved puzzle, I would take the single-candidate cells as given. Is the puzzle valid, considering only these cells? If so ... |
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ronk,
I was writing that in response to the idea that the 4s in R7C12 imply that R7C7 has not been solved.
Keith |
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