The New Sudoku Players' Forum

[Yogi]

..6...93..1.7.4............8.9...7.....1.....2.........4......2....9..8.7...6....

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+---+---+---+
|..6|...|93.|
|.1.|7.4|...|
|...|...|...|
+---+---+---+
|8.9|...|7..|
|...|1..|...|
|2..|...|...|
+---+---+---+
|.4.|...|..2|
|...|.9.|.8.|
|7..|.6.|...|
+---+---+---+


[pjb]

Code: Select all

 5       7       6      | 8      2      1      | 9      3      4     
 9       1       2      | 7      3      4      | 8      56     56     
 3       8       4      | 69     5      69     | 2      7      1     
------------------------+----------------------+---------------------
 8       356     9      |g356    4      2      | 7      1     h356   
 4       356     7      | 1      8     f356    |e35     2      9     
 2       356     1      | 3569   7      3569   | 4      56     8     
------------------------+----------------------+---------------------
 6       4       8      |c35     1      7      |d35     9      2     
 1       2      a35     | 4      9     b35     | 6      8      7     
 7       9       5-3    | 2      6      8      | 1      4     i35     


(3=5)r8c3 - (5=3*)r8c6 - (3=5^)r7c4 - (5=3)r7c7 - (3=5)r5c7 - (5|3*=6)r5c6 - (6|5^=3)r4c4 - (3)r4c9 = (3)r9c9 => -3 r9c3; stte

Phil

[jco]

One would say: not that thing again!
My apologies for what follows (not much fun).

After basics

Code: Select all

.------------------------------------------.
| 5  7    6  | 8     2  1    | 9   3   4   |
| 9  1    2  | 7     3  4    | 8   56  56  |
| 3  8    4  | 69    5  69   | 2   7   1   |
|------------+---------------+-------------|
| 8  356  9  | 356   4  2    | 7   1   356 |
| 4  356  7  | 1     8  356  | 35  2   9   |
| 2  356  1  | 3569  7  3569 | 4   56  8   |
|------------+---------------+-------------|
| 6  4    8  | 35    1  7    | 35  9   2   |
| 1  2    35 | 4     9  35   | 6   8   7   |
| 7  9    35 | 2     6  8    | 1   4   35  |
'------------------------------------------'

Letting X be the correct digit at r9c3, Y the correct digit at r8c3,
we must have

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.------------------------------------------.
| 5  7    6  | 8     2  1    | 9   3   4   |
| 9  1    2  | 7     3  4    | 8   XY6 X6  |
| 3  8    4  | 69    5  69   | 2   7   1   |
|------------+---------------+-------------|
| 8  XY6  9  | X6    4  2    | 7   1   X6  |
| 4  XY6  7  | 1     8  Y6   | Y   2   9   |
| 2  XY6  1  | X69   7  Y69  | 4   X6  8   |
|------------+---------------+-------------|
| 6  4    8  | Y     1  7    | X   9   2   |
| 1  2    Y  | 4     9  X    | 6   8   7   |
| 7  9    X  | 2     6  8    | 1   4   Y   |
'------------------------------------------'

Looking at r2c9, we infer that X=5, so Y=3
and only singles remain (r2c8=6,r5c6=6,r4c9=6,etc).

Edit: This is not correct (a wrong shortcut I saw while editing the solution).
Many thanks to marek stefanik for pointing this out.
Correction in my next post (starts with r5c6=6, etc)

[SteveG48]

Code: Select all

 *--------------------------------------------------------------*
 | 5     7     6     |   8     2     1     |  9     3     4     |
 | 9     1     2     |   7     3     4     |  8     56    56    |
 | 3     8     4     |   69    5     69    |  2     7     1     |
 *-------------------+---------------------+--------------------|
 | 8    g356   9     |efh356   4     2     |  7     1    g56-3  |
 | 4     356   7     |   1     8   ef356   |gh35    2     9     |
 | 2     356   1     |   3569  7     3569  |  4     56    8     |
 *-------------------+---------------------+--------------------|
 | 6     4     8     |cd35    1     7      | b35    9     2     |
 | 1     2     35    |   4     9    d35    |  6     8     7     |
 | 7     9     35    |   2     6     8     |  1     4    a35    |
 *--------------------------------------------------------------*


3r9c9 = r7c7 - 3r7c4 = (5,3)b8p16 - (5r4c4)|(3r5c6) = (3r4c4)|((6,5)b5p16) - (3r4c29)&(5r5c7) = 3r4c4,r5c7 => -3 r4c9 ; stte

[P.O.]

Code: Select all

after singles + intersection:

5     7     6     8        2     1         9      3     4             
9     1     2     7        3     4         8      56    56             
3     8     4     69       5     69        2      7     1             
8     356   9    e-3(-5+6) 4     2         7      1    d+356           
4     356   7     1        8    f(+3-5)-6 c-3(+5) 2     9             
2     356   1     3569     7     3569      4      56    8             
6     4     8    a-3(+5)   1     7        b+3-5   9     2             
1     2     35    4        9     35        6      8     7             
7     9     35    2        6     8         1      4     35   

depth: 3  candidate: 3  from cells
(((4 4 5) (3 5 6)) ((6 4 5) (3 5 6 9)) ((8 6 8) (3 5)))

((3 0) (7 4 8) (3 5))          if R7C4 is not 3
((3 0) (7 7 9) (3 5))          R7C7 is 3
((3 1 1) (4 9 6) (3 5 6))      R4C9 is 3
((6 2 102) (4 4 5) (3 5 6))    R4C4 is 6 from a pair (e a)
((3 3 101) (5 6 5) (3 5 6))    R5C6 is 3 from a pair (f c)

ste.


[marek stefanik]

-5r2c8 (otherwise 35 would be unresolvable in the rest of the grid), stte

Does anyone know what the technique is called?

Looking at r2c9, we infer that X=5, so Y=3

I don't think that's correct, if 6 were true in that cell, both 5 and X would be false. How would you then know they're the same digit?

Marek

[jco]

-5r2c8 (otherwise 35 would be unresolvable in the rest of the grid), stte

Does anyone know what the technique is called?

Looking at r2c9, we infer that X=5, so Y=3

I don't think that's correct, if 6 were true in that cell, both 5 and X would be false. How would you then know they're the same digit?

Marek

Thanks for this observation. Originally I had

Code: Select all

.-----------------------------------------.
| 5  7    6  | 8    2  1    | 9   3   4   |
| 9  1    2  | 7    3  4    | 8   XY6 X6  |
| 3  8    4  | 69   5  69   | 2   7   1   |
|------------+--------------+-------------|
| 8  XY6  9  | X6   4  2    | 7   1   X6  |
| 4  XY6  7  | 1    8  Y6   | Y   2   9   |
| 2  XY6  1  | X69  7  Y69  | 4   X6  8   |
|------------+--------------+-------------|
| 6  4    8  | Y    1  7    | X   9   2   |
| 1  2    Y  | 4    9  X    | 6   8   7   |
| 7  9    X  | 2    6  8    | 1   4   Y   |
'-----------------------------------------'

due to r7c5=Y, r5c6=6 and after some eliminations

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.-------------------------------------.
| 5  7   6  | 8   2  1  | 9   3   4   |
| 9  1   2  | 7   3  4  | 8   Y6  X   |
| 3  8   4  | 6   5  9  | 2   7   1   |
|-----------+-----------+-------------|
| 8  Y   9  | X   4  2  | 7   1   6   |
| 4  X   7  | 1   8  6  | Y   2   9   |
| 2  6   1  | 9   7  Y  | 4   X   8   |
|-----------+-----------+-------------|
| 6  4   8  | Y   1  7  | X   9   2   |
| 1  2   Y  | 4   9  X  | 6   8   7   |
| 7  9   X  | 2   6  8  | 1   4   Y   |
'-------------------------------------'

Looking at block b3, r2c8=6 (only 6 in the row/column/box).
Thus, X=5, Y=3 and the puzzle is solved.

Unfortunately, while editing the solution I thought there was that (wrong) shortcut.
Again, thanks for pointing this out.
The older post using this approach that I have found (searching for "ABC") is this (eleven).

Edit2: removed unnecessary references, since misunderstood previous question.

[Leren]

Code: Select all

*----------------------------------------*
| 5 7    6  | 8    2  1     | 9  3   4   |
| 9 1    2  | 7    3  4     | 8  56  56  |
| 3 8    4  | 69   5  69    | 2  7   1   |
|-----------+---------------+------------|
| 8 356  9  | 356  4  2     | 7  1   356 |
| 4 356  7  | 1    8  6-35  |A35 2   9   |
| 2 356  1  | 3569 7  35-69 | 4  56  8   |
|-----------+---------------+------------|
| 6 4    8  |A35   1  7     |B35 9   2   |
| 1 2   A35 | 4    9 B35    | 6  8   7   |
| 7 9   B35 | 2    6  8     | 1  4  A35  |
*----------------------------------------*

Remote Pairs (35) => - 35 r5c6, - 69 r6c6; singles

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*--------------------------------------*
| 5  7     6  | 8  2  1  | 9  3   4    |
| 9  1     2  | 7  3  4  | 8  56  56   |
| 3  8     4  | 6  5  9  | 2  7   1    |
|-------------+----------+-------------|
| 8  356   9  |A35 4  2  | 7  1   6-35 |
| 4 A35    7  | 1  8  6  |B35 2   9    |
| 2  6-35  1  | 9  7 B35 | 4  56  8    |
|-------------+----------+-------------|
| 6  4     8  |B35 1  7  |A35 9   2    |
| 1  2    B35 | 4  9 A35 | 6  8   7    |
| 7  9    A35 | 2  6  8  | 1  4  B35   |
*--------------------------------------*

Remote Pairs (35) => - 35 r4c9, r6c2; stte

Leren

[denis_berthier]

.

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Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 5    7    6    ! 8    2    1    ! 9    3    4    !
   ! 9    1    2    ! 7    3    4    ! 8    56   56   !
   ! 3    8    4    ! 69   5    69   ! 2    7    1    !
   +----------------+----------------+----------------+
   ! 8    356  9    ! 356  4    2    ! 7    1    356  !
   ! 4    356  7    ! 1    8    356  ! 35   2    9    !
   ! 2    356  1    ! 3569 7    3569 ! 4    56   8    !
   +----------------+----------------+----------------+
   ! 6    4    8    ! 35   1    7    ! 35   9    2    !
   ! 1    2    35   ! 4    9    35   ! 6    8    7    !
   ! 7    9    35   ! 2    6    8    ! 1    4    35   !
   +----------------+----------------+----------------+

No need for anything complicated ("relabelling" or long chains):
finned-x-wing-in-columns: n5{c7 c4}{r7 r5} ==> r5c6 ≠ 5
finned-x-wing-in-columns: n3{c7 c4}{r7 r5} ==> r5c6 ≠ 3
singles ==> r5c6 = 6, r3c6 = 9, r3c4 = 6, r6c4 = 9
finned-x-wing-in-columns: n3{c4 c9}{r4 r7} ==> r7c7 ≠ 3
stte

BTW, "relabelling" is a very bad name for this technique, it's much more than relabelling. Relabelling means replacing some digits by other digits in a well determined way, which is not the case in this technique.

If you absolutely want a 1-step solution, it requires at least a whip[5] - absurd considering the elementary solution above - e.g.:

Code: Select all

whip[5]: r5c7{n3 n5} - r7n5{c7 c4} - r8c6{n5 n3} - r5c6{n3 n6} - r4c4{n6 .} ==> r4c9 ≠ 3
stte

[denis_berthier]

-5r2c8 (otherwise 35 would be unresolvable in the rest of the grid), stte
Does anyone know what the technique is called?

T&E. Nishio if you restrict it to considering only digit 5.

[marek stefanik]

It has nothing to do with T&E, it's based on uniqueness.

It looks like an extended UR (35r123c158), except instead of including no given it includes all of them.
In the rest of the grid 35 would be interchangeable (provided there were a solution).

Marek

[denis_berthier]

You didn't describe your technique apart from saying "-5r2c8 otherwise 35 would be unresolvable in the rest of the grid".
It means literally "if I suppose n5r2c8 is True, then I get I get a contradiction". This is T&E (or T&E(XX), where XX is some undefined set of rules, uniqueness in your case). Now, there may be other ways of presenting your reasoning, e.g. as some chain, but this is not what you did.

[marek stefanik]

"If I suppose n5r2c8 is True, then I get a contradiction". This is...

...whip[1]. But I'm sure there is a name more descriptive of the contradiction used.

[denis_berthier]

"If I suppose n5r2c8 is True, then I get a contradiction". This is...

...whip[1]. But I'm sure there is a name more descriptive of the contradiction used.

There's no whip[1] that could eliminate n5r2c8.
If there was one, I don't see how it could be "not perfectly descriptive of the contradiction".

[marek stefanik]

There are no CSP variables for uniqueness contradictions, which makes it impossible to write it as a whip.
However, it's a candidate causing an immediate conflict, much like in a whip[1].

I said what candidate it was and then described the contradiction.
I don't know what else I should have done...