## Another Way to Represent Candidates

Advanced methods and approaches for solving Sudoku puzzles

### Another Way to Represent Candidates

Hi,
As a newcomer to the forum, I wish to share my experience with you and if possible receive some feedback.

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Another Way to Represent Candidates

When I do sudoku, I do the usual slicing and dicing until I come to a dead end. Then I take a plain sheet of paper and put down the candidate situation of the nine blocks as it is at this stage. The blocks are numbered from 1 to 9 in a left to right, up to down fashion and in the same way I relate to each empty cell within each of the 9 blocks. Taking the following block of a puzzle as an example:

{ 6 4 * }
{ * * 7 }
{ * 1 * }

I notice that there are 5 missing candidates in this block. They are: 2 3 5 8 and 9, which means there are also 5 empty cells in wait to be filled by the above mentioned candidates. So I relate or enumerate by heart the empty cells from 1 to 5 in the same left to right, up to down fashion. Then, upon the sheet of paper I put down the 5 candidates in 5 rows, each row for one of the 5 empty cells, in this way:

2 3 5 8 9
2 3 5 8 9
2 3 5 8 9
2 3 5 8 9
2 3 5 8 9

and start checking each cell, crossing out the candidates that are’nt possible for that cell. For example, if after examination, the above table of candidates would look like this:

2 3 5 8 9
2 3 5 8 9
2 3 5 8 9
2 3 5 8 9
2 3 5 8 9

it means that nothing was yet achieved. So I go on to the next block, make a table of its candidates and cross out those which are not feasible for its empty cells. Now, if I’m more lucky and my present table looks like this:

2 4 5 6 7
2 4 5 6 7
2 4 5 6 7
2 4 5 6 7
2 4 5 6 7

it means that we have found 6 to be a naked single for cell No.1 and cell No.3 to be the only single candidate cell which may receive a 4. So I encircle the 6, cross out horizontally the first row of candidates for cell No.1, cross out vertically all other appearances of 6 in column 4 of the table, and fill cell No.1 with a 6. Next I do the same with the 4 in column 2, row 3 and fill cell No.3 with a 4. If possible, I then update the table of candidates of the preceding block and see if a breakthrough can be achieved there, or in the neighboring blocks. The updating is very important. Not doing it acurately or not doing it at all, leads to disaster. Only in the final stages, when your puzzle falls apart like a house of cards, may you afford not to update.

By the way, instead of making tables of candidates for blocks, you can do the same for rows and columns, or in emergency conditions you may even choose to do it in addition to tables for blocks. Once I did so and was surprised to crack down on a candidate which came in view only by means of a column table representation.

Of special interest to the solver are pairs, and maybe triples or quads. Fortunately, these too are quite visible in such a candidate representation. Sometimes, in order to get a better view of the pairs’ orientation, I pencil them in, in the usual way, but never do I clutter the puzzle with the galaxy of all other candidates.[/u]
Kibitzer

Posts: 25
Joined: 17 September 2005

I’m sure your technique is solid even if it has overtones of – well, an SAS operation! Towards the end I was checking out places to duck and hide. Just kidding!

Everyone finds a technique that suits them and hopefully the more puzzles you do the more you will be able to cut out some of the early footwork by scanning and figuring a few steps in your head in advance.

The ‘galaxy clutter’ can be a problem and for this reason solvers are good for the harder puzzles, not necessarily to ‘solve’ the puzzle but just to keep a track of the candidates so you can concentrate on ‘higher strategies’.
emm

Posts: 987
Joined: 02 July 2005

em wrote:The ‘galaxy clutter’ can be a problem and for this reason solvers are good for the harder puzzles, not necessarily to ‘solve’ the puzzle but just to keep a track of the candidates so you can concentrate on ‘higher strategies’.

I don’t think that if you have a jumble of candidates all messed up in your puzzle, you are able to keep track of them, much less so are you able for that very reason to concetrate on ‘higher strategies’.

Most people use programs to solve sudoku. This makes the candidate jumble somewhat bearable. But if you want to solve manually and have all the fun the “pencilling in” besides from being a drag, does’nt help you a bit, quite to the contrary.

My presentation of course was’nt perfect. For instance, I could’nt print and therefore show stricken out numbers, rows and columns, but it is meant for people who solve manually (and yes, have all the fun). What’s more, it works and bypasses successfully I think the impossibility of “pencilling in”. Thanks for making a try at it!

So far, so good.

Now, I’m just curious, what in the world is an “SAS operation”?

Regards
Kibitzer
Kibitzer

Posts: 25
Joined: 17 September 2005

Thanks for the reply Kibitzer - the last thing we want is to take the fun out of Sudoku!

PS : The SAS is a branch of the British special forces and it was the thought of you cracking down on candidates as they came into view that reminded me of them. Sort of like a seek-and-destroy video game. Hey, I wonder if the SAS do play Sudoku? Maybe the real-life kind! Maybe I won’t go there…!
emm

Posts: 987
Joined: 02 July 2005

Kibitzer wrote:what in the world is an “SAS operation”?

Each one of us in an SAS, Kibitzer. SAS stands for "Someone Addicted to Sudoku". SAS Operations are the higher-level complexities of logic applied only by us elite SAS's, that would never even be comprehensible to TWITS ("Those With Inhibitions Towards Sudokus").
zebedeezbd

Posts: 60
Joined: 14 September 2005

em wrote:Thanks for the reply Kibitzer - the last thing we want is to take the fun out of Sudoku!

PS : The SAS is a branch of the British special forces and it was the thought of you cracking down on candidates as they came into view that reminded me of them. Sort of like a seek-and-destroy video game. Hey, I wonder if the SAS do play Sudoku? Maybe the real-life kind! Maybe I won’t go there…!

Hi em,

I'm sure the SAS play the real-life kind of Sudoku. Trouble is, it took them 4 years to find Bin Laden... in the encyclopedia.

Regards
Kibitzer

Posts: 25
Joined: 17 September 2005

I KNEW I shouldn't go there!
emm

Posts: 987
Joined: 02 July 2005

### doubles

When I get to the point where every cell in every squars contains a double, that is there are two candidates for each cell, and no amount of logic can get me out of this jam, I hate to rely on elaborate methodes such as swordfish, etc, because that is no better than trial and error which is not the point of Sudoku, is it. Does any one solve these problems by sheer mental acuity? Just knowing that for instance the 8 and 2 must be in one of these two cells, never reveals a single candidate so the conundrum is impassable.
guitry

Posts: 1
Joined: 19 September 2005

Just because every cell has more than one cadidate, doesn't necessarily mean you'll need to use very advanced methods. There could still be, for example, a row where only one cell can hold the 4. Frankly, I find that for all but the most difficult of puzzles (ones that require swordfich, chains and the like), candidate lists are more of a distraction than a help.
PaulIQ164

Posts: 533
Joined: 16 July 2005

zebedeezbd wrote:
Kibitzer wrote:what in the world is an “SAS operation”?

Each one of us in an SAS, Kibitzer. SAS stands for "Someone Addicted to Sudoku". SAS Operations are the higher-level complexities of logic applied only by us elite SAS's, that would never even be comprehensible to TWITS ("Those With Inhibitions Towards Sudokus").

Hi Zebedeezbd,

I liked very much this one and also the TWITS. Maybe we should have more of this stuff besides naked pairs, foul fish and things lide that.
Due thanks must go also to em who first suggested the SAS.

Kibitzer
Kibitzer

Posts: 25
Joined: 17 September 2005

Kibitzer
Kibitzer

Posts: 25
Joined: 17 September 2005