The New Sudoku Players' Forum

[dummy]

There seems to be a typo in today's Sudoku in the Augusta Chronicle. When I type in 34462, it says there is no puzzle with that number. My Palm Sudoku program says there are 2+ solutions to this puzzle:

Code: Select all

 . . 3 | . . . | . . 4
 . . 4 | . . 6 | . 2 .
 . 7 . | 3 5 . | 9 . 6
-------+-------+------
 . . 6 | 5 . 9 | . . .
 . . . | . . . | . . .
 . . . | 1 . 8 | 2 . .
-------+-------+------
 2 . 5 | . 4 3 | . 9 .
 . 4 . | 9 . . | 8 . .
 3 . . | . . . | 1 . .



[Luke]

If you've copied the grid correctly from the paper or web site, then you're right. It's invalid, with seven solutions, regular Sudoku of Shame candidate. However, if you change r4c6 to [2] you'll have a unique solution and a valid puzzle (SE = 7.1.)

Code: Select all

 . . 3 | . . . | . . 4
 . . 4 | . . 6 | . 2 .
 . 7 . | 3 5 . | 9 . 6
-------+-------+------
 . . 6 | 5 . 2 | . . .
 . . . | . . . | . . .
 . . . | 1 . 8 | 2 . .
-------+-------+------
 2 . 5 | . 4 3 | . 9 .
 . 4 . | 9 . . | 8 . .
 3 . . | . . . | 1 . .



There may be other givens that can be changed to yield a unique solution, but I'll leave that to our programmers and wizards.

[Pat]

a SuDoku Explainer rating of 7.1
would be far beyond any Pappocom puzzle


one possibility is to add a clue at r5c5

this makes a very easy puzzle

Code: Select all

 . . 3 | . . . | . . 4
 . . 4 | . . 6 | . 2 .
 . 7 . | 3 5 . | 9 . 6
-------+-------+------
 . . 6 | 5 . 9 | . . .
 . . . | . 7 . | . . .
 . . . | 1 . 8 | 2 . .
-------+-------+------
 2 . 5 | . 4 3 | . 9 .
 . 4 . | 9 . . | 8 . .
 3 . . | . . . | 1 . .



[udosuk]

Great observation Pat!

Perhaps that's the original intention of the publisher - the puzzle has multiple solutions but the challenge is to add one clue to the puzzle which produces a unique solution while keeping the clue pattern symmetrical.

In that case there is only one answer - r5c5=7 (all other values either lead to no solution or 2 solutions). So that's an interesting paradox - the invalidity of the sudoku puzzle grid makes it a valid logical challenge.

Then again, the publisher is probably not that clever.

[Luke]

a SuDoku Explainer rating of 7.1
would be far beyond any Pappocom puzzle

You know, the same thought occurred to me when after I put it in SE. I just learned how to do this so I may have erred, because this puzzle is not difficult at all:

Code: Select all

 *-----------------------------------------------------------*
 | 189   6     3     | 2     189   19    | 57    57    4     |
 | 1589 *58    4     | 7     189   6     | 3     2     1-8   |
 | 18    7     2     | 3     5     4     | 9    *18    6     |
 |-------------------+-------------------+-------------------|
 | 78   *38    6     | 5     379   2     | 4    *18    189   |
 | 578   2     1     | 4     36    79    | 57    36    89    |
 | 4     35    9     | 1     67    8     | 2     67    35    |
 |-------------------+-------------------+-------------------|
 | 2     1     5     | 8     4     3     | 6     9     7     |
 | 6     4     7     | 9     12    15    | 8     35    235   |
 | 3     9     8     | 6     27    57    | 1     4     25    |
 *-----------------------------------------------------------*


Just this little cycle and one XY chain tips it over. A newspaper's Saturday puzzle is often the toughest of the week and this one doesn't seem unreasonable in that context. Here's the Saturday puzzle from the San Francisco Chronicle. Strangely enough, SE also gives it a 7.1. (??)
6.7.....59...2..7...3...2..4..5....9....1....7...39..4..5...6...9..7..831.....5.2

May I ask how you determined a 7 in the middle would do the trick? Just logic as Udosuk suggested, or is there a program that can look for this kind of thing?

BTW, Udosuk, changing one value also preserves the symmetry. Maybe the publisher was craftier than you thought

[ronk]

May I ask how you [edit: Pat] determined a 7 in the middle would do the trick? Just logic as Udosuk suggested, or is there a program that can look for this kind of thing?

Pat used old-fashioned brain power, ala Sherlock Holmes, I think.

Most puzzles published in newspapers have some sort of symmetry, and inspection reveals this puzzle to have 180-degree rotational symmetry.

When a puzzle has multiple solutions, the omission of a single clue is a frequent occurrence. To preserve existing symmetry, a single clue can only be added at r5c5, and r5c5 already sees digits 1, 4, 5, 8 and 9.

With only 4 values to try, a text editor and your favorite solver can quickly verify existence of a valid solution.

[udosuk]

A newspaper's Saturday puzzle is often the toughest of the week and this one doesn't seem unreasonable in that context.

Yes, depending on different publishers your SE 7.1 puzzle could be acceptable in a printed material. However, for puzzles from Pappocom (Wayne Gould & co) most should be solvable without pencilmarks, and yours perhaps is a touch too tough to do so.

May I ask how you determined a 7 in the middle would do the trick? Just logic as Udosuk suggested, or is there a program that can look for this kind of thing?

BTW, Udosuk, changing one value also preserves the symmetry. Maybe the publisher was craftier than you thought

I used the software JSudoku to verify #solutions for me. In that case Pat's approach (adding a clue in r5c5 and check for validity) is not hard to do (as ronk described above), while your approach (changing one of the existing given clues) is quite tedious to exhaust every possibility (considering there are 26 given clues), and thus quite hard to check whether your example is the only possible way to make it a valid puzzle.

[udosuk]

Code: Select all

 *-----------------------------------------------------------*
 | 189   6     3     | 2     189   19    | 57    57    4     |
 | 1589 *58    4     | 7     189   6     | 3     2     1-8   |
 | 18    7     2     | 3     5     4     | 9    *18    6     |
 |-------------------+-------------------+-------------------|
 | 78   *38    6     | 5     379   2     | 4    *18    189   |
 | 578   2     1     | 4     36    79    | 57    36    89    |
 | 4     35    9     | 1     67    8     | 2     67    35    |
 |-------------------+-------------------+-------------------|
 | 2     1     5     | 8     4     3     | 6     9     7     |
 | 6     4     7     | 9     12    15    | 8     35    235   |
 | 3     9     8     | 6     27    57    | 1     4     25    |
 *-----------------------------------------------------------*

Just this little cycle and one XY chain tips it over.

But you don't need that little cycle - only the XY-chain is required:

Code: Select all

+-------------------+-------------------+-------------------+
| 189   6     3     | 2     189   19    | 57   *57    4     |
| 1589  58    4     | 7     189   6     | 3     2     18    |
| 18    7     2     | 3     5     4     | 9     18    6     |
+-------------------+-------------------+-------------------+
| 78    38    6     | 5     379   2     | 4     18    189   |
| 578   2     1     | 4     36    79    | 57    36    89    |
| 4     35    9     | 1    *67    8     | 2    *67    35    |
+-------------------+-------------------+-------------------+
| 2     1     5     | 8     4     3     | 6     9     7     |
| 6     4     7     | 9     12    15    | 8     3-5   235   |
| 3     9     8     | 6    *27    57    | 1     4    *25    |
+-------------------+-------------------+-------------------+

r1c8+r6c58+r9c59 can't be [77622] => r8c8 can't be 5

On the other hand, I don't like chains so this might be how I crack it:

Code: Select all

+-------------------+-------------------+-------------------+
| 189   6     3     | 2     189   19    | 57    57    4     |
|-1589  58    4     | 7     189   6     | 3     2    *18    |
|*18    7     2     | 3     5     4     | 9    -18    6     |
+-------------------+-------------------+-------------------+
| 78    38    6     | 5     379   2     | 4     18    189   |
|*578   2     1     | 4     36    79    | 57    36   *89    |
| 4     35    9     | 1     67    8     | 2     67    35    |
+-------------------+-------------------+-------------------+
| 2     1     5     | 8     4     3     | 6     9     7     |
| 6     4     7     | 9     12    15    | 8     35    235   |
| 3     9     8     | 6     27    57    | 1     4     25    |
+-------------------+-------------------+-------------------+

W-wing/Y-wing/semi-remote-pair:
8 @ r5 locked @ r5c19
=> r2c9+r3c1 can't be both 8
=> r2c1+r3c8, seeing r2c9+r3c1, can't be 1
=> r3c18=[18], r2c9=r4c8=1

Code: Select all

+----------------+----------------+----------------+
|*89   6    3    | 2    189 *19   | 57   57   4    |
| 589  58   4    | 7    89   6    | 3    2    1    |
| 1    7    2    | 3    5    4    | 9    8    6    |
+----------------+----------------+----------------+
| 78   38   6    | 5    379  2    | 4    1    89   |
| 57-8 2    1    | 4    36  *79   | 57   36  *89   |
| 4    35   9    | 1    67   8    | 2    67   35   |
+----------------+----------------+----------------+
| 2    1    5    | 8    4    3    | 6    9    7    |
| 6    4    7    | 9    12   15   | 8    35   235  |
| 3    9    8    | 6    27   57   | 1    4    25   |
+----------------+----------------+----------------+

W-wing/Y-wing/semi-remote-pair:
9 @ c6 locked @ r15c6
=> r1c1+r5c9 can't be both 9
=> r5c1, seeing r1c1+r5c9, can't be 8

[udosuk]

Okay, to settle the issue, I've done the tedious work to check all 26 given clues to see if any of them can be changed to give a valid puzzle (btw I know there are programs for this task, but just like a workout). Aside from Luke's way there are only 3 others:

Code: Select all

change r2c8 from 2 to 7
..3.....4
..4..6.7.
.7.35.9.6
..65.9...
.........
...1.82..
2.5.43.9.
.4.9..8..
3.....1..

change r1c9 from 4 to 1
..3.....1
..4..6.2.
.7.35.9.6
..65.9...
.........
...1.82..
2.5.43.9.
.4.9..8..
3.....1..

change r1c9 from 4 to 8
..3.....8
..4..6.2.
.7.35.9.6
..65.9...
.........
...1.82..
2.5.43.9.
.4.9..8..
3.....1..

But none of these requires anything harder than naked pairs, so Luke have found the cream of the crop.

[Luke]

...your approach (changing one of the existing given clues) is quite tedious to exhaust every possibility (considering there are 26 given clues), and thus quite hard to check whether your example is the only possible way to make it a valid puzzle.

Exactly. That's why I was wondering if there was software that could do it. I found the one that I did when I checked for the number of solutions. Since there were only seven, I took a look at which cells had the changes.

Code: Select all

..3.....4..4..6.2..7.35.9.6..65.9...............1.82..2.5.43.9..4.9..8..3.....1..
963281574584796321172354986726539418831462759459178263215843697647915832398627145
963281754584796321172354986726539418831427569459168273215843697647912835398675142
963281754584796321172354986726539418831427569459168273215843697647915832398672145
963281754584796321172354986726539418831462579459178263215843697647915832398627145
963281754584796321172354986726539418831472569459168273215843697647915832398627145
963281754584796321172354986736529418821437569459168273215843697647912835398675142
963281754584796321172354986736529418821437569459168273215843697647915832398672145

Then I marked the cells on the grid.

Code: Select all

 . . 3 | . . . | . . 4
 . . 4 | . . 6 | . 2 .
 . 7 . | 3 5 . | 9 . 6
-------+-------+------
 . . 6 | 5 # 9 | . . .
 . # . | . # # | # # .
 . . . | 1 # 8 | 2 . .
-------+-------+------
 2 . 5 | . 4 3 | . 9 .
 . 4 . | 9 . . | 8 . .
 3 . . | . # # | 1 . #


The cells that could see the most marks were r46c6. I started with r4c6, and since 1 was a given, I tried 2, and voila. Found it on the first try and it took only a couple of minutes.

Either I got lucky or I've got too much time on my hands or both . Thanks for doing "all the tedious work" and for posting your right-brain approach to solving the puzzle.

[dummy]

[quote="change r1c9 from 4 to 1
Code:
..3.....1
..4..6.2.
.7.35.9.6
..65.9...
.........
...1.82..
2.5.43.9.
.4.9..8..
3.....1..

Thanks, udosuk. Your second of three solutions (see above) must be the "right" one. I entered all three in the solution finder and only this one gave a valid answer. Obviously, the Chronicle screwed up and changed the 1 to a 4 in R1C9.

To those who have conjectured that the puzzle was edited to make it more challenging: that would imply that intelligent life exists at the Augusta Chronicle. I have not observed that in the 27 years I've lived in Augusta.

BTW, nice anagram on SUDOKU on your ID -- but I don't think you "SUK" at all

Thanks,

--Paul

[udosuk]

Happy New Year Paul,

Thanks, udosuk. Your second of three solutions (see above) must be the "right" one. I entered all three in the solution finder and only this one gave a valid answer. Obviously, the Chronicle screwed up and changed the 1 to a 4 in R1C9.

Guess I hit the jackpot!

To those who have conjectured that the puzzle was edited to make it more challenging: that would imply that intelligent life exists at the Augusta Chronicle. I have not observed that in the 27 years I've lived in Augusta.

LOL!

BTW, nice anagram on SUDOKU on your ID -- but I don't think you "SUK" at all

Likewise, I don't think you're a "dummy" at all.

As a matter of fact, "Udo" is a proper European first name, and "Suk" is also a proper European/African/Asian surname.

As stated before, I believe the proper pronounciation should be "U-Doh-Sook".

[Pat]

Thanks, udosuk. Your 2nd of 3 must be the "right" one. I entered all 3 in the solution finder and only this one gave a valid answer. Obviously, the Chronicle screwed up and changed the 1 to a 4 in R1C9.

on the contrary, the "Solutions" sections does not find new puzzles ( a problem we've seen for quite some time now ), and the puzzle it finds for that code is an old ( un-related ) puzzle -- if anything, this proves that the 2nd puzzle is not the one intended.

also you could've told us that the puzzle was published with an "Easy" rating -- this too would provide proof that the intended puzzle was the 1st or the 3rd of the 3

[dummy]

> on the contrary, the "Solutions" sections does not find new puzzles
> ( a problem we've seen for quite some time now ), and the puzzle
> it finds for that code is an old ( un-related ) puzzle -- if anything,
> this proves that the 2nd puzzle is not the one intended.

I've not observed that. Any other puzzle I've looked up was always found. I admit I've not looked up that many. Maybe it depends on the paper.

> also you could've told us that the puzzle was published with an
> "Easy" rating -- this too would provide proof that the intended
> puzzle was the 1st or the 3rd of the 3

Actually, I couldn't have: the Chronicle stopped printing the rating with the puzzle about a month ago. They still seem to be following the previous pattern of starting out "easy" on Monday and printing the hardest puzzles on Saturday and Sunday.

--Paul

[Pat]

the code 31462 does bring up a puzzle (as you had reported)
-- and this puzzle is definitely not the 2008.Dec.27 puzzle (the first clue is in r1c1)

i'm sorry to hear they've stopped printing the ratings.

anyway the 1st and 3rd puzzles can be solved by "hidden singles"
and are therfore probably not tougher than "Medium"

sorry, i shouldn't have said "Easy",
it could be "Very Easy" or "Easy" or "Medium"
(or on rare occasions perhaps even "Hard");
in the present case,
the 1st and 3rd puzzles are rated "Medium"

the 2nd puzzle is the one solved at the level of duos
therefore "Hard"