The New Sudoku Players' Forum

[vidarino]

This one is a beauty!

Code: Select all

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

29 steps, of which the 20(!) first are one-single;
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,4,3,4,4,11,6,4

Vidar

[Ruud]

It certainly is a beauty, Vidar.

You are counting hidden singles and naked singles separately. My solver sees a hidden single in R3C9 and a naked single in R1C7 at the same time.

Having said that, your puzzle has a longer intro than mine. The "Pappocom was a rolling stone" of Sudoku.

Ruud.

[vidarino]

You are counting hidden singles and naked singles separately. My solver sees a hidden single in R3C9 and a naked single in R1C7 at the same time.

Indeed I am. I just changed that now, though, so let's see what it can conjure up.

I still think hidden singles should have some presedence, though, because they are much easier to spot than naked singles when solving without candidates. But for the sake of the rules of this thread, I'm giving it a shot.

Having said that, your puzzle has a longer intro than mine. The "Pappocom was a rolling stone" of Sudoku.

Vidar

[ab]

Of course, no two solvers are identical, so there could be things I have overlooked, but I don't think I'm too far off.

Vidar

If we're talking about singles, every solver should give the same results.

I think everyone's got the idea of the thread, narrow solution paths on singles, which would exclude locked candidates.

When I mentioned using all techniques and still getting a narrow path, then that would be different for different solvers. My solver is just about the right strength for Tarek's superior thread and the puzzles I posted take at least 8 steps when I use all the techniques of my solver. The narrowest path of singles in the puzzles I posted takes 18 steps, so I think you've beaten that.

[ab]

according to my solver Ruud's puzzle comes top at 26 steps.

Vidarino's last puzzle is 22 steps for instance there's a hidden single 9 and a naked single 6 in the same box at the start.

Next is my second puzzle at 18 steps

Then my third puzzle at 17 steps

Then vidarino's first puzzle at 16 steps

all of vidarino's other puzzles are invalid as they contain locked candidates (Ishould have made that clear at the start).

Tarek's puzzle comes in at 10 steps.

You can ignore the bit I said about using all techniques available to your solver, as it will vary enormously.

[vidarino]

Thanks for those numbers, ab. I have tuned my solver a bit, and it now produces the same number of steps as yours.

Also thanks for the clarification regarding locked candidates. I'll edit my posts to remove the invalid entries.

In the mean time, here's a 26-stepper from me as well:

Code: Select all

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

Vidar

[Mage]

Don't understood exactly how you count solving steps.

I propose that one, for wich Susser needs 31 steps.

Code: Select all

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

But I am perhaps in a totally wrong direction...

Mage

[Ruud]

If we're talking about singles, every solver should give the same results.

That would be true if all our solvers would solve all singles cycle by cycle. That, according to comments posted, is not always the case. Human solvers take singles one by one, and the choice of a particular single determines how many alternatives are unlocked and the narrowness of the subsequent path.

I like this thread because it helps us focus on the other aspects of sudoku difficulty, completely ignoring elimination techniques. Solving sudokus with singles only is simply a search operation. For a search, there are 3 aspects IMO that influence difficulty:

1. Size of the set to be searched (number of empty cells/candidates)
2. Number of available singles (narrowness of the path)
3. Recognizability of the singles

We can all agree on the first 2 aspects, because they are easy to measure. For the third aspect, I would like to take Vidar's 26-stepper as an example.

The sudoku opens with 2 "eyecatchers". Both the 6 in r5c5 and the 2 in r8c1 are forced into position with 3 cross-hatching lines. They are both singles in box AND column. The 6 locks another "eyecatcher" 3 in r5c4. This 3 is single in row and box.

Same story for the 8 in r5c6. These are 3 subsequent placements in the same row & box. As the player's attention is already focused here, this cuts a lot off the search time. The placement of 2 in r4c4 is almost a freebee.

My point is: A narrow solving path alone does not make a sudoku difficult. Visibility of the singles is also an important factor.

BTW, I do not see these sudokus as inferior. I a database of 600K I could find only a single 26-stepper.

Don't understand exactly how you count solving steps.

Locate every single available in the sudoku, but do not solve them yet. Then add 1 to the number of cycles and make all the placements. Repeat until the sudoku is solved.


This brings me to my next contribution:

Code: Select all

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

25 rounds, but 3 embarrassing eyecatchers in the opening.

Ruud.

[gsf]

the step count seems to be a loop where each iteration scans the grid for
singles moves and makes the moves as a batch

an alternate way of counting would be to incrementally make the moves as they are
found during each scan, which would tend to increase the per-scan count and
decrease the total number of scans, closer I think to what human solvers do

scan count is how I measured the ones I posted to the superior thread, some of
which were inferior -- the ones with the most scans are included below

the label is followed by the (incremental) scan count and method (F:naked-single N:hidden-single)
#001 and #004 solve with naked singles only
#002 (which probably doesn't qualify because of low scan count) has no naked singles

Code: Select all

Puzzle gsf#001 18 F

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

Puzzle gsf#002 4 N

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

Puzzle gsf#003 21 FN

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

Puzzle gsf#004 16 F

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

Puzzle gsf#005 20 FN

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


[vidarino]

Don't understood exactly how you count solving steps.

My solver, and I believe ab's too, counts like this;
1. locate singles (naked or hidden) - but don't place any numbers
2. place all located singles in one sweep
3. rinse and repeat until solved

Your puzzle required 9 such steps. It had the following number of singles per step; 5,8,9,2,6,9,7,10,2

In other words, the opening grid has 5 singles. After placing all of those, the grid now has 8 singles. Place those and you'll have 9 more, etc.

This one appears to need 27 steps:

Code: Select all

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

Path "breadth"; 3,1,1,1,1,2,3,1,1,1,1,1,1,2,2,2,1,2,1,2,2,2,5,6,4,5,2

[Ruud]

This one appears to need 27 steps:

And 9 naked singles in the path

Ruud.

[gsf]

counting batched singles these take 29 steps
(edit: 28 -- the final solution was counted as a step)

Code: Select all

Puzzle gsf#006 29 FN

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

Puzzle gsf#007 29 FN

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

Puzzle gsf#008 29 FN

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

Puzzle gsf#009 29 F

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

Puzzle gsf#010 29 FN

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

Puzzle gsf#011 29 F

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

Puzzle gsf#012 29 F

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

Puzzle gsf#013 29 F

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


[vidarino]

counting batched singles these take 29 steps
(edit: 28 -- the final solution was counted as a step)

Hmm, not from where I'm standing, I'm afraid...

E.g. your last one;

Code: Select all

Step 1:
F: Cell R4C4 can only be 2
F: Cell R5C9 can only be 3
N: Cell R4C7 is the only place in R4 for a 5.
N: Cell R8C9 is the only place in C9 for a 5.
N: Cell R8C3 is the only place in C3 for a 9.
N: Cell R6C4 is the only place in C4 for a 9.

Step 2:
F: Cell R6C9 can only be 7
F: Cell R8C2 can only be 8
N: Cell R5C1 is the only place in C1 for a 2.
N: Cell R8C5 is the only place in C5 for a 2.
N: Cell R9C7 is the only place in R9 for a 2.
N: Cell R3C7 is the only place in B3 for a 3.
N: Cell R3C9 is the only place in C9 for a 6.
N: Cell R4C3 is the only place in R4 for a 7.
N: Cell R6C6 is the only place in B5 for a 8.

Step 3:
F: Cell R1C9 can only be 2
F: Cell R3C5 can only be 1
F: Cell R8C7 can only be 6
N: Cell R3C3 is the only place in R3 for a 2.
N: Cell R8C6 is the only place in R8 for a 3.
N: Cell R2C5 is the only place in B2 for a 6.
N: Cell R9C3 is the only place in R9 for a 6.
N: Cell R2C1 is the only place in C1 for a 8.
N: Cell R5C3 is the only place in B4 for a 8.

...


I counted only 8 steps from start to finish.

(Note that I'm "borrowing" your one-letter step codes... ;-) )

Vidar

[Ruud]

Puzzle gsf#006 29 FN

Code: Select all

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

This is how I solved your first puzzle in 15 rounds:

Code: Select all

 1: R2C9=7,R7C8=1,R2C4=2,R5C7=4
 2: R5C1=2,R3C9=8
 3: R7C6=2,R3C7=3,R5C3=7
 4: R6C3=8,R1C7=9
 5: R1C3=1,R8C7=2,R6C8=9
 6: R9C2=2,R4C8=2,R8C8=7,R7C3=9,R8C6=9,R9C9=9
 7: R8C1=4,R8C2=5,R9C7=6,R7C1=7,R4C7=8,R9C8=8
 8: R9C3=3,R2C3=5
 9: R2C2=3,R2C8=4,R1C8=5
10: R4C1=3,R1C1=6
11: R4C6=1,R6C4=3,R4C2=6
12: R3C5=1,R6C2=1,R7C5=3,R7C4=6
13: R5C9=1,R1C6=3,R1C5=4,R5C5=6,R6C9=6
14: R3C2=4,R9C4=4,R9C5=5,R1C2=7,R1C4=8,R5C6=8
15: R3C6=5,R5C4=5,R3C4=7,R9C6=7

Ruud

[Mage]

Thanks both, Ruud and Vidarino.

I was searching in a completely diferent ... and wrong direction.

Mage