The New Sudoku Players' Forum

[JPF]

I must not understand what the word 'cracker' means...

What eleven is doing is the ox plow (brute force) method. Actually, I have been using it for a while.
I have shorter response times, around 1.5 seconds per puzzle, which I consider to be far too long compared to the times required for canonical determination.
That's why I believe this approach (using canonical determination) remains to be studied.
Note that MinLex is not necessary; gsf/Mladen do the job perfectly.

The champagne method is clever, but it's only effective for very specific puzzles.
What does it become for a solution grid or this one?

Code: Select all

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

2..8..5...8..9..6...9..7..86..5..4...7..4..5...1..2..68..3..7...1..7..4...4..5..1
..31..6...1...4..87...2..4.4...1..6...96..4...7...5..9.3...6..58...7..9...75..1..


JPF

[champagne]

Maybe there will be a counter example in some puzzles ..and in artols puzzle its quite tricky to identify a reference clue

Code: Select all

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


here champagne could say
we have 2 boxes with a unique count
box 8 no clue
box 6 2 clues

take any of them as first box
and have the second box as next row, next column, next "both" depending on the pattern status

As in a manual match we don't try a minimal pattern, the most important is to locate boxes with the smallest number of boxes having the same count.
Here, if as above, we choose the empty box as first box and the box with 2 clues as box 5, we are more or less back to my post

EDIT; unhappily sometimes, we have several options for the first/second box and band/stack choice

[coloin]

I must not understand what the word 'cracker' means...

cracked it as in solved it, cracker as in very good, was a slip of the keyboard and not in the slang dictionary !

.and in artols puzzle its quite tricky to identify a reference clue

Yes I was a bit hasty there - its not tricky..

But JPFs is only slightly more....

Code: Select all

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


The 3 in box 8 is the only instance of a 3 clue ... so this position coluld be utilized as a reference...

concurrently i made a few like this one, which is minimal and has clue distibution 222333333

Code: Select all

+---+---+---+
|1..|2..|3..|
|.3.|.9.|...|
|..7|..8|..4|
+---+---+---+
|8..|3..|7..|
|.4.|...|.1.|
|..9|..5|..6|
+---+---+---+
|6..|8..|4..|
|...|.5.|.2.|
|..5|..2|..9|
+---+---+---+  untouchable clue 3@r1c7


Thinking more about it - It will be a very rare puzzle where we cant identify a Unique Reference Clue !!! URC

[JPF]

Thinking more about it - It will be a very rare puzzle where we cant identify a Unique Reference Clue !!! URC

Code: Select all

+---+---+---+
|243|861|579|
|587|293|164|
|169|457|328|
+---+---+---+
|632|589|417|
|978|146|253|
|451|732|986|
+---+---+---+
|826|314|795|
|315|978|642|
|794|625|831|
+---+---+---+


JPF

[eleven]

Good example by JPF. I got 504 fitting cell transformations. Having them, it's easy e.g. to filter those, which have the same digit at the positions of 1 (two remaining) and 4, one remaining:

Code: Select all

2..8..5...8..9..6...9..7..86..5..4...7..4..5...1..2..68..3..7...1..7..4...4..5..1
..31..6...1...4..87...2..4.4...1..6...96..4...7...5..9.3...6..58...7..9...75..1..

..97..4...7...5..28...3..5.5...7..4...64..5...8...1..6.9...4..12...8..6...81..7..      [1, 5, 4, 5, 1, 1, 4, 0, 2]
equivalent with digit cycle (1,7,8,2,3,9,6,4,5)


Manually, in this case it might be better to look at the digits first, e.g. we know that the only 3r7c4 in the first puzzle has to go 2r3c4 in the second.
And the (three) 5's of the first to the three 1's in the second.

Added: Concerning Coloin's 'untouchable clue' puzzle, it can be noted, that transformations are restricted to reflection, band/stack changes and simultaneously switching the first and 3rd rows and cols in all bands/stacks. So depending on the given puzzles, different approaches can be useful.

[JPF]

Last attempt!

Code: Select all

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

..61..3...8..4..2.4....9..5..87..1...7..9..5.1....5..2.4..7..6.8....6..3..39..2..
.1..4...5..6..9.8.5..3..7....2..6.7..4..3...61..4..2..2..8..5....1..3.9..8..9...7


JPF

[coloin]

Last attempt!

Very good attempt ! Am currently generating same pattern ....with 333333333 clue distribution
Diagonal pattern clues and 3 of each value.
no untouchable clues and no unique 3 clue pattern ....

Code: Select all

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


but box 7 is the only box with 3 non-mutable clues
the 8 clue is different as it has two other 8s in stack 1...

[eleven]

This is a harder one, i got 432 fitting cell transformations, 36 with fitting digits for the three number 1 cells (2,8 and 9), then 3 for number 2.
For that one all digits go to the same:

Code: Select all

.1..4...5..6..9.8.5..3..7....2..6.7..4..3...61..4..2..2..8..5....1..3.9..8..9...7      puzzle to test
.9..5...4..1..3.6.4..2..8....7..1.8..5..2...19..5..7..7..6..4....9..2.3..6..3...8      [0, 4, 0, 4, 4, 4, 2, 5, 5]
cycles (from transformed to equivalent puzzle): (1687239)(45)


Manually the pattern does not give much help, but i noticed, that solving can give you hints. There is a single in both patterns, 1r5c6 and 6r6c2. So the 1 in the left puzzle has to go to 6 in the right. Further solving (x-wing, swordfishs, xyz-wing) would show, that 2 goes to 3. Does not make it much easier, but shows, that solving can simplify the calculation.

[Added:]An explanation to the notation:
To get from the left to the right puzzle, apply the transformations from right to left (rows in bands 3 to 1, columns in stacks 3 to 1, bands, stacks, refeflection at main diagonal)
[0, 4, 0, 4, 4, 4, 2, 5, 5] (1687239)(45)
0:012, 1:102, 2:201, 3:210, 4:120, 5:021
Band 3: switch rows 2 and 3 (012->021)
Band 2: switch rows 2 and 3 (012->021)
Band 1: move 3rd to 1st row (012->201)
Stacks 3 to 1: move 1st to 3rd column (012->120)
Move 1st to 3rd stack
Then apply the cyclic digit changes (1687239)(45),
i.e. 1->6,6->8,8->7,7->2,2->3,3->9,9->1 and 4<->5

[coloin]

Great work eleven. And delving into the solving is another way to identify the clues.
Was going to ask about the notation as it is not as intuitive for me.

Would it not be better to have the 0 as 123 and the other 5 versions are what the final end up is ?
0=123 - 1=132 [ 1 stays the same] 2=321 [ 2 stays the same] 3= 213 [ 3 stays the same] either 4= 312 , 5= 231 ? / or 4= 231 , 5= 312 ?
How do we identify which are the first bands to swap from the 9 digit code ? EDIT Ah Its from right to left with the 0 = no reflection [ it is either 0 or 1]

The cyclic digit clues are good - have to say !!!

[JPF]

If anyone needs a pair of equivalent puzzles without an obvious single...

Code: Select all

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

P : 1..2..3...2..4..5...4..6..17..6..8...6..8..7...2..7..95..4..9...9..1..3...3..8..5
Q : 2...1...3.5.7..9....4..9.6..4.1..2..5...8...4..2..5.3...8..1.7..3.8..6..6...7...9



JPF

[eleven]

This is a possible manual way to get the previous one to the equivalent (not hard, not short, no solving).

Code: Select all

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

Left: 8,9,2 three times in same stack
Right: 1,3,7 in the same stack -> no reflection
Look at band 2: in each box there is a given which sees the same 2 givens in box and row (8: 17, 9: 57, 2:15)
In the right puzzle this is band 2 (1:24,3:46, 7:26)
-> band 2 -> band 2, 8/9/2 -> 1/3/7 (in any order)

Left: (only) in band 3 digits 3 and 6 are twice, both 36 in r8 with 8
Right: in band 3 8 and 9 are twice, both 89 in r9 with 7
band 3 -> band 3, 3/6 -> 8/9, row 8 -> row 9, third digits 8->7

Left: in band 1 4 is twice, not in r1.
Right: In band 1 5 is twice, not in row 2
-> r1 -> r2, 4->5, 6/1/3->6/9/8

So we came here:

Code: Select all

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

no reflection or band switching possible, rows 2,9 fixed
4->5, 8->7, 3/6->8/9, 9/2 -> 1/3, 6/1/3->6/9/8
Left: 4's are in col 12/5 (stack 1/2), Right: 5 in 79/1 (stack 3/1)
-> stack 1->3, 2->1, col 3 (no 4)->col 8 (no 5), col 5->1

Code: Select all

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

box 1: Left 9, Right no 3: 9->1, 4->5, 1->6
-> 2->3
box 7: 6->8 (right is no 9), 7->2
box 8: 3->9
so we have (1687239)(45), change digits,
col 2 -> col 3, col4 -> col6, col5 -> col4, col7 <-> col9

Code: Select all

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

Now switch rows 13,56 to finish

[Added:] To the new one: 7 in band 2 is the only digit 3 times in a band/stack, right puzzle: 1 in stack 2. So you can start with reflection, and 7 must go to 1.
Without a tool to make the transformations graphically it's cumbersome to work it out.

[champagne]

same puzzle, a variant

Code: Select all

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

no clue count signal; we look at the digit status per band/stack

Code: Select all


V1 bands        V1 stacks           V2 bands        V2 stacks
123456789       123456789           123456789       123456789

1.3..6...       1..4...8.           1..45....       12..5....
.2.4...8.         .4..78.           .....6.89       1..4...8. 
...45...9       ..3..6.8.           ..3.5.7..       12...6...

8 digits        6 digits            8 digits         6 digits
_______________________________________________________________

1.....78.       1.....7.9           .2...6.7..      ..34...8.
....5.7.9       ...4..7.9           ..34.6...       ..34....9
12..5....       ....56..9           12.4.....       ..3..6..9

6 digits        6 digits            6digits         5 digits
______________________________________________________________

...4.67..       123......           .2..5..8.         .2..5.7..
..3..6.8.       .2..56...           1.3.....9         ......789
.23.....9       .23.5....           ......789         ....567..

7 digits        5 digits            7 digits        6 digits     


we have only 2 possible match with the bands unchanged

V2s ??2 => V1s123

building the digit mapping v2 ->V1, we have immediately

v2-2 => v1-7 from the digit missing in band1
V2-5 => v2-4 form the pair in band 1
v2-3 => v1-2 from the 3 occurrences in v1s3/v2s2

so the mapping starts with
123456789 v2
.72.4.... v1

this solves the match in stack due to the pairs {2 in V2s1) and {7in V1s2}

so the only possible match is v2s312 => V1s123


From here, finding missing digit mappings is easy
v2_1 => V1_9 in V1s2/V2s1
v2_7 => V1_8 in V1s1/V2s3
v2_4 => V1_5 in V1b2/V2b2 after 2=>7 then
v2_9 => V1_3 in V1s3/V2s2
v2-6 => v1-1 in band 2
leaving 8 =>6 and the mapping

123456789 v2
972541863 v1

with no seen contradiction

the job is nearly over, we have to morph after relabeling
v2box3 to v1_box1
v2box4 to v1box5
v2box8 to vbox9
and check that we have no contradiction

Code: Select all

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


Code: Select all

box 3 + relabeling => box 1

..5     ..4             ..6
.8. =>  .6.  to move to .8.
7..     8..             4..

Code: Select all

box 4 + relabeling => box 5

..2     ..7              7..
.4. =>  .5. to move to   .9.
1..     9..              ..5

Code: Select all

box 8 + relabeling => box9

8..    6               .6.
..3 => ..2 to move to  ..3
.9.    .3.             2..

[eleven]

Last example manually:

Code: Select all

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

Left: Only band 2 has a digit (7) 3 times
Right: Only stack 2 has a digit (1) 3 times
=> reflection needed, then stack 2 is fixed, digit 7->1

Code: Select all

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

Left: Boxes 39 have only digits 359
Right: Boxes 14 have only digits 245
=> box 6 -> box 7, swap bands 2,3 and stacks 1,3

Code: Select all

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

7->1, 359->245, 418->368 => 26->79, box 2 -> box 2
So neither bands nor stacks can be in other positions, the boxes are fixed.
From digit 7->1 col 4 <-> col 5, row 5->row 4, row9->row7 (cols 456, rows 147 fixed then)

Code: Select all

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

Now we have 6->7, 2->9, 8->8, 9->5, row 8 <-> row 9
In stack3 we have to move col 7->9,8->7,9->8

Code: Select all

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

This already fits with number cycles (13467)(295)(8)
The transformations were reflection, swap bands 23, swap stacks 13, swap cols 45,
rows 456->546, cols 789->978, rows 789->987.

[coloin]

.....Without a tool to make the transformations graphically it's cumbersome to work it out.

If it helps this program achieves this when in architect mode Sudoku Architest from havard

Excellent find by JPF. maybe if we look hard enough we are always going to find a way .. eg with 2 digit clue combinations , or mutable clues
eleven spotted the 3 clues in a band pattern, but 7 of the other clue digits did have the "L" pattern...

Code: Select all

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

The 1 digit in box 8 is identifiable....as the 1 is not in an "L" pattern

[eleven]

Thanx for the link, but i have troubles to run windows programs on linux.
Didn't need it for that example, and i don't think, that i want to try another one.
The less clues and the more single patterns we have to compare, the easier it will be manually.
But when we compare full grids, this probably would become a torture.