The New Sudoku Players' Forum

[tarek]

Code: Select all

+-------+-------+-------+
| . . . | 4 . . | . . . |
| . 8 1 | . 9 3 | . . . |
| . 4 5 | . . . | . . 2 |
+-------+-------+-------+
| 8 . . | . . 9 | . 6 . |
| . 1 . | . 6 . | . . 7 |
| . 9 . | 5 . 1 | . 3 . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | 1 . 7 | . 5 6 |
| . . 6 | . 5 . | . 7 9 |
+-------+-------+-------+
...4......81.93....45.....28....9.6..1..6...7.9.5.1.3.............1.7.56..6.5..79


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[Mauriès Robert]

Hi,
My resolution with TDP and two conjugated tracks :
P(5r4c2) : 5r4c2->5r5c7->9r5c8
P(5r5c1) : 5r5c1->7r4c2->7r6c5->8r5c4->(23r9c24->4r9c6->2r5c6)->9r5c8
=>r5c8=9, stte.
Robert

[Cenoman]

Code: Select all

 +---------------------+--------------------+-----------------------+
 |  2379   6    2379   |  4     127    5    |  13789   189   138    |
 |  27     8    1      |  267   9      3    |  67      4     5      |
 |  379    4    5      |  67    17     8    |  13679   19    2      |
 +---------------------+--------------------+-----------------------+
 |  8     b57   247-3  | c237  c2347   9    |  1245    6     14     |
 | a2345   1   a234    |  8-23  6    ca24   |  24589   289   7      |
 |  6      9    247    |  5     2478   1    |  248     3     48     |
 +---------------------+--------------------+-----------------------+
 |  1457   57   478    |  9     2348   6    |  12348   128   1348   |
 |  49     23   489    |  1     2348   7    |  2348    5     6      |
 |  14     23   6      |  238   5      24   |  12348   7     9      |
 +---------------------+--------------------+-----------------------+

(234=5)r5c136 - (5=7)r4c2 - (7=432)b5p126 => -23r5c4, -3r4c3; ste

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 | 2379   6      2379   | 4      127    5      |  13789  189    138    |
 | 27     8      1      | 267    9      3      |  67     4      5      |
 | 379    4      5      | 67     17     8      |  13679  19     2      |
 *----------------------+----------------------+-----------------------|
 | 8     b57     2347   | 237    2347   9      | a1245   6     a14     |
 | 2345   1      234    | 238    6      24     |  24589  289    7      |
 | 6      9     c247    | 5      247-8  1      |ac248    3    ac48     |
 *----------------------+----------------------+-----------------------|
 | 1457   57     478    | 9      2348   6      |  12348  128    1348   |
 | 49     23     489    | 1      2348   7      |  2348   5      6      |
 | 14     23     6      | 238    5      24     |  12348  7      9      |
 *---------------------------------------------------------------------*


(8=1245)b6p1379 - (5=7)r4c2 - (7=248)r6c379 => -8 r6c5 ; stte

[SteveG48]

(234=5)r5c136 - (5=7)r4c2 - (7=432)b5p126 => -23r5c4, -3r4c3; ste

Lovely!

[Mauriès Robert]

Hi Cenoman,
If I understood your resolution correctly, this is a Death Blossom?
Robert

[eleven]

To speak for me only: yes, you can call it a Dead Blossom (Cenoman's being one for 2 digits simultaneously), as well as Steve's solution.

Personally i just ignore DB's.
If the stem cell has only 2 candidates, you always can write it as an ALS-XY-wing (as was done here).
If it has 3, i always could handle it with an or (|) expression.

Samples for the latter, which i quickly found, were Hodukus ex. 2 and one by Mike Barker here
I would write them e.g. as
(5=269)r8c345 - (6|9=3)r7c6 - (3=2695)r8c3456 => -5r8c2
and
(7=1349)r7c1289 - (925=3|4)r9c139 - (34=7)r7c12 => 7r312
resp.

[added:] If i understood it right, Leren's way to find a 3 digit DB was to look if a candidate kills all 3 digits of a cell with an ALS.

There are also examples with 5 digit stem cells around. But i think all of them can be expressed in a simpler way like the last one on sudowiki there:
(1237=3|6)r6c2345 - (36=185)r5c456 - r5c1 = 5r6c1 => -7r6c1

[Cenoman]

Hi Cenoman,
If I understood your resolution correctly, this is a Death Blossom?
Robert

Hi Robert,
I'd just call that an ALS XY-wing (or ALS Y-wing)
To be very accurate, I'd rather call it ANS Y-wing (ANS: Almost Naked Set). Because of the double digit 2 & 3 elimination, I need to consider the Almost Naked Triples (234) in row 5 and box 5, and this is the reason why the "standard" Eureka writing of ALSs doesn't fit for my chain.

If you refer to the definition given by sudopedia here or by Andrew Stuart's here, you could call that a Death Blossom (of the two-petal species)

Personally, I use the name Death Blossom when the stem has at least three petals, as I did in the very recent example here

Added: I agree with eleven, that it's more elegant to write three-petal DBs as a chain with an OR (|) operator whenever it's possible. I failed to, in the link above...

[SpAce]

There are also examples with 5 digit stem cells around. But i think all of them can be expressed in a simpler way like the last one on sudowiki there:
(1237=3|6)r6c2345 - (36=185)r5c456 - r5c1 = 5r6c1 => -7r6c1

Even more simply as an ALS-XZ:

Code: Select all

.-------------------------.--------------------------.--------------------.
|  1378     5      1278   |  14789    1789      478  | 23489  6      2347 |
|  1378     9      4      |  2        1678      678  | 5      378    37   |
|  78       278    6      |  459      59        3    | 49     278    1    |
:-------------------------+--------------------------+--------------------:
|  6        3     b18(7)  |  14578    2         4578 | 18     158    9    |
| b1489'5  b1248  b1289   | a138     a1368     a68'5 | 7      12358  2356 |
|  158-7   b2(7)  b128(7) | a138[7]  a1368[7]   9    | 12368  4      2356 |
:-------------------------+--------------------------+--------------------:
|  2        148    3      |  5789     5789      578  | 146    157    4567 |
|  79       6      79     |  35       4         1    | 23     235    8    |
|  148      148    5      |  6        378       2    | 134    9      347  |
'-------------------------'--------------------------'--------------------'

(7=1368'5)b5p78456 - (5'12489=7)b4p415689 => -7 r6c1

Of course even that only makes sense if we're restricted to using the same cells as the Death Blossom. Otherwise this would be simpler:

(7=185)r4c378 - r6c9 = (5)r6c1 => -7 r6c1

[eleven]

Personally, I use the name Death Blossom when the stem has at least three petals, as I did in the very recent example here

Good example with 3 disjoint ALS's !
I only could see this:
(9278=1)r8c6789 - (17=8)r9c39 - (8=9)r3c9|r7c1
But in this case (and probably many others) i would prefer the DB ...

On second thought: maybe we just have to get more familiar with (fixed digits and) or'ed cells (as we are in the meantime with fixed cells and or'ed digits).

[SpAce]

Hi eleven,

I only could see this:
(9278=1)r8c6789 - (17=8)r9c39 - (8=9)r3c9|r7c1

On second thought: maybe we just have to get more familiar with (fixed digits and) or'ed cells (as we are in the meantime with fixed cells and or'ed digits).

Problem is, that notation is ambiguous. You'll see why if you reverse it. What you mean is this:

(9278=1)r8c6789 - (17=8)r9c39 - (8)r7c1&r3c9 = (9)r7c1|r3c9 => -9 r7c9

Thus, when the blue part is replaced with (8=9)r3c9|r7c1, the fact that the 8s are ANDed gets lost. It doesn't seem like a problem when read from left to right, but it becomes obvious the other way. So, as per current rules, that shortcut is incorrect, and I can't see a good way to make it work if the integrity and reversibility of the AIC are to be maintained.

I do agree that it's short and nice and perfectly understandable when read from left to right, but it also has a big downside. We've discussed this before with Steve and agreed that, while tempting, such an exception is not a good idea. I'm all ears if someone has opposite arguments.

Btw, here's another (ugly) possibility:

(9=8,87)r3c9,b7p19 - (8|7=1)r9c9 - (1=2789)r8c6789 => -9 r7c9

I followed your lead here for that first term. At first it seemed weird to reuse a digit within a bracketed node, but I don't think there's anything logically incorrect.

But in this case (and probably many others) i would prefer the DB ...

Me too, for any practical purposes. Cenoman's DB was very nice. That said, writing complex AICs is always fun. In fact, it's often more fun than reading them

[SteveG48]

To speak for me only: yes, you can call it a Dead Blossom (Cenoman's being one for 2 digits simultaneously), as well as Steve's solution.

Personally i just ignore DB's.
If the stem cell has only 2 candidates, you always can write it as an ALS-XY-wing (as was done here).
If it has 3, i always could handle it with an or (|) expression.

For what it's worth, a DB, regardless of the number of stem candidates, can always be written as an ALS chain if you don't mind it getting a bit awkward. Nevertheless, I find DBs with 3 or more stem cell candidates to be fun.