The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.7.|5..|
 |...|..1|.6.|
 |.4.|56.|31.|
 |---+---+---|
 |.12|...|6..|
 |...|...|1.3|
 |..9|...|42.|
 |---+---+---|
 |.81|.4.|73.|
 |.5.|7..|...|
 |..6|.38|...|
 *-----------*


Play/Print this puzzle online

[storm_norm22]

Code: Select all

+----------------+------------------+----------------+
| 1      6   38  | 3489   7     349 | 5    489  2    |
| (35)   29  357 | -3(4)  289   1   | 89   6    7(4) |
| 29     4   78  | 5      6     29  | 3    1    78   |
+----------------+------------------+----------------+
| 458    1   2   | 348    58    34  | 6    7    9    |
| 4568   7   45  | 24689  2589  249 | 1    58   3    |
| 68(5)  3   9   | 68     1     7   | 4    2    8(5) |
+----------------+------------------+----------------+
| 29     8   1   | 29     4     5   | 7    3    6    |
| 34     5   34  | 7      29    6   | 289  89   1    |
| 7      29  6   | 1      3     8   | 29   45   (45) |
+----------------+------------------+----------------+

(3=5)r2c1 - (5)r6c1 = (5)r6c9 - (5=4)r9c9 - (4)r2c9 = (4)r2c4; r2c4 <> 3

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 1       6      c38       | 3489    7       349      | 5       49-8    2        |
| 35      29      357      | 34      289     1        | 89      6       47       |
| 29      4      c78       | 5       6       29       | 3       1      b78       |
|--------------------------+--------------------------+--------------------------|
| 458     1       2        | 348     58      34       | 6       7       9        |
| 4568    7      c45       | 24689   2589    249      | 1      a58      3        |
| 568     3       9        | 68      1       7        | 4       2       5-8      |
|--------------------------+--------------------------+--------------------------|
| 29      8       1        | 29      4       5        | 7       3       6        |
| 34      5      c34       | 7       29      6        | 289     89      1        |
| 7       29      6        | 1       3       8        | 29      45      45       |
*--------------------------------------------------------------------------------*

ALS XY Wing: (8=5) r5c8 - r5c3 = 7r3c3 [ALS r1357c3] - (7=8) r3c9 => r1c8, r6c9 <8>

Leren

[ArkieTech]

Code: Select all

*--------------------------------------------------------------------------------*
| 1       6      c38       | 3489    7       349      | 5       49-8    2        |
| 35      29      357      | 34      289     1        | 89      6       47       |
| 29      4      c78       | 5       6       29       | 3       1      b78       |
|--------------------------+--------------------------+--------------------------|
| 458     1       2        | 348     58      34       | 6       7       9        |
| 4568    7      c45       | 24689   2589    249      | 1      a58      3        |
| 568     3       9        | 68      1       7        | 4       2       5-8      |
|--------------------------+--------------------------+--------------------------|
| 29      8       1        | 29      4       5        | 7       3       6        |
| 34      5      c34       | 7       29      6        | 289     89      1        |
| 7       29      6        | 1       3       8        | 29      45      45       |
*--------------------------------------------------------------------------------*

ALS XY Wing: (8=5) r5c8 - r5c3 = 7r3c3 [ALS r1357c3] - (7=8) r3c9 => r1c8, r6c9 <8>

Leren

Can anyone find the reverse bug?

[tlanglet]

This started as an AXY-wing(35-8)r2c1,r1c3,r6c1 & 6r6c1 with transport but I think it is better posted as an AAIC with (58=6)r6c1

[8r2c5=8r1c4-(8=3)r1c3-(3=5)r2c1-(5=8)r6c1-r6c9=r5c8-r8c8=r8c7-r2c7=r2c5 => r2c5=8] = [6r6c1-(6=8)r6c4-r6c9=r5c8-r8c8=r8c7-r2c7=r2c5 => r2c5=8] => r2c5=8

Ted

[David P Bird]

Can anyone find the reverse bug?

Is this what you mean?

After (2)SwordFish:r357c146 => r5c5 <> 2

Code: Select all

 *-------------------*---------------------*-------------------*
 | 1     6     38    | 348-9   7     34-9  | 5     9-48  [2]   |
 | 35    29    357   | 34      29-8  1     | 8-9   6     47    |
 | 29    4     78    | 5       6     29    | 3     1     78    |
 *-------------------*---------------------*-------------------*
 | 458   1     <2>   | 348     58    34    | 6     7     [9]   |
 | 4568  7     45    | 29-4689 58-9  29-4  | 1     58    3     |
 | 568   3     <9>   | 68      1     7     | 4     <2>   58    |
 *-------------------*---------------------*-------------------*
 | 29    8     1     | 29      4     5     | 7     3     6     |
 | 34    5     34    | 7       29    6     | 29-8  8-9   1     |
 | 7     29    6     | 1       3     8     | 29    45    45    |
 *-------------------*---------------------*-------------------*

In the grid the instances of 2 & 9 shown bracketed <> are givens and those shown bracketed [] are solved.
The eliminations shown are those that would follow if (9)r1c8 was assumed to be true when a (29)BUG would be made. They consist of the (9)s in sight if r1c8 and the other candidates in the (29) hidden pairs that would be created.
Hence (9)r1c8 must be false.

This loop of alternating digits cannot be allowed to survive:
[2]r1c9 – [9]r4c9 – <2>r4c3 – <9>r6c3 - <2>r6c8 – (9?)r1c8 – Loop

It should be impossible to construct one or more loops like this that cover all the givens for the two digits and visit two cells in every box they enter unless they visit all 9 boxes, otherwise a BUG will be formed.

[Marty R.]

Code: Select all

+-------------+----------------+------------+
| 1    6  38  | 3489   7   349 | 5   489 2  |
| 35   29 357 | 34     289 1   | 89  6   47 |
| 29   4  78  | 5      6   29  | 3   1   78 |
+-------------+----------------+------------+
| 458  1  2   | 348    58  34  | 6   7   9  |
| 4568 7  45  | 246899 589 249 | 1   58  3  |
| 568  3  9   | 68     1   7   | 4   2   58 |
+-------------+----------------+------------+
| 29   8  1   | 29     4   5   | 7   3   6  |
| 34   5  34  | 7      29  6   | 289 89  1  |
| 7    29 6   | 1      3   8   | 29  45  45 |
+-------------+----------------+------------+


Play this puzzle online at the Daily Sudoku site

Some nameless (to me) kind of chain.

(5=3)r2c1-(34=7)r2c49-(7=8)r3c9-(8=5)r6c9=>r6c1<>5

[ArkieTech]

Is this what you mean?
...
Hence (9)r1c8 must be false.

Yes. The way I see it --

Code: Select all

 *--------------------------------------------------------------------*
 |                      |                      |        9      2      |
 |        29            |        29            |                      |
 | 29                   |               29     |                      |
 |----------------------+----------------------+----------------------|
 |               2      |                      |               9      |
 |                      | 29     29     29     |                      |
 |               9      |                      |        2             |
 |----------------------+----------------------+----------------------|
 | 29                   | 29                   |                      |
 |                      |        29            | 29                   |
 |        29            |                      | 29                   |
 *--------------------------------------------------------------------*
The 29 can be swapped in b346 making multiple solutions

[Leren]

Marty R. wrote :

Some nameless (to me) kind of chain.

(5=3)r2c1-(34=7)r2c49-(7=8)r3c9-(8=5)r6c9=>r6c1<>5

I believe this can be viewed as an ALS XY Wing. In this case the "base cell" is the 2 cell ALS r2c49 and

the second "pincer cell" is the 2 cell ALS r36c9. In fact you can also consider the first pincer cell r2c1 as a 1 cell ALS!

Leren

[Leren]

Code: Select all

Arkietech wrote: The 29 can be swapped in b346 making multiple solutions.

I don''t understand this comment. I can see that the 2s and 9s in b346 are a DP allowing multiple solutions
but only if none of them are givens. Is there some deeper theorem that says that this pattern can't occur even
when some of them are givens ?

Leren

[JasonLion]

If R1C8 is 9, you get the pattern of 2's and 9's shown a few posts back, which has multiple solutions, not in B346, but in all of the other 29s in all of the other blocks. Or to put that another way, once R1C8 is set to 8, the remaining 2 & 9 pencil marks collectively form a deadly pattern. Therefore R1C8 is not 9.

[Luke]

Marty R. wrote :

Some nameless (to me) kind of chain.

(5=3)r2c1-(34=7)r2c49-(7=8)r3c9-(8=5)r6c9=>r6c1<>5

I believe this can be viewed as an ALS XY Wing. In this case the "base cell" is the 2 cell ALS r2c49 and

the second "pincer cell" is the 2 cell ALS r36c9. In fact you can also consider the first pincer cell r2c1 as a 1 cell ALS!

Leren

Take another look, guys. It's just an xy chain...

[Marty R.]

Marty R. wrote :

Some nameless (to me) kind of chain.

(5=3)r2c1-(34=7)r2c49-(7=8)r3c9-(8=5)r6c9=>r6c1<>5

I believe this can be viewed as an ALS XY Wing. In this case the "base cell" is the 2 cell ALS r2c49 and

the second "pincer cell" is the 2 cell ALS r36c9. In fact you can also consider the first pincer cell r2c1 as a 1 cell ALS!

Leren

Take another look, guys. It's just an xy chain...

It certainly is. I have no idea why I didn't see it that way and had that 2nd term as (34=7).

[David P Bird]

A few more words on Reverse BUGs:

This puzzle is an excellent example of the effect of being able to find a "deadly" two-digit loop because in every other box (29) pairs are immediately formed, and the BUG created is obvious. This isn't always the case however and the pairs might only become apparent much later on in the solution, but they will inevitably emerge sooner or later.

This is because the without a given in one of these loops, solvers would have no way of distinguishing the difference between the two digits in these cells. From the puzzle composers viewpoint, for every 2-digit loop that exists in the solution grid it is unavoidable that a given for one of the digits must be provided for the puzzle to be solvable, and so they are called 2-digit Unavoidable Sets (UAs). (UAs for more than 2 digits also exist but these are of no use to solvers.)

Code: Select all

 *-------*-------*
 | a . . | b . . |
 | . . . | . . . |
 | . . b | . . a |
 *-------*-------*
 | b . . | a . . |
 | . . . | . . . |
 | . . a | . . b |
 *-------*-------*

This is an example of an UA which would take two loops to cover using links confined to rows and columns (the easiest way to explore them), but each one would only visit one cell in a box and the two loops would have to be taken together.