USA Today puzzle - Jan 13

Post the puzzle or solving technique that's causing you trouble and someone will help

USA Today puzzle - Jan 13

Postby donmckeown » Sat Jan 14, 2006 3:51 pm

Easily got 8 numbers placed and then hit a brick wall. Help?
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Postby Crazy Girl » Sun Jan 15, 2006 12:54 am

donmckeown,

For those of us not in the USA please post your puzzle and your candidate grid (what numbers you have as possible candidates for the empty cells) so we may help you:D

It may be worthwile stating also how good you are at solving sudoku's so that the forum members can give advice better suited to your level
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USA Today puzzle - Jan 13

Postby donmckeown » Sun Jan 15, 2006 2:10 am

Hi Crazy Girl

[(67) (89) 1 ] [(4689) 2 (4689)] [(478) (5) 3 ]
[(37) 4 (89)] [ 5 (39) (1) ] [(278) (289) 6 ]
[(36) 2 (5) ] [ 7 (369) (4689)] [(48) (89) 1 ]

[(124)(579) 6 ] [(239) 8 (579)] [(23) (123) (247)]
[(24) (578) 3 ] [(26) 1 (567)] [ 9 (268) (2478)]
[(12) (789) (89)] [(2369) 4 (679)] [ 5 (12368) (278)]

[ 5 (136) (4) ] [(1689) (69) 2 ] [(368) 7 (89) ]
[ 8 (16) (7) ] [(169) (5) 3 ] [ (26) 4 (29) ]
[ 9 (36) (2) ] [(468) 7 (468)] [ 1 (368) (5) ]

The single numbers in parentheses are those that I was able to figure out.

I think maybe I'm a pretty good amateur, but this one has me stumped. I can proceed only by trial and error.

Thanks.
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Postby Shazbot » Sun Jan 15, 2006 5:42 am

6s in box 5 will only go in column 8 (locked candidates) so you can remove the 6 from r9c8

You might want to reformat your lists when posting for assistance - using the CODE button will keep your even spacing:
Code: Select all
 *-----------*
 |..1|.2.|..3|
 |.4.|5..|..6|
 |.2.|7..|..1|
 |---+---+---|
 |..6|.8.|...|
 |..3|.1.|9..|
 |...|.4.|5..|
 |---+---+---|
 |5..|..2|.7.|
 |8..|..3|.4.|
 |9..|.7.|1..|
 *-----------*


 *-----------*
 |..1|.2.|.53|
 |.4.|5.1|..6|
 |.25|7..|..1|
 |---+---+---|
 |..6|.8.|...|
 |..3|.1.|9..|
 |...|.4.|5..|
 |---+---+---|
 |5.4|..2|.7.|
 |8.7|.53|.4.|
 |9.2|.7.|1.5|
 *-----------*

 
|------------------------------------------------------|
| 67   89   1   | 4689  2    4689  | 478  5      3     |
| 37   4    89  | 5     39   1     | 278  289    6     |
| 36   2    5   | 7     369  4689  | 48   89     1     |
|---------------+------------------+-------------------|
| 124  579  6   | 239   8    579   | 23   123    247   |
| 24   578  3   | 26    1    567   | 9    268    2478  |
| 12   789  89  | 2369  4    679   | 5    12368  278   |
|---------------+------------------+-------------------|
| 5    136  4   | 1689  69   2     | 368  7      89    |
| 8    16   7   | 169   5    3     | 26   4      29    |
| 9    36   2   | 468   7    468   | 1    38     5     |
|------------------------------------------------------|


not sure of the next step - suspect it'll be forcing chains, but I'm not too good with those so I'll let someone else volunteer....
Shazbot
 
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USA Today puzzle - Jan 13

Postby donmckeown » Sun Jan 15, 2006 1:33 pm

Thank you Shazbot. I had seen that but made an error when posting the matrix. Thanks also for your advice regarding use of the "code" feature.
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Postby MCC » Sun Jan 15, 2006 5:10 pm

This dosen't move the puzzle on, but for interest only.

Besides the x-wing in 7's in (r12c1)(r12c7)
there is a 3x3 swordfish in 7's in (r456c2)(r456c6)(r456c9).

MCC
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Postby tarek » Sun Jan 15, 2006 7:59 pm

Shazbot wrote:not sure of the next step - suspect it'll be forcing chains, but I'm not too good with those so I'll let someone else volunteer....


you are right , here is what my solver brings out, somebody else may have a shorter way, but this easy for paper & pencil players to follow:

Code: Select all
*-----------------------------------------------------------------*
| 67     89     1     | 4689   2      4689  | 478    5      3     |
| 37     4      89    | 5      39     1     | 278    289    6     |
| 36     2      5     | 7      369    4689  | 48     89     1     |
|---------------------+---------------------+---------------------|
| 124    579    6     | 239    8      579   | 23     123    247   |
| 24     578    3     | 26     1      567   | 9      268    2478  |
| 12     789    89    | 2369   4      679   | 5      12368  278   |
|---------------------+---------------------+---------------------|
| 5      136    4     | 1689   69     2     | 368    7      89    |
| 8      16     7     | 169    5      3     | 26     4      29    |
| 9      36     2     | 468    7      468   | 1      38     5     |
*-----------------------------------------------------------------*
Candidates in r9c8 will force r8c2 to have only 1 as valid Candidates
r9c8=3: r9c8=3 => r9c2=6 => r8c2=1
r9c8=8: r9c8=8 => r7c9=9 => r8c9=2 => r8c7=6 => r8c2=1
Threfore r8c2=1

*-----------------------------------------------------------------*
| 67     89     1     | 4689   2      4689  | 478    5      3     |
| 37     4      89    | 5      39     1     | 278    289    6     |
| 36     2      5     | 7      369    4689  | 48     89     1     |
|---------------------+---------------------+---------------------|
| 124    579    6     | 239    8      579   | 23     123    247   |
| 24     578    3     | 26     1      567   | 9      268    2478  |
| 12     789    89    | 2369   4      679   | 5      12368  278   |
|---------------------+---------------------+---------------------|
| 5      36     4     | 1      69     2     | 368    7      89    |
| 8      1      7     | 69     5      3     | 26     4      29    |
| 9      36     2     | 468    7      468   | 1      38     5     |
*-----------------------------------------------------------------*
Eliminating 8 From r9c8 (Row 7 & Box 9 Box-line interaction)

*--------------------------------------------------------*
| 67    89    1    | 4689  2     4689 | 478   5     3    |
| 37    4     89   | 5     39    1    | 278   289   6    |
| 36    2     5    | 7     369   4689 | 48    89    1    |
|------------------+------------------+------------------|
| 124   579   6    | 29    8     579  | 3     12    247  |
| 24    578   3    | 26    1     567  | 9     268   2478 |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
r1c4 Must only have 48 as valid Candidates (48 is a Hidden Double in Column 4)
*--------------------------------------------------------*
| 67    89    1    | 48    2     4689 | 478   5     3    |
| 37    4     89   | 5     39    1    | 278   289   6    |
| 36    2     5    | 7     369   4689 | 48    89    1    |
|------------------+------------------+------------------|
| 124   579   6    | 29    8     579  | 3     12    247  |
| 24    578   3    | 26    1     567  | 9     268   2478 |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
Eliminating 2 From r5c9 (9 & 6 in r8c4 form an XY wing with 2 in r8c9 & r5c4)
*--------------------------------------------------------*
| 67    89    1    | 48    2     4689 | 478   5     3    |
| 37    4     89   | 5     39    1    | 278   289   6    |
| 36    2     5    | 7     369   4689 | 48    89    1    |
|------------------+------------------+------------------|
| 124   579   6    | 29    8     579  | 3     12    247  |
| 24    578   3    | 26    1     567  | 9     268   478  |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
Candidates in r2c7 will force r3c7 to have only 4 as valid Candidates
r2c7=2: r2c7=2 => r8c7=6 => r7c7=8 => r3c7=4
r2c7=7: r2c7=7 => r2c1=3 => r2c5=9 => r7c5=6 => r7c7=8 => r3c7=4
r2c7=8: r2c7=8 => r3c7=4
Threfore r3c7=4

*--------------------------------------------------------*
| 67    89    1    | 48    2     4689 | 78    5     3    |
| 37    4     89   | 5     39    1    | 278   289   6    |
| 36    2     5    | 7     369   689  | 4     89    1    |
|------------------+------------------+------------------|
| 124   579   6    | 29    8     579  | 3     12    247  |
| 24    578   3    | 26    1     567  | 9     268   478  |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
Candidates in r4c4 will force r1c1 to have only 6 as valid Candidates
r4c4=2: r4c4=2 => r5c4=6 => r8c4=9 => r7c5=6 => r7c7=8 => r1c7=7 => r1c1=6
r4c4=9: r4c4=9 => r8c4=6 => r7c5=9 => r2c5=3 => r2c1=7 => r1c1=6
Threfore r1c1=6

*--------------------------------------------------------*
| 6     89    1    | 48    2     489  | 7     5     3    |
| 7     4     89   | 5     3     1    | 28    289   6    |
| 3     2     5    | 7     69    689  | 4     89    1    |
|------------------+------------------+------------------|
| 124   579   6    | 29    8     579  | 3     12    247  |
| 24    578   3    | 26    1     567  | 9     268   478  |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
Candidates in r5c8 will force r5c1 to have only 4 as valid Candidates
r5c8=2: r5c8=2 => r5c1=4
r5c8=6: r5c8=6 => r5c4=2 => r5c1=4
r5c8=8: r5c8=8 => r3c8=9 => r3c5=6 => r7c5=9 => r8c4=6 => r5c4=2 => r5c1=4
Threfore r5c1=4

*--------------------------------------------------------*
| 6     89    1    | 48    2     489  | 7     5     3    |
| 7     4     89   | 5     3     1    | 28    289   6    |
| 3     2     5    | 7     69    689  | 4     89    1    |
|------------------+------------------+------------------|
| 12    579   6    | 29    8     579  | 3     12    4    |
| 4     578   3    | 26    1     567  | 9     268   78   |
| 12    789   89   | 3     4     679  | 5     1268  278  |
|------------------+------------------+------------------|
| 5     3     4    | 1     69    2    | 68    7     89   |
| 8     1     7    | 69    5     3    | 26    4     29   |
| 9     6     2    | 48    7     48   | 1     3     5    |
*--------------------------------------------------------*
r4c4 Must only have 9 as valid Candidates (12 is a Naked Double in Row 4)
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USA Today puzzle - Jan 13

Postby donmckeown » Mon Jan 16, 2006 4:15 pm

Thanks Tarek. Wow! There's a lot more to Sudoku than I thought. I understand about half of your analysis. I'll do some research on the other half. Thanks again.
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Postby Carcul » Tue Jan 17, 2006 9:56 pm

Hi Donmckeown.

For your grid

Code: Select all
|------------------------------------------------------|
| 67   89   1   | 4689  2    4689  | 478  5      3     |
| 37   4    89  | 5     39   1     | 278  289    6     |
| 36   2    5   | 7     369  4689  | 48   89     1     |
|---------------+------------------+-------------------|
| 124  579  6   | 239   8    579   | 23   123    247   |
| 24   578  3   | 26    1    567   | 9    268    2478  |
| 12   789  89  | 2369  4    679   | 5    12368  278   |
|---------------+------------------+-------------------|
| 5    136  4   | 1689  69   2     | 368  7      89    |
| 8    16   7   | 169   5    3     | 26   4      29    |
| 9    36   2   | 468   7    468   | 1    38     5     |
|------------------------------------------------------|

here is my solution:

1. [r7c2]=3=[r7c7]-3-[r4c7]-2-[r8c7]-6-[r8c2]-1-[r7c2]

which implies that r7c2 cannot be "1". Now the grid need to be updated. After that, we have:

2. [r6c8]=6=[r6c6]-6-[r5c4]=6=[r8c4]-6-[r8c7]-2-[r2c7]=2=[r2c8](-2-[r6c8])-2-[r4c8]-1-[r6c8]

which implies that r6c8 cannot be "1,2", and that solve the puzzle.

Regards, Carcul
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Postby Jeff B » Wed Jan 18, 2006 12:02 am

This puzzle has changed since it was originally posted. I was stuck on it too after I got 8 numbers. I've been doing these for about a month and I've never gotten stuck on one like that - even the 5-star ones I've been able to finish in well under an hour. I worked on it for a couple of hours over the weekend and still was unable to fill in another number that I was certain of.

So I thought I'd just start over and maybe even resort to guessing, but when I opened it today it was completely different. I'm wondering if perhaps there was a mistake and it wasn't solvable with the starting numbers provided. I had suspected that might be the case, but I'm sorta new to these and their Friday puzzles are supposed to be the hardest of the week.

Carcul - I'm new at this and not sure I understand your notation - are you starting off saying that [R7C2] is 3? If so, how do you come to that conclusion?
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Posts: 4
Joined: 17 January 2006

Postby Crazy Girl » Wed Jan 18, 2006 12:38 am

To solve this puzzle one is required to use chains, something that is hard to spot especially for the pencil/paper crowd who have no experience of these puzzles. Ideally your newspaper should have posted a puzzle that did not require the use of chains, but other techniques more easily spotted by pencil/paper solvers.

To learn basic techniques on how to solve sudoku puzzles (of less difficulty than this one) look here and here

To learn more about chains there is a explaination of this advanced technique (and others) by Jeff in the Advanved Solving Techniques thread (link below) worth taking a look at when you know the basics.
Forcing chains: Terminology and Definition
This will help you understand the technique better and then you may be able to follow the solution by Carcul a little more (but maybe not alot:!: )

If you are still trying ( and failing:!: ) to get your head around all of this, come back to the forum and some kind soul will try and help you:)

p.s.
Jeff B wrote: This puzzle has changed since it was originally posted


how:?: , all we've done (specifically Shazbot) is make it more readable and computer solver friendly, and in the blank cells listed the possible candidates according to the sudoku rules.
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Postby Carcul » Wed Jan 18, 2006 12:58 am

Hi Jeff B.

Jeff B wrote:Carcul - I'm new at this and not sure I understand your notation - are you starting off saying that [R7C2] is 3? If so, how do you come to that conclusion?


Consider the following logic: r7c2=3 or r7c2 is not "3"; if r7c2 is "3" then obviously it is not "1"; if r7c2 is not "3", then r7c7=3 => r4c7=2 => r8c7=6 => r8c2=1 => r7c2 cannot be "1" - so, in any case, r7c2 cannot be 1.

Hope this will help.

Regards, Carcul
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Joined: 04 November 2005

Postby Jeff B » Wed Jan 18, 2006 3:57 am

Crazy Girl wrote:p.s.
Jeff B wrote: This puzzle has changed since it was originally posted


how:?: , all we've done (specifically Shazbot) is make it more readable and computer solver friendly, and in the blank cells listed the possible candidates according to the sudoku rules.

I don't think you understood what I meant. I'm saying the puzzle in USA Today (on puzzles.usatoday.com) for Friday Jan. 13 is no longer the same puzzle. Perhaps you were correct that they didn't intend to publish a puzzle that required the techniques you were talking about. I haven't had to use anything like those before on their puzzles. But, that is what led me here so hopefully that will have been a good thing.

Thanks for the other suggestions, too.
Jeff B
 
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Joined: 17 January 2006

Postby Jeff B » Wed Jan 18, 2006 4:13 am

Carcul wrote:Hi Jeff B.

Jeff B wrote:Carcul - I'm new at this and not sure I understand your notation - are you starting off saying that [R7C2] is 3? If so, how do you come to that conclusion?


Consider the following logic: r7c2=3 or r7c2 is not "3"; if r7c2 is "3" then obviously it is not "1"; if r7c2 is not "3", then r7c7=3 => r4c7=2 => r8c7=6 => r8c2=1 => r7c2 cannot be "1" - so, in any case, r7c2 cannot be 1.

Hope this will help.

Regards, Carcul

I think I understand now - you're considering both possibilities for R7C2, and since one of them leads to an impossible conclusion, it is obviously the wrong choice - correct? If so, that makes total sense. That's cool, I just thought I'd make it more confusing trying to solve it that way. I've been able to solve these (just been doing the usatoday ones) only by narrowing each cell down to one possible number and building on the cells I've figured out for sure. Obviously this one was more complicated. Thanks for the help!
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Joined: 17 January 2006

Postby Crazy Girl » Wed Jan 18, 2006 1:53 pm

Jeff B wrote:I don't think you understood what I meant. I'm saying the puzzle in USA Today (on puzzles.usatoday.com) for Friday Jan. 13 is no longer the same puzzle.


As a british citizen, I did not know the website for USAtoday, so did not check out the puzzle. You said the puzzle had changed so i assumed you were refering to the format of the puzzle, and not the puzzle itself, which you did not make clear in your post.

Is the new puzzle easier to solve:?:
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