## Guidance for eliminating candidates

All about puzzles in newspapers, magazines, and books

### Guidance for eliminating candidates

My wife and I have been enjoying Su-Do-Ku since the Washington Post starting carrying it several months ago. Not surprisingly, we've hit some that we are unable to solve. We've developed several techniques for eliminating candidates, but sometimes it seems that there is a "next step" in logic that is eluding us. As a result, we've had to take a peek at the solution to get missing numbers, one number per peek, to try to continue to the solution.

I've been stymied by the variable font of this forum, so the following is a little difficult to read. I've had to use the underscore to represent blank space. My apologies. Here is the original puzzle:

___|___|___|___|___|___|___|___|___
_8_|___|___|___|_3_|___|___|___|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|_2_|___|_1_|___|___|_6_|___|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
_5_|___|___|___|_6_|___|___|___|_3_
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|___|___|___|___|_8_|_1_|_6_|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|___|_8_|___|___|___|_7_|___|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|_6_|_5_|_9_|___|___|___|___|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
_3_|___|___|___|___|_4_|___|___|_2_
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|___|_1_|___|___|_5_|___|_7_|___
___|___|___|___|___|___|___|___|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
___|___|___|___|_9_|___|___|___|_8_
___|___|___|___|___|___|___|___|___

After a fair amount of work, we've been able to eliminate a lot of the candidates, but the remaining ones are shown below in the partially solved puzzle:

___|___|___|___|___|_2_|_2_|_2_|___
_8_|___|_6_|45_|_3_|___|45_|45_|_1_
___|7_9|___|___|___|7__|__9|__9|___
++++++++++++++++++++++++++
___|___|___|___|___|___|___|___|___
_4_|_2_|_3_|_1_|_5_|_9_|_6_|_5_|_7_
___|___|___|___|_8_|___|___|_8_|___
++++++++++++++++++++++++++
___|___|___|___|___|_2_|_2_|_2_|___
_5_|_1_|___|4__|_6_|___|4__|4__|_3_
___|___|7_9|_8_|___|7__|_89|_89|___
++++++++++++++++++++++++++
_2_|__3|_2_|_23|_2_|___|___|___|___
___|4__|4__|_5_|45_|_8_|_1_|_6_|_5_
7_9|__9|___|7__|7__|___|___|___|__9
++++++++++++++++++++++++++
12_|__3|___|_23|12_|___|___|_23|___
___|4__|_8_|_5_|45_|_6_|_7_|___|_5_
__9|__9|___|___|___|___|___|___|__9
++++++++++++++++++++++++++
12_|___|___|___|12_|1_3|_23|_23|___
___|_6_|_5_|_9_|___|___|___|___|_4_
7__|___|___|___|7__|___|_8_|_8_|___
++++++++++++++++++++++++++
___|___|___|___|1__|___|___|1__|___
_3_|_5_|___|_6_|___|_4_|_5_|_5_|_2_
___|789|7_9|___|78_|___|__9|__9|___
++++++++++++++++++++++++++
_2_|___|___|_23|_2_|___|__3|___|___
___|4__|_1_|___|___|_5_|4__|_7_|_6_
__9|_89|___|_8_|_8_|___|__9|___|___
++++++++++++++++++++++++++
___|___|_2_|_23|___|1_3|__3|1_3|___
_6_|45_|4__|___|_9_|___|45_|45_|_8_
___|7__|___|7__|___|___|___|___|___

Can anyone give us a hint or two on how we can eliminate more of the candidates? Obviously, we aren't asking for a solution to the puzzle--simply a boost in the right direction. Thanks.
Guest

I dubbed this into Simple Sudoku and it said it had 10 solutions. It was also asymmetrical, which isn't a problem in itself but most puzzle makers use symmetry in the clues to make it more pleasing to the eye. I suspect you may have missed entering one of the clues in your graph above or listed it in the wrong cell. (It's also possible I entered it incorrectly).

For help in entering puzzles on this forum there is a sticky at the top that offers some advice.

Tracy
Last edited by TKiel on Sun Jan 29, 2006 12:24 pm, edited 1 time in total.
TKiel

Posts: 209
Joined: 05 January 2006

I should have been more specific about the sticky. It is in the Sudoku: the Puzzle-Help with particular puzzles forum. But you are correct to have posted your question in this forum, as the forum with the sticky deals with puzzles that have not been published. Hope I'm not confusing you too much.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

If the 6 in r3 is placed in column 4 the puzzle becomes both symmetrical and valid (one solution). Here's the starting grid and initial candidate listing for that puzzle:
Code: Select all
` |8..|.3.|...| |.2.|1..|6..| |5..|6..|..3| |---+---+---| |...|..8|16.| |..8|...|7..| |.65|9..|...| |---+---+---| |3..|..4|..2| |..1|..5|.7.| |...|.9.|..8|   *--------------------------------------------------------------------* | 8      1479   4679   | 2457   3      279    | 2459   12459  14579  | | 479    2      3479   | 1      4578   79     | 6      4589   4579   | | 5      1479   479    | 6      2478   279    | 2489   12489  3      | |----------------------+----------------------+----------------------| | 2479   3479   23479  | 23457  2457   8      | 1      6      459    | | 1249   1349   8      | 2345   12456  1236   | 7      23459  459    | | 1247   6      5      | 9      1247   1237   | 2348   2348   4      | |----------------------+----------------------+----------------------| | 3      5789   679    | 78     1678   4      | 59     159    2      | | 2469   489    1      | 238    268    5      | 349    7      469    | | 2467   457    2467   | 237    9      12367  | 345    1345   8      | *--------------------------------------------------------------------*`

If this is the correct clue placement, judging by what you had elimated already in your origional post, you can solve this using only techniques you already know. Are you solving on paper or are you entering the origional clues into a program and solving that way?

Tracy

(If your origional grid is correct, I apologize for confusing the issue but when a puzzle has more than one solution, it is my understanding that guessing will be required and logic alone will not suffice.)
TKiel

Posts: 209
Joined: 05 January 2006

### Stuck on Hard puzzle from Wash. Post, id: 22, 22 Oct 2005

Thanks for the tip on the sticky, Tracy. I rechecked my entry and it looks good to me, but let me use the advice from the sticky for the benefit of any other potential respondents.

Code: Select all
`8 - - | - 3 - | - - -- 2 - | 1 - - | 6 - -5 - - | - 6 - | - - 3------+------+------- - - | - - 8 | 1 6 -- - 8 | - - 6 | 7 - - - 6 5 | 9 - - | - - -------+------+------3 - - | - - 4 | - - 2- - 1 | - - 5 | - 7 -- - - | - 9 - | - - 8`

And the partial solution that we've come up with:
Code: Select all
`8    79   6    |45   3    27   |2459 2459 14    2    3    |1    58   9    |6    58   75    1    79   |48   6    27   |2489 2489 3---------------+---------------+---------------279  349  24   |2357 2457 8    |1    6    59129  349  8    |235  1245 6    |7    23   59127  6    5    |9    127  13   |238  238  4---------------+---------------+---------------3    5789 79   |6    178  4    |59   159  229   489  1    |238  28   5    |349  7    66    457  24   |237  9    13   |345  1345 8`

Hopefully, this will display better, if I've understood the sticky.

I understand that there are solutions to the puzzle--we're just looking for a logical process to continue from here. For example, one of the rules we use is: if there are only two n candidates (n = any number, 1 - 9) in a row and they are both in the same box, then any other n candidates in the same box can be eliminated. We have several others, but this is the kind of logical help we are looking for.
Guest

### Re: Stuck on Hard puzzle from Wash. Post, id: 22, 22 Oct 200

Ralph&Cynthia wrote:For example, one of the rules we use is: if there are only two n candidates (n = any number, 1 - 9) in a row and they are both in the same box, then any other n candidates in the same box can be eliminated. We have several others, but this is the kind of logical help we are looking for.

This technique is known as locked candidates or box/row (or box column) interaction - you could also exclude n candidates from the same row (or column).

Your puzzle as posted does have 10 solutions - either it's not a Pappocom puzzle or you have missed an entry, possible at r5c4?
CathyW

Posts: 316
Joined: 20 June 2005

Cathy & Tracy--you are both right. We do have an error in the puzzle. The 6 in r3c5 should be in r3c4. We're embarrassed. We copy puzzles to a larger piece of paper for solving to allow more room for pencil marks and there was a transcription error. We should have checked this before asking others to look at it. We'll start again.

Cathy--we're new to these fora. You refer to the locked candidates technique--is there a place within these fora that documents various other techniques?
Guest

Ralph & Cynthia,

A good place to start is www.angusj.com. The site has a downloadable Sudoku program that generates puzzles with 5 difficulty levels and also allows you to enter puzzles from other sources. In addition it has a guide that explains a lot of the techniques used to solve puzzles. I believe every puzzle it generates can be solved using the techniques described, although it does not describe every known solving technique (at least it didn't the last time I visited). There are also other websites that do much the same thing.

In this forum, there is also a sub-forum for advanced solving techniques, in which there are very detailed (sometimes mind numbingly so, at least for my simple mind) descriptions for techniques not covered in many of the guides, which list only 'basic' and 'intermediate' stuff. (The definition of basic, intermediate and advanced techniques is not set in stone.)

Hope this helps.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

Tracy is right - Angus J's website is excellent. An alternative is Sadman Sudoku from Simes: http://www.simes.clara.co.uk/programs/sudokutechniques.htm

With that 6 in the right place I'm sure you will be able to solve the puzzle
CathyW

Posts: 316
Joined: 20 June 2005

### Puzzle Solved

Tracy and Cathy--thanks again for your help. The puzzle was much more solvable with the numbers in the right cells. It wasn't until yesterday afternoon that something both of you said struck me. Both of you mentioned 10 solutions. I thought, hmm, I wonder what that means. Then it hit me that a proper puzzle has only one solution and therefore, something was wrong with the placement of the numbers.

We'll take a look at the referenced sites. Thanks again.
Guest