Ulterior Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Ulterior Puzzles

Postby Ruud » Fri May 26, 2006 3:41 pm

Following the success the Superior and Inferior threads, I would like to introduce the new Ulterior category.

Ulterior Puzzles

1. Puzzles do not require symmetry, but compete for their symmetry class.
2. Puzzles must be minimal, or symmetrical minimal when submitted for a symmetry class.
3. Puzzles must be solvable with hidden singles and pointing pairs only.
4. Techniques that require pencilmarks for real humans (not including RW) are not allowed.
5. This also excludes naked singles and locked candidates type 2.

Background

The Inferior thread proved to be an interesting breeding ground for puzzles that stretched the limits in many ways.

When I solve a puzzle in the newspaper, I do not want to use pencilmarks. They're messy and require a lot of work. I have written software to do the harder puzzles, but that's a different game for me. This category must provide the best puzzles that do not require pencilmarks. I want to be able to solve them with "slicing & dicing" only, nothing else.

There are 2 types of locked candidates. Type 1 occurs when all candidates in a box are confined to a single row or column. We call these pointing pairs, because the remaining candidates point the way to a crosshatching line we can mentally draw. Type 2 occurs when all candidates in a row or column are confined to a single box. You can then eliminate the remaining candidates in that box. This is a pencilmark operation, because you cannot use it in crosshatching. That's why it is not allowed.

My ulterior motive is that I needed a catchy name that fitted with the other two.

Records

We can try and find the best Ulterior puzzles in the following categories:

1. Highest number of steps
2. Lowest number of steps
3. Highest number of pointing pairs

Steps are counted as specified in the Inferior thread (scan-execute-rinse), but with the pointing pairs immediately taking effect when they occur. No steps are counted for the pointing pairs.

Statistics

To give you an idea about Ulterior puzzles, I have performed a few tests on the most recent 17-clue collection.

Code: Select all
+-----------+----------+------------------------+
|sudoku17   | 36628    |                        |
+-----------+----------+-----------+------------+
|Techniques | solved   | low steps | high steps |
+-----------+----------+-----------+------------+
|NS (N)     |     0    |         - |          - |
|HS (F)     | 13375    |   5 x   9 |  1 x    31 |
|NS+HS (FN) | 16867    |   2 x   8 |  2 x    27 |
|Ulterior   | 21084    |   2 x   5 |  1 x    26 |
|(FNB)      | 27665    |  54 x   5 |  4 x    21 |
+-----------+----------+-----------+------------+


Current Records

Lowsteppers by symmetry class

Code: Select all
36 clues, Symmetry Class I - Full dihedral
*-----------------*
|. 3 .|8 5 4|. 1 .|
|4 . 5|. . .|7 . 6|
|. 9 .|. 1 .|. 5 .|
|-----+-----+-----|
|8 . .|6 . 3|. . 2|
|3 . 9|. . .|5 . 8|
|6 . .|5 . 2|. . 1|
|-----+-----+-----|
|. 8 .|. 7 .|. 4 .|
|1 . 4|. . .|8 . 3|
|. 6 .|4 2 8|. 9 .|
*-----------------*
Ulterior (FB) Rating: 2 steps (27 18)
Other test results:
 F  : 3 steps
 FN : 3 steps
 N  : 5 steps
 FNB: 2 steps


33 clues, Symmetry Class II - Full rotational
*-----------------*
|. . 3|4 . .|. 9 .|
|4 . 5|9 . 1|. . .|
|. . .|. 6 5|. 1 3|
|-----+-----+-----|
|. 1 8|. . .|. 3 9|
|. . 6|. 8 .|2 . .|
|9 3 .|. . .|7 5 .|
|-----+-----+-----|
|7 4 .|1 2 .|. . .|
|. . .|8 . 4|1 . 6|
|. 8 .|. . 3|9 . .|
*-----------------*
Ulterior (FB) Rating: 2 steps (26 22)
Other test results:
 F  : 3 steps
 FN : 3 steps
 N  : 6 steps
 FNB: 2 steps


36 clues, Symmetry Class III - Horizontal and vertical reflection
*-----------------*
|. 1 9|4 . 3|6 2 .|
|. . .|1 . 5|. . .|
|. 4 .|. 9 .|. 1 .|
|-----+-----+-----|
|4 . 1|6 . 7|2 . 9|
|2 . .|. . .|. . 1|
|3 . 7|8 . 1|4 . 5|
|-----+-----+-----|
|. 6 .|. 8 .|. 5 .|
|. . .|7 . 6|. . .|
|. 2 8|3 . 4|7 9 .|
*-----------------*
Ulterior (FB) Rating: 2 steps (24 21)
Other test results:
 F  : 4 steps
 FN : 4 steps
 N  : 7 steps
 FNB: 2 steps


32 clues, Symmetry Class IV - Diagonal and antidiagonal reflection
*-----------------*
|. . 1|5 6 .|7 . .|
|. . 4|. . 3|. . .|
|2 3 .|1 . .|. . 9|
|-----+-----+-----|
|3 . 2|. 7 .|. 1 .|
|9 . .|4 . 1|. . 8|
|. 1 .|. 3 .|6 . 7|
|-----+-----+-----|
|4 . .|. . 9|. 8 6|
|. . .|3 . .|1 . .|
|. . 7|. 4 6|5 . .|
*-----------------*
Ulterior (FB) Rating: 2 steps (22 27)
Other test results:
 F  : 5 steps
 FN : 4 steps
 N  : 9 steps
 FNB: 2 steps


25 clues, Symmetry Class V - 180-degree rotational
*-----------------*
|. . .|. . 8|. . .|
|. 5 8|2 . .|. . .|
|. 4 9|. . .|. 7 6|
|-----+-----+-----|
|5 . 7|. . 4|. . 8|
|. . .|. 3 .|. . .|
|1 . .|6 . .|9 . 3|
|-----+-----+-----|
|3 2 .|. . .|1 9 .|
|. . .|. . 7|3 4 .|
|. . .|5 . .|. . .|
*-----------------*
Ulterior (FB) Rating: 3 steps (15 21 20)
Other test results:
 F  : 5 steps
 FN : 5 steps
 N  : (invalid)
 FNB: 3 steps


30 clues, Symmetry Class VI - Vertical reflection
*-----------------*
|. . 7|. . .|2 . .|
|. . 8|4 . 2|5 . .|
|. 9 .|7 5 6|. 3 .|
|-----+-----+-----|
|. 1 .|. . .|. 9 .|
|5 . .|8 2 9|. . 1|
|. 2 .|. . .|. 8 .|
|-----+-----+-----|
|2 . 1|5 . 3|6 . 7|
|. . .|6 . 7|. . .|
|6 . .|. . .|. . 8|
*-----------------*
Ulterior (FB) Rating: 3 steps (12 17 22)
Other test results:
 F  : 5 steps
 FN : 5 steps
 N  : 10 steps
 FNB: 3 steps


33 clues, Symmetry Class VII - Antidiagonal reflection
*-----------------*
|1 . 3|. 9 .|. 7 4|
|. . 5|2 . .|. 6 .|
|6 4 .|. . 3|2 1 .|
|-----+-----+-----|
|. 5 .|9 6 .|. . .|
|3 . .|4 . .|1 . .|
|. . 1|. . .|4 5 .|
|-----+-----+-----|
|. . 4|. 5 2|9 . 1|
|5 1 2|. . 9|. . .|
|9 . .|. . .|6 . .|
*-----------------*
Ulterior (FB) Rating: 3 steps (18 11 19)
Other test results:
 F  : 6 steps
 FN : 6 steps
 N  : (invalid)
 FNB: 3 steps


30 clues, No Symmetry (Tarek)
*-----------------*
|7 . 5|1 2 .|. . 8|
|8 . 9|. . 7|1 . .|
|4 . .|9 . .|6 . .|
|-----+-----+-----|
|. 2 .|. . 4|. . .|
|1 . .|5 . 8|. . 3|
|. . .|. . .|. 9 .|
|-----+-----+-----|
|. . 7|. . .|. . 6|
|. . 1|7 . .|5 . 9|
|5 . .|. 6 1|8 . 4|
*-----------------*
Ulterior (FB) Rating: 3 steps (18 21 12)
Other test results:
 F  : 4 steps
 FN : 4 steps
 N  : (invalid)
 FNB: 3 steps


22 clues, No Symmetry (Ruud)
*-----------------*
|4 9 .|. . .|7 1 .|
|. . .|. . 3|8 . .|
|6 . .|. 5 .|. . .|
|-----+-----+-----|
|3 . 6|. . .|. . 1|
|. . .|. . .|. . .|
|. . 8|. 7 .|. 2 4|
|-----+-----+-----|
|. . .|. . 9|. . .|
|9 1 .|. . 8|. . .|
|. . .|. 3 .|. 7 5|
*-----------------*
Ulterior (FB) Rating: 4 steps (14 17 16 12)
Other test results:
 F  : 6 steps
 FN : 6 steps
 N  : (invalid)
 FNB: 4 steps


Highsteppers by symmetry class

Code: Select all
20 clues, Symmetry Class I - Full dihedral (Ocean)
*-----------------*
|. . .|. . .|. . .|
|. . 1|. . .|2 . .|
|. 3 .|1 . 4|. 5 .|
|-----+-----+-----|
|. . 2|. 4 .|6 . .|
|. . .|7 . 5|. . .|
|. . 8|. 2 .|1 . .|
|-----+-----+-----|
|. 5 .|9 . 3|. 7 .|
|. . 6|. . .|9 . .|
|. . .|. . .|. . .|
*-----------------*
Ulterior (FB) Rating: 23 steps (4 3 2 1 2 2 2 2 2 2 2 1 3 3 2 4 1 1 3 5 6 4 4)
Other test results:
 F  : 28 steps
 FN : 14 steps
 N  : (invalid)
 FNB: 13 steps


24 clues, Symmetry Class II - Full rotational
*-----------------*
|. 6 2|. 9 .|. . .|
|. . 3|6 . .|. . 7|
|. . .|8 . .|. 4 1|
|-----+-----+-----|
|. . .|. . .|3 6 .|
|7 . .|. . .|. . 2|
|. 2 9|. . .|. . .|
|-----+-----+-----|
|9 8 .|. . 4|. . .|
|2 . .|. . 3|5 . .|
|. . .|. 5 .|1 2 .|
*-----------------*
Ulterior (FB) Rating: 19 steps (3 3 4 3 3 1 3 3 1 1 2 3 3 3 4 5 3 5 4)
Other test results:
 F  : 25 steps
 FN : 12 steps
 N  : (invalid)
 FNB: 9 steps


29 clues, Symmetry Class III - Horizontal and vertical reflection
*-----------------*
|. 9 8|. . .|6 7 .|
|. . 1|9 . 8|2 . .|
|2 . .|. . .|. . 1|
|-----+-----+-----|
|. . .|2 . 3|. . .|
|. . 9|6 8 7|4 . .|
|. . .|1 . 9|. . .|
|-----+-----+-----|
|8 . .|. . .|. . 3|
|. . 3|8 . 2|7 . .|
|. 6 5|. . .|8 2 .|
*-----------------*
Ulterior (FB) Rating: 16 steps (2 2 2 3 3 3 5 3 4 2 1 3 6 6 4 3)
Other test results:
 F  : (invalid)
 FN : (invalid)
 N  : (invalid)
 FNB: 11 steps



29 clues, Symmetry Class IV - Diagonal and antidiagonal reflection
*-----------------*
|. 4 .|. . .|1 . .|
|8 5 .|. 4 .|. . .|
|. . 7|2 . 6|. . 4|
|-----+-----+-----|
|. . 1|. 2 .|8 . .|
|. 6 .|8 9 7|. 1 .|
|. . 8|. 5 .|7 . .|
|-----+-----+-----|
|9 . .|3 . 2|6 . .|
|. . .|. 6 .|. 9 2|
|. . 6|. . .|. 7 .|
*-----------------*
Ulterior (FB) Rating: 20 steps (2 1 1 1 1 1 1 1 1 6 6 3 3 4 3 3 2 4 5 3)
Other test results:
 F  : (invalid)
 FN : (invalid)
 N  : (invalid)
 FNB: 10 steps


23 clues, Symmetry Class V - 180-degree rotational
*-----------------*
|6 . 1|. . .|5 2 .|
|. 7 .|. 8 4|. . .|
|2 . .|. . .|. . .|
|-----+-----+-----|
|. . .|8 . .|. . .|
|. . 5|9 1 6|3 . .|
|. . .|. . 5|. . .|
|-----+-----+-----|
|. . .|. . .|. . 1|
|. . .|7 3 .|. 4 .|
|. 8 9|. . .|6 . 7|
*-----------------*
Ulterior (FB) Rating: 22 steps (3 2 1 2 1 2 4 2 2 3 3 3 4 4 2 2 2 2 3 3 4 4)
Other test results:
 F  : 26 steps
 FN : 11 steps
 N  : (invalid)
 FNB: 9 steps


22 clues, Symmetry Class VI - Vertical reflection
*-----------------*
|. . .|4 7 3|. . .|
|. . .|. . .|. . .|
|. . 5|. 6 .|9 . .|
|-----+-----+-----|
|. . 4|7 . 5|6 . .|
|7 . .|. . .|. . 2|
|. 6 .|. . .|. 1 .|
|-----+-----+-----|
|. . 6|. . .|1 . .|
|3 . .|2 . 9|. . 8|
|. 1 .|. . .|. 5 .|
*-----------------*
Ulterior (FB) Rating: 20 steps (3 4 4 3 1 1 1 1 1 1 1 2 3 5 8 2 2 7 7 2)
Other test results:
 F  : (invalid)
 FN : 15 steps
 N  : (invalid)
 FNB: 10 steps


24 clues, Symmetry Class VII - Diagonal reflection
*-----------------*
|. . 5|. . .|. 8 .|
|. 9 .|. . .|5 . 1|
|4 . .|. 6 1|. 7 .|
|-----+-----+-----|
|. 6 .|. . .|4 . .|
|. . .|. 9 .|8 . .|
|. . 1|4 . .|. . .|
|-----+-----+-----|
|1 . .|3 . .|. . 7|
|. 3 .|. . 7|. 9 .|
|2 . 8|. . .|1 . .|
*-----------------*
Ulterior (FB) Rating: 19 steps (6 2 1 2 3 1 3 6 1 2 1 3 3 5 5 5 2 4 2)
Other test results:
 F  : (invalid)
 FN : (invalid)
 N  : (invalid)
 FNB: 12 steps


22 clues, No Symmetry
*-----------------*
|. 8 .|1 . 5|. . 2|
|. . .|. . .|. 1 .|
|2 . .|9 . .|. 3 .|
|-----+-----+-----|
|. . .|. 3 .|. . .|
|. . .|4 1 .|. . 7|
|9 . .|8 . .|. . 6|
|-----+-----+-----|
|6 5 .|. . .|. . .|
|. . .|. . .|4 6 8|
|. . .|. 7 .|. . 5|
*-----------------*
Ulterior (FB) Rating: 25 steps (1 1 1 2 1 1 1 1 1 2 1 2 2 3 5 4 3 4 5 4 2 2 4 4 2)
Other test results:
 F  : 27 steps
 FN : 14 steps
 N  : (invalid)
 FNB: 11 steps


Highest number of clues being Symmetrical Minimal

Code: Select all
44 clues, Symmetry Class III - Horizontal and vertical reflection
*-----------------*
|4 5 .|2 . 3|. 9 7|
|. 6 9|4 . 5|2 8 .|
|3 8 .|. . .|. 4 5|
|-----+-----+-----|
|. 4 6|8 . 7|5 2 .|
|. . .|. . .|. . .|
|. 9 7|6 . 2|3 1 .|
|-----+-----+-----|
|9 3 .|. . .|. 6 2|
|. 7 4|3 . 8|9 5 .|
|2 1 .|7 . 9|. 3 8|
*-----------------*
Ulterior (FB) Rating: 3 steps (19 14 4)
Other test results:
 F  : 4 steps
 FN : 4 steps
 N  : 6 steps
 FNB: 3 steps


(awaiting further submissions and updates)

Ruud.
Last edited by Ruud on Sat May 27, 2006 7:14 pm, edited 3 times in total.
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Postby tarek » Fri May 26, 2006 3:59 pm

This should be interesting Ruud, however insisting on hidden singles & no naked singles will produce puzzles which are otherwise quicker to solve using naked singles & You do not need PMs to find naked singles.

My generator is ready for the challenge in any case!!!!!!!!!!!!!!!


tarek
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Re: Ulterior Puzzles

Postby gsf » Fri May 26, 2006 5:52 pm

Ruud wrote:There are 2 types of locked candidates. Type 1 occurs when all candidates in a box are confined to a single row or column. We call these pointing pairs, because the remaining candidates point the way to a crosshatching line we can mentally draw. Type 2 occurs when all candidates in a row or column are confined to a single box. You can then eliminate the remaining candidates in that box. This is a pencilmark operation, because you cannot use it in crosshatching. That's why it is not allowed.

just to be sure about locked candidate types
can you post two examples
one with type 1 that would make the list
and one type 2 that would make the list modulo the type 2 locked candidate
gsf
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Postby Red Ed » Fri May 26, 2006 6:30 pm

Ruud wrote:1. Puzzles do not require symmetry, but compete for their symmetry class.
2. Puzzles must be minimal, or symmetrical minimal when submitted for a symmetry class.
3. Puzzles must be solvable with hidden singles and pointing pairs only.
OK, easy enough. Er, but ...
4. Techniques that require pencilmarks for real humans (not including RW) are not allowed.
... how are you supposed to do pointing pairs without pencilmarks? By default, I'd have coded that up based on candidate lists in each cell, but you seem to be saying those "pencilmarks" aren't allowed.
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Posts: 633
Joined: 06 June 2005

Postby Ruud » Fri May 26, 2006 6:58 pm

Here is a type 1 example for digit 7:

Code: Select all
.------------------.------------------.------------------.
| 5     9     2    | 34    6     138  | 13478 47    3478 |
| 17    4     17   | 2     78    1389 | 13789 5     6    |
| 3     6     8    | 45    457   159  | 1479  2     47   |
:------------------+------------------+------------------:
| 46    2     5    | 8     1     36   | 347   9     347  |
| 146   7     146  | 356   9     356  | 34    8     2    |
| 9     8     3    | 7     2     4    | 6     1     5    |
:------------------+------------------+------------------:
| 4678  1     467  | 456   458   568  | 2     3     9    |
| 2     3     9    | 1     48    7    | 5     6     48   |
| 4678  5     467  | 9     3     2    | 478   47    1    |
'------------------'------------------'------------------'


Here is a situation picture:

Image

The yellow cells are the type 1 locked candidates. R3C5 is secundary. The red(ish) cells are eliminated as candidate.


This is a type 2 example for digit 1 (it does not qualify)

Code: Select all
.---------------------.---------------------.---------------------.
| 5      9      6     | 2478   2478   248   | 3      2478   1     |
| 1      4      2     | 3      789    6     | 5      78     789   |
| 78     3      78    | 124789 124789 5     | 249    6      4789  |
:---------------------+---------------------+---------------------:
| 6      2      17    | 5      149    149   | 8      347    3479  |
| 9      57     157   | 1248   3      1248  | 14     47     6     |
| 4      8      3     | 19     6      7     | 19     5      2     |
:---------------------+---------------------+---------------------:
| 78     1      4578  | 6      45789  489   | 24     2348   348   |
| 2      6      48    | 148    148    3     | 7      9      5     |
| 3      57     9     | 2478   24578  248   | 6      1      48    |
'---------------------'---------------------'---------------------'


Here is the picture:

Image

Notice that it is useless to try and draw lines from the locked candidates, making them impossible to use in cross hatching.

Red Ed wrote:how are you supposed to do pointing pairs without pencilmarks? By default, I'd have coded that up based on candidate lists in each cell, but you seem to be saying those "pencilmarks" aren't allowed.

How you code it does not matter. I also use pencilmarks in my code. I just want to avoid techniques that would require me as a human player to use pencilmarks.

If it is a problem for you to filter the 2 types of locked candidates, we can decide to allow type 2 too.

Ruud.
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Postby tarek » Fri May 26, 2006 7:32 pm

Just testing the waters with these, I'm not sure if I got everything right with the criteria.

What are the resulte on these Ruud:

1st should be invalid
2nd valid
3rd valid
Code: Select all
 9 3 . | 6 . . | 4 . . 
 . . . | 4 . . | . . 6 
 7 . . | . 8 . | . . . 
-------+-------+------
 . . . | . . . | . 5 9 
 . . 8 | . . . | 2 . . 
 1 9 . | . . . | . . . 
-------+-------+------
 . . . | . 5 . | . . 3 
 6 . . | . . 1 | . . . 
 2 . 4 | . . 3 | . 1 5 

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

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


& one final query....dRegarding row/column/band permutation, does it affectt the result....

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Postby Red Ed » Fri May 26, 2006 9:12 pm

Ruud wrote:
Red Ed wrote:how are you supposed to do pointing pairs without pencilmarks? By default, I'd have coded that up based on candidate lists in each cell, but you seem to be saying those "pencilmarks" aren't allowed.
How you code it does not matter. I also use pencilmarks in my code. I just want to avoid techniques that would require me as a human player to use pencilmarks.
I'm still having trouble with this. Maybe it's because I never solve these puzzles by hand and we're talking about manual techniques. Here's the problem: you showed some very pretty pictures with candidates written into each cell; those are "pencilmarks" aren't they? But we're supposed to be emulating a non-pencilmarking human solver, so where are those pencilmarks supposed to have come from? I would've thought that each step of a no-pencilmarks strategy should be obvious from the values currently filled in, not relying on pencilmarks gradually pruned over several previous steps. The way you described Pointing Pairs implies they can only be used to prune pencilmarks, not to actually set values in cells: but in a no-pencilmarks strategy, surely I'm not allowed to remember those candidate eliminations for future steps.

Perhaps I just need an answer to this question: what state (cell values + candidates) am I allowed to carry over between steps?
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Postby Ruud » Fri May 26, 2006 9:32 pm

Tarek:

1st is invalid
2nd is valid, the stepcount is: N = 8, F = 4, FN = 3, FB = 3, FNB = 2
3rd is invalid. requires FNB. Stepcount FNB = 11

Permutations have no effect on the score, because the pointing pairs are integrated in the steps. I will run a few tests on scrambled puzzles and confirm this hunch...:D

Red Ed:

Not a smart move to show these pictures with pencilmarks. Pretend they are not there. Focus on the colors. When solving manually, I also focus on a single digit and figure out where they fit in the grid. Pointing pairs can be reused each time I revisit the digit.

Your last question is easier to answer. You can detect hidden singles and eliminate candidates eliminated by a placement. You can detect pointing pairs and eliminate candidates in the same row or column. You are not allowed to detect naked singles.

Ruud.
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Postby motris » Fri May 26, 2006 10:26 pm

I like the spirit of what you are proposing here Ruud as mainly a pencil-puzzle solver and someone who prefers pencilmark-less solving except obviously when I'm competing for time. I would however say it is fair (albeit harder) to allow the second type of locked candidates in without needing pencilmarks. For me, on your example, my thought process would go "looking at the 1's, looking by row: ok in the top it has to be in C4 or C5 in R3, can't say much about the middle, at the bottom, it has to be C4 or C5 in R8 - oh, so in the middle its in C6 in R4R5 - oh, but look the same R4R5 lock is present in C3 is well, so R6C7 is 1". No, its not cross-hatching, but maybe just one level above cross-hatching - where I scan each of the three rows and then combine "speculative" information in them to see if anything can come out of it, and then scan the three columns and do the same, before I move onto the next digit. I at least don't find this unreasonable as a human solver, but then I've spent a fair bit of time getting good at seeing things like these type 2 locked candidates to get faster.


The naked single is a more valid concern, as it is still a challenge sometimes to find them efficiently unless it is placed in a clever and obvious way so that it jumps off the page. The only naked singles I've ever liked have been in "gimmicky" hand-made puzzles such as those by Nikoli where because you see, for example, the digits 1234 in a row in order and 5678 in a column in order, the naked single 9 is clear as a starting point. Somehow, it always seems though that the targeted box in these cases is R5C5 and so its a little obvious that it was put there on purpose. Kind of ironic that the final puzzle at the world sudoku championships placed a naked single 8 in R5C5 in exactly this way. So maybe you should allow just naked singles in R5C5 as an alternative to excluding them all:) .

I do like, though, how your description seems to fit with how I rate different puzzles as a solver. There's something a lot more comfortable about seeing a newspaper puzzle that fits into your "ulterior" description when I don't think people on a plane or riding a bus should be stuck marking candidates in tiny little boxes in their newspaper.
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Postby Ruud » Sat May 27, 2006 12:18 am

Thomas,

thank you for the support. You've convinced me on the type 2 locked pairs. Looking at a few examples, I can spot them without pencilmarks, but I probably immediately forget them if they do not expose a single. To program such behaviour is very complex, so I'll allow type 2 unconditionally. For the contributors: to be fair, locked pairs must be detected as they occur and the eliminations are mandatory. You will notice that the step count significantly drops when you make this change. For example, my 28-stepper from the Inferior thread drops to 15 steps when I test it with FNB. It does not qualify as Ulterior because it requires the dreaded naked singles.

The naked single in R5C5 is an interesting premium. Not sure whether anyone will fine-tune their generator for it, but here are the conditions:
1. A naked single is allowed in R5C5.
2. The naked single must be present in the starting grid.
3. We'll call this naked single the Bulls Eye

A puzzle containing a Bulls Eye will replace a puzzle without it that has equal stats for any record held.

I will update the starting post shortly. I'm off to change my Ulterior Checker and retest 1.2M puzzles:(

Ruud.
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Postby ab » Sat May 27, 2006 12:45 am

Interesting idea for a new search. I disagree on the type 2 locked candidates. But then I also disagree on naked singles.

When solving a puzzle the first thing I look for is hidden singles. I often use type 1 locked candidates to help this search, and don't find a need to put in pencil marks to do this. I find type 2 locked candidates much harder to spot and would agree with your original decision to leave them out.

I often find naked singles hard to spot, but I don't think they require pencil marks. On this you should either include them or leave them out, I definately don't like the idea of the bullseye!

On implementing solvers to count steps I suggest that when you search for locked candidates you do not make the eliminations until you have searched the whole grid, also search for the locked candidates first. Otherwise we'll have the problem of people counting steps differently.

I think you should stick to your original definition of ulterior puzzles Ruud. Although I disagree with you on naked singles, I can see where you're coming from.
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Postby tarek » Sat May 27, 2006 2:31 am

Don't tell me you're changing the rules now:(

Not after I found this
Code: Select all
 . . . | 4 2 1 | . . . 
 . . 9 | . . . | 5 . . 
 . 3 . | . . . | . 1 . 
-------+-------+------
 6 . . | . 1 . | . . 9 
 2 . . | 5 . 8 | . . 1 
 4 . . | . 7 . | . . 3 
-------+-------+------
 . 8 . | . . . | . 7 . 
 . . 6 | . . . | 2 . . 
 . . . | 8 6 3 | . . . 


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Postby gsf » Sat May 27, 2006 3:31 am

tarek wrote:Don't tell me you're changing the rules now

right
don't change the rules at least for another day
it takes a while for "no naked singles" to sink in
as well as differentiating box-lines types
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Postby gsf » Sat May 27, 2006 3:45 am

Ruud wrote:Tarek:

1st is invalid
2nd is valid, the stepcount is: N = 8, F = 4, FN = 3, FB = 3, FNB = 2
3rd is invalid. requires FNB. Stepcount FNB = 11

huh
the second can be solved with three rounds of hidden singles
Code: Select all
[1]  N17 [17]=9 [22]=6 [32]=1 [35]=8 [78]=1 [75]=5 [85]=4 [92]=9 [41]=9
         [62]=5 [24]=4 [74]=8 [36]=5 [16]=6 [48]=8 [33]=2 [66]=2
     N18 [18]=4 [38]=3 [49]=5 [43]=6 [55]=9 [67]=4 [63]=8 [81]=6 [82]=8
         [52]=4 [94]=2 [86]=3 [77]=3 [28]=5 [58]=6 [29]=2 [12]=3 [25]=3
     N12 [39]=7 [45]=1 [44]=3 [57]=2 [61]=3 [71]=2 [72]=7 [88]=2 [93]=3
         [98]=7 [69]=1 [53]=7
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Postby fermat » Sat May 27, 2006 5:47 am

Please do not stop posting interesting puzzles. BUT

From the first post this assumes programmers only are able to understand, or play, in this thread.

Is this the correct site?
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