The New Sudoku Players' Forum

[JPF]

Here is a “symmetric” 23-stepper :

Code: Select all

 JPF #B02


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



23 steps : 3,2,1,1,1,2,4,6,2,2,2,1,1,2,3,3,1,1,1,3,8,6,1


JPF

[Ocean]

Here are two candidates:

Code: Select all

 Ocean #1 (23 steps)
+-------+-------+-------+
| . . . | . 7 . | . . . |
| . . 5 | . . . | 9 . . |
| . 3 . | 5 . 4 | . 2 . |
+-------+-------+-------+
| . . 3 | . 4 . | 1 . . |
| 4 . . | 3 . 1 | . . 9 |
| . . 1 | . 5 . | 8 . . |
+-------+-------+-------+
| . 8 . | 7 . 2 | . 5 . |
| . . 9 | . . . | 6 . . |
| . . . | . 1 . | . . . |
+-------+-------+-------+

 Ocean #2 (23 steps)
+-------+-------+-------+
| 1 . 3 | . . . | . 9 . |
| 8 . . | . . . | 5 3 4 |
| 6 . . | . . . | . 8 . |
+-------+-------+-------+
| . . . | . 1 4 | . . . |
| . . . | 7 5 9 | . . . |
| . . . | 6 3 . | . . . |
+-------+-------+-------+
| . 1 . | . . . | . . 6 |
| 3 5 6 | . . . | . . 8 |
| . 8 . | . . . | 2 . 7 |
+-------+-------+-------+

[ab]

Yeah, I finally made it to my own party (just), with this 20 step puzzle:

Code: Select all

...|.6.|...
...|3.8|...
..1|5.9|7..
-----------
.65|...|14.
9..|...|..2
.72|...|36.
-----------
..4|7.5|9..
...|8.1|...
...|.2.|...


[Ocean]

This is a contender for the Absolute inferior place, the Absolute Bottom.

Code: Select all

 Ocean (3 steps)
+-------+-------+-------+
| 9 4 . | . . 3 | 7  .. |
| 5 . . | . 6 . | 3 . . |
| . . . | . . 1 | . . 9 |
+-------+-------+-------+
| . 6 . | . . 9 | 5 2 . |
| . . . | 8 . 6 | . . . |
| . 8 4 | 2 . . | . 1 . |
+-------+-------+-------+
| 7 . . | 1 . . | . . . |
| . . 3 | . 2 . | . . 7 |
| . . 5 | 7 . . | . 4 2 |
+-------+-------+-------+

[tarek]

For that challenge Ocean we need to limit the number of clues to <30....

So let's see if we can beat the 3-stepper (By the way Ocean, my solver says in 4 steps......)...I'll double check.

Tarek

[vidarino]

Hehe, nice one.

I assume the puzzles will also need to be minimal / irreducable while keeping symmetry? (I.e. you can't take a 28-clue puzzle and add a pair of clues, since that would make it symmetrically reducable?)

Hmm, this is actually a quest for the absolutely easiest sudoku puzzle ever.

Anyway, here's a 4-stepper from me:

Code: Select all

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

It would become a 3-stepper if I added a clue to the center cell, but then it wouldn't be minimal anymore, so...

Vidar

PS! And my solver agrees that Ocean's puzzle is a 3-stepper.

[tarek]

This would not count as it has >30 cells......

It is a 3 stepper (6,24,18)

Code: Select all

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

My solver says 5 steps for your puzzle Vidar (2,13,23,13,2)

Tarek

[vidarino]

OK, just for sh*ts and giggles, here is a 1-stepper. It has no less than 48 givens, so it's way out of the "competition", but interestingly, it *is* minimal. You can't remove a set of clues without breaking the (all-axis) symmetry or losing the unique solution.

Code: Select all

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

[vidarino]

My solver says 5 steps for your puzzle Vidar (2,13,23,13,2)

Yes, if you count naked and hidden singles separately, as separate steps. I was under the impression that they should be "merged", in which case my puzzle solves in 4 (11,17,17,8). That's the "rule" in the first post, at least.

[vidarino]

And a 30-clued 3-stepper:

Code: Select all

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

[tarek]

Yes, if you count naked and hidden singles separately, as separate steps

I do not count them seperately, but hidden singles (the easiest) that cannot be deduced from looking at the candidates list at the start of the step are relegated to the next step, what do you think ( your last puzzle, 4 steps 5,21,19,6) ???

Tarek

[ab]

the Guardian actually published a 3 stepper:
http://image.guardian.co.uk/sys-files/Guardian/documents/2006/01/16/GdnSudoku223_060124.indd.pdf
And the last step contains 1 cell!!

If you allow locked candidates, it's actually a 2 step puzzle.

[vidarino]

I do not count them seperately, but hidden singles (the easiest) that cannot be deduced from looking at the candidates list at the start of the step are relegated to the next step, what do you think ( your last puzzle, 4 steps 5,21,19,6) ???

Hmm, I'm not quite sure I follow you...

Here's the log of the first step for my (alleged ) 3-stepper.

Code: Select all

Step 1
Cell R3C7 can only be 2
Cell R4C4 can only be 6
Cell R6C4 can only be 2
Cell R7C3 can only be 7
Cell R9C6 can only be 1
Cell R4C9 is the only place in R4 for a 1.
Cell R5C3 is the only place in C3 for a 3.
Cell R6C6 is the only place in C6 for a 4.
Cell R8C5 is the only place in B8 for a 4.
Cell R5C2 is the only place in C2 for a 5.
Cell R1C9 is the only place in B3 for a 5.
Cell R3C3 is the only place in R3 for a 5.
Cell R2C7 is the only place in R2 for a 6.
Cell R6C1 is the only place in B4 for a 7.
Cell R9C4 is the only place in C4 for a 7.
Cell R1C4 is the only place in C4 for a 9.
Cell R5C5 is the only place in B5 for a 9.
17 placements


All of these can be seen from the starting candidate grid. I assume the "5" in your "step size log" is the naked ones in the beginning? Why postpone the hiddens? They are all there, regardless of the naked/hidden scanning order. (No numbers are placed until both checks are done.)

[tarek]

In your (3 stepper vidar):

Eliminating 9 From r4c9 (Naked Single in Column 9)
Eliminating 4 From r4c9 (Naked Single in Row 4)
Eliminating 2 From r4c9 (Naked Single in Row 4)
Eliminating 7 From r4c9 (Naked Single in Box 6)
Eliminating 5 From r4c9 (Naked Single in Box 6)
Eliminating 6 From r4c9 (Naked Single in Box 6)
r4c9 value MUST be 1 (Hidden Single in Row 4)

r4c9 can only be uncovered as a hidden single........

if you looked at the board at the start you can't deduce that.......

If you place hidden singles AFTER naked singles then you are right, but clearly hidden singles are easier to spot than naked singles...

Naked singles uncovered by hidden singles are in the same step
Hidden singles uncovered by naked singles are in the next step

so r4c9 has to be in step 2 (out of 4 ), that is how I see it.....

Tarek

[vidarino]

Sorry, I wholeheartedly disagree.

Here are rows 4, 5 and 6:

Code: Select all

+-------+-------+-------+
| . 4 2 | . . . | 7 9 . |
| . . . | 1 . 7 | . . . |  <- has a 1
| . 9 1 | . . . | 5 6 . |  <- has a 1
+-------+-------+-------+

There is but one spot for a 1 in box 6, and that is in R4C9.

Vidar