The New Sudoku Players' Forum

[Ocean]

Two minimal 20-steppers and one minimal 21-stepper with special symmtries.
(D=diagonal. L=90-degrees rotational. X=double diagonal.)

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#M23. 20 steps. D-symmetry.
+-------+-------+-------+
| . . . | . . 1 | . . . |
| . . . | . 7 . | 3 . 5 |
| . . . | 5 . . | 9 . . |
+-------+-------+-------+
| . . 3 | 4 6 . | . . . |
| . 4 . | 3 . 2 | 6 . . |
| 2 . . | . 1 . | . . 7 |
+-------+-------+-------+
| . 6 1 | . 5 . | . 9 . |
| . . . | . . . | 2 . . |
| . 5 . | . . 4 | . . . |
+-------+-------+-------+


#M24. 20 steps. L-symmetry.
+-------+-------+-------+
| 3 . . | . . . | . . 6 |
| . . . | 9 7 . | 2 . . |
| . 7 9 | . . . | 4 . . |
+-------+-------+-------+
| . . . | . 5 . | . 2 . |
| . 3 . | 7 . 8 | . 1 . |
| . 4 . | . 1 . | . . . |
+-------+-------+-------+
| . . 8 | . . . | 1 5 . |
| . . 1 | . 9 4 | . . . |
| 6 . . | . . . | . . 8 |
+-------+-------+-------+


#M24. 21 steps. X-symmetry.
+-------+-------+-------+
| . 7 . | . . 8 | . 6 . |
| 9 3 . | . 4 . | . . 5 |
| . . . | 2 . . | . . . |
+-------+-------+-------+
| . . 9 | 1 . . | . . 4 |
| . 2 . | . . . | . 3 . |
| 5 . . | . . 4 | 7 . . |
+-------+-------+-------+
| . . . | . . 6 | . . . |
| 7 . . | . 8 . | . 9 6 |
| . 1 . | 5 . . | . 2 . |
+-------+-------+-------+

[ab]

a 20 stepper with full symmetry:

Code: Select all

...|...|...
.4.|...|.6.
..2|9.7|5..
-----------
..7|.6.|2..
...|538|...
..8|.4.|9..
-----------
..9|2.6|8..
.6.|...|.5.
...|...|...


[Ocean]

A minimal and fully symmetric 21-stepper:

Code: Select all

M24. 21 steps. Minimal. Full symmetry [code 8-0-6-1-0].
+-------+-------+-------+
| . 9 . | . . . | . 7 . |
| 1 . . | . . . | . . 6 |
| . . 5 | 4 . 9 | 3 . . |
+-------+-------+-------+
| . . 7 | . 8 . | 6 . . |
| . . . | 5 . 6 | . . . |
| . . 2 | . 9 . | 4 . . |
+-------+-------+-------+
| . . 3 | 6 . 7 | 9 . . |
| 2 . . | . . . | . . 3 |
| . 5 . | . . . | . 1 . |
+-------+-------+-------+

[Ocean]

Two minimal sudokus with 21 clues: One 25-stepper, and one 23-stepper. Both with diagonal symmetry.

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# M21. 25 steps. Diagonal symmetry.
+-------+-------+-------+
| . 1 . | . . 2 | . 3 . |
| 4 . . | . . . | 1 5 . |
| . . . | . . 6 | . . . |
+-------+-------+-------+
| . . . | . . . | . . 7 |
| . . . | . . 1 | 8 . . |
| 2 . 7 | . 8 . | . . . |
+-------+-------+-------+
| . 3 . | . 4 . | . . . |
| 8 4 . | . . . | . . 6 |
| . . . | 5 . . | . 2 9 |
+-------+-------+-------+

Code: Select all

# M21. 23 steps. Diagonal symmetry.
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | . 2 . | . 3 . |
| . 4 . | 5 6 . | 7 . . |
+-------+-------+-------+
| . . 2 | . . . | . . . |
| . 1 8 | . . . | . . . |
| . . . | . . . | 4 6 5 |
+-------+-------+-------+
| . . 3 | . . 2 | . . . |
| . 5 . | . . 9 | . . 3 |
| . . . | . . 8 | . 9 1 |
+-------+-------+-------+

[Ocean]

This one popped up: A 26-stepper with 20 clues.

Code: Select all

# M20. 26 steps. (Minimal + Full symmetry).
 *-----------*
 |...|.1.|...|
 |...|234|...|
 |..1|...|5..|
 |---+---+---|
 |.2.|...|.6.|
 |63.|...|.24|
 |.4.|...|.7.|
 |---+---+---|
 |..5|...|8..|
 |...|967|...|
 |...|.4.|...|
 *-----------*

[ab]

a 22 step puzzle:

Code: Select all

...|...|.5.
35.|7..|..2
8.7|.2.|...
-----------
...|.6.|...
.19|..8|4..
74.|...|.1.
-----------
...|.1.|3..
.3.|59.|.4.
...|4..|26.


[JPF]

a 23-stepper :

Code: Select all

SM 26   ; 23 steps 

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

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


JPF

[Red Ed]

A nice simple self-referential puzzle ...

Code: Select all

6 8 7 3 . . . . .
. . . . . . 7 2 .
. . . . . 4 . . 1
. 6 4 . . 8 . . 2
8 . . 1 . . 4 5 .
. . 2 . . . . . .
. 5 . . . . . . .
4 1 3 7 . . . . .
. . . . . 1 3 4 8

Seriously non-minimal, but who cares!

[Ruud]

Inspired by Ed,
I created this puzzle:

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

It is self-explaining.

- There are 26 clues forming 2 digits.
- There are 13 steps. 13 * 2 = 26.
- The sum of all the clues is 156, which equals 2 * 6 * 13

Ruud.

[JPF]

Just in case, if you need one more

Code: Select all

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



Prime divisors :

21 =3*7 digits
26 =2*13 clues
11 =1*11 steps.

JPF

[Red Ed]

Ruud, JPF -- nice work!

But can you create examples where the puzzle spells out the number of steps, as in my 20? (Although it seems like nit-picking to find any fault in Ruud's spectacular example)

[JPF]

... But can you create examples where the puzzle spells out the number of steps, as in my 20?...

Yes

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



JPF

[Red Ed]

Here's a self-referential 23, which is not quite minimal ...

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. . . . . . 2 3 .
. . . . . 7 . . 1
. 5 3 . . . . . 8
2 . . 1 . . 3 4 .
. . . 7 . . . . 6
. . 8 . . 6 . . 7
. 4 . . . . 1 5 .
5 . . . . . . . .
8 1 6 4 . . . . .

It took 316 million iterations (digit replacements in the pattern above) to find this thing. I don't know how you people are finding 25+ steppers!

[JPF]

Here's a self-referential ...

Well ...
2^3 = 8 # 23

JPF

[Red Ed]

Ha! I knew someone would pick me up on that. But it's not my fault, it's my wonky downward-sloping monitor: to me, the puzzle looks like a italicised 23, honest ...

OK, how about this: a minimal 29-stepper

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. 9 . . 8 . 2 . .
. 1 . . . . 5 . .
. 3 . . . . . 4 .
. . . 6 . 3 4 . .
8 . . . . . . . .
5 . . . . . . . .
. . . 1 . . . . 7
. . . . . . . 8 9
9 . . . 6 . . . .

(it's a modification of one of Gordon's 17s)