The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|2..|7.4|
 |...|.94|...|
 |6.4|.5.|1..|
 |---+---+---|
 |5..|...|21.|
 |...|821|...|
 |.91|...|..7|
 |---+---+---|
 |..2|.8.|6.9|
 |...|31.|...|
 |3.7|..2|...|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *--------------------------------------------------*
 | 19  b13  a9-3  | 2    6    8    | 7    5    4    |
 | 78   578  58   | 1    9    4    | 3    2    6    |
 | 6    2    4    | 7    5    3    | 1    9    8    |
 *----------------+----------------+----------------|
 | 5   b48  a68   | 46   7    9    | 2    1    3    |
 | 47   347 a36   | 8    2    1    | 9    46   5    |
 | 2    9    1    | 46   3    5    | 8    46   7    |
 *----------------+----------------+----------------|
 | 14  b14   2    | 5    8    7    | 6    3    9    |
 | 89   58   589  | 3    1    6    | 4    7    2    |
 | 3    6    7    | 9    4    2    | 5    8    1    |
 *--------------------------------------------------*


(9=368)r145c3 - (8=143)r147c2 => -3 r1c3 ; stte

Or

Code: Select all

 *--------------------------------------------------*
 |U19   13   39   | 2    6    8    | 7    5    4    |
 |U78  S578  58   | 1    9    4    | 3    2    6    |
 | 6    2    4    | 7    5    3    | 1    9    8    |
 *----------------+----------------+----------------|
 | 5  TV48   68   | 46   7    9    | 2    1    3    |
 | 47   347  36   | 8    2    1    | 9    46   5    |
 | 2    9    1    | 46   3    5    | 8    46   7    |
 *----------------+----------------+----------------|
 |U14   1-4  2    | 5    8    7    | 6    3    9    |
 |U89  T58   589  | 3    1    6    | 4    7    2    |
 | 3    6    7    | 9    4    2    | 5    8    1    |
 *--------------------------------------------------*

3 petal death blossom, stem [578]r2c2 => -4 r7c2 ; stte

Petal T [458]r48c2 ;     T-5 => -4 r7c2

Petal U [14789]r1278c1 ; U-7 => -4 r7c2

Petal V [48]r4c2 ;       V-8 => -4 r7c2



[Leren]

Code: Select all

*--------------------------------------------------------------*
| 19    13    39     | 2     6     8      | 7     5     4      |
| 8-7  b578   58     | 1     9     4      | 3     2     6      |
| 6     2     4      | 7     5     3      | 1     9     8      |
|--------------------+--------------------+--------------------|
| 5    b48    68     | 46    7     9      | 2     1     3      |
|a47    34-7  36     | 8     2     1      | 9     46    5      |
| 2     9     1      | 46    3     5      | 8     46    7      |
|--------------------+--------------------+--------------------|
| 14    14    2      | 5     8     7      | 6     3     9      |
| 89   b58    589    | 3     1     6      | 4     7     2      |
| 3     6     7      | 9     4     2      | 5     8     1      |
*--------------------------------------------------------------*

ALS XZ Rule: X = 4, Z = 7: (7=4) r5c1 - (4=7) r248c2 => - 7 r2c1, r5c2; stte

Leren

[pjb]

Code: Select all

 19      13     d39     | 2      6      8      | 7      5      4     
 8-7    *578    *58     | 1      9      4      | 3      2      6     
 6       2       4      | 7      5      3      | 1      9      8     
------------------------+----------------------+---------------------
 5       48      68     | 46     7      9      | 2      1      3     
a47      34-7   c36     | 8      2      1      | 9     b46     5     
 2       9       1      | 46     3      5      | 8      46     7     
------------------------+----------------------+---------------------
 14      14      2      | 5      8      7      | 6      3      9     
 89     *58     *589    | 3      1      6      | 4      7      2     
 3       6       7      | 9      4      2      | 5      8      1     


(7=4)r5c1 - (4=6)r5c8 - (6=3)r5c3 - (3=9)r1c3 - (9=7)UR:r28c23 => -7 r2c1, r5c2; stte

Phil

[gurth]

CW:

[Marty R.]

Code: Select all

+------------+--------+--------+
| 19 13  39  | 2  6 8 | 7 5  4 |
| 78 578 58  | 1  9 4 | 3 2  6 |
| 6  2   4   | 7  5 3 | 1 9  8 |
+------------+--------+--------+
| 5  48  68  | 46 7 9 | 2 1  3 |
| 47 347 36  | 8  2 1 | 9 46 5 |
| 2  9   1   | 46 3 5 | 8 46 7 |
+------------+--------+--------+
| 14 14  2   | 5  8 7 | 6 3  9 |
| 89 58  589 | 3  1 6 | 4 7  2 |
| 3  6   7   | 9  4 2 | 5 8  1 |
+------------+--------+--------+


Play this puzzle online at the Daily Sudoku site

(4=7)r5c1-(7=3418)r5714c2-(8=6)r4c3-(6=4)r4c4=>r4c2<>4

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 19    13    39     | 2     6     8      | 7     5     4      |
| 78   S578   58     | 1     9     4      | 3     2     6      |
| 6     2     4      | 7     5     3      | 1     9     8      |
|--------------------+--------------------+--------------------|
| 5   ba48    68     | 46    7     9      | 2     1     3      |
| 7-4  c347  c36     | 8     2     1      | 9    c46    5      |
| 2     9     1      | 46    3     5      | 8     46    7      |
|--------------------+--------------------+--------------------|
| 14    14    2      | 5     8     7      | 6     3     9      |
| 89   b58    589    | 3     1     6      | 4     7     2      |
| 3     6     7      | 9     4     2      | 5     8     1      |
*--------------------------------------------------------------*

3 Petal Death Blossom: Stem Cell r2c2 (578);

(4=8) r4c2   - (8) r2c2;

(4=5) r48c2  - (5) r2c2;

(4=7) r5c238 - (7) r2c2; => - 4 r5c1; stte

Leren

[bat999]

Hi
In gurth's answer above it seems to show too many red 4's in box 4.
I suppose that indicates the puzzle won't solve if there is a 1 in r1c2.
=> -1 r1c2; stte

I tried CW starting in r1c1.
The result is red and blue 8's in r4c2.
=> -4 r4c2; stte

cw.png (33.39 KiB) Viewed 876 times

[gurth]

Hi
In gurth's answer above it seems to show too many red 4's in box 4.
I suppose that indicates the puzzle won't solve if there is a 1 in r1c2.
=> -1 r1c2; stte

I tried CW starting in r1c1.
The result is red and blue 8's in r4c2.
=> -4 r4c2; stte

cw.png

Hi bat,
Colouring the conjugates alternately red and blue means you create two sets of equivalents: the red set and the blue. If one red is false, then all the reds are false and can be eliminated. And of course if two reds contradict each other, at least one of them must be false, so both, and all other red conjugates, are false.
Note that this does not apply to derived reds, which are simply truth markings conditional upon their colour being true. But there are no derived markings in this puzzle.

[bat999]

.. If one red is false, then all the reds are false and can be eliminated. And of course if two reds contradict each other, at least one of them must be false, so both, and all other red conjugates, are false.

Hi gurth
1 What do you mean by "false"?

2 OK, In this puzzle you are saying that because there are too many red 4's in box 4 (the contradiction) then you can automatically eliminate ALL the red circled candidates (not just the 1 from r1c2)?
(Though if you do remove just the 1 from r1c2 it seems that in this puzzle all the other red circles can then be eliminated one by one)

[Ngisa]

Code: Select all

+------------+--------+--------+
| i19 j13  k39  | 2  6 8 | 7 5  4 |
| g78 578 58  | 1  9 4 | 3 2  6 |
| 6  2   4   | 7  5 3 | 1 9  8 |
+------------+--------+--------+
| 5  48  a68  | b46 7 9 | 2 1  3 |
| f47 347 l3-6  | 8  2 1 | 9 e46 5 |
| 2  9   1   | c46 3 5 | 8 d46 7 |
+------------+--------+--------+
| 14 14  2   | 5  8 7 | 6 3  9 |
| h89 58  589 | 3  1 6 | 4 7  2 |
| 3  6   7   | 9  4 2 | 5 8  1 |
+------------+--------+--------+


(6)r4c3=r4c4-r6c4=r6c8-(6=4)r5c8-(4=7)r5c1-(7=8)r2c1-(8=9)r8c1-(9=1)r1c1-(1=3)r1c2-r1c3=(3)r5c3 => -6r5c3; stte

[daj95376]

alternatively BUG+3 => -3 r1c3; stte
(3=9)r1c3 => -9 r8c3
(3=9)r1c3 - (9=1)r1c1 - (1=4)r7c1 - (4=7)r5c1 => -7 r5c2
(3=9)r1c3 - (9=1)r1c1 - (1=4)r7c1 - (4=7)r5c1 - (7=8)r2c1 => -8 r2c2

???

I don't know what you are trying to show. At least one of { r2c2=8, r5c2=4, r8c3=8 } must be true.

_

[pjb]

daj95376 wrote:
I don't know what you are trying to show. At least one of { r2c2=8, r5c2=4, r8c3=8 } must be true.

I stuffed up here: I got confused and thought r5c2 had to equal 7. In any event, if this were true then r1c3 would have to equal 3 which again is wrong!!
Phil

[gurth]

.. If one red is false, then all the reds are false and can be eliminated. And of course if two reds contradict each other, at least one of them must be false, so both, and all other red conjugates, are false.

Hi gurth
1 What do you mean by "false"?

2 OK, In this puzzle you are saying that because there are too many red 4's in box 4 (the contradiction) then you can automatically eliminate ALL the red circled candidates (not just the 1 from r1c2)?
(Though if you do remove just the 1 from r1c2 it seems that in this puzzle all the other red circles can then be eliminated one by one)

Hi bat
1 By false I mean false - there is no clearer word than that. It means that a 'false' candidate an be eliminated (deleted) from the puzzle.

2 Yes. I am saying that. You need to understand the difference between Conjugate Reds (jreds) and Conditional Reds (ireds, ifreds). And mark this difference clearly in your diagram, otherwise you are not using CW, but some other variety of Extended or Simple Medusa.
In your solution, you have marked the 8r4c2 as blue, but that is not a jblue, it's an iblue derived from the jblue4r72, and should be marked differently.
The essential practical difference is this: if there is a contradiction in one colour, using both j and i markings, then all the j marked candidates of that colour can be removed, but none of the i marked ones. Because these may be true!
Note that no candidate can ever be both a jblue and a jred. If it is marked both red and blue, then one at least of those markings must be an i marking.

[JasonLion]

Another way to think about "false" is to view each pencil mark as a hypothesis that that pencil mark is part of the final solution. When you have proved or disproves each of the hypothesizes the puzzle will be solved (or proves insolvable).