The New Sudoku Players' Forum

[bat999]

...Are you with me so far?

Yes, that's what happened in Leren's post above.
If r5c1 is 6 it knocks out the two sixes at r3c1, r5c3.
If r5c1 is 3 it puts a 6 into r1c3 (through the chain) to zap them.
I can see the two possible values for r5c1 and the same result.
That's OK.

I wasn't able to follow Steve's logic though.

I can see now the various ways to determine => -2 r1c5.
Steve chose to set up a chain and express it using Eureka notation, and I asked for an explanation because I couldn't follow it.

[eleven]

Code: Select all

 *--------------------------------------------------*
 | 4  TU13  T26   | 7   T23   5    | 6-1  8    9    |
 | 5    9    38   | 6    38   1    | 2    7    4    |
 | 168  78-1 267  | 9    28   4    | 16   3    5    |
 *----------------+----------------+----------------|
 | 18   5    189  | 3    79   6    | 4    2    17   |
 | 36  U37  S67   | 4    1    2    | 9    5    8    |
 | 2    4-1  149  | 5    79   8    | 3    6    17   |
 *----------------+----------------+----------------|
 | 13   6    13   | 8    4    7    | 5    9    2    |
 | 9    48   48   | 2    5    3    | 7    1    6    |
 | 7    2    5    | 1    6    9    | 8    4    3    |
 *--------------------------------------------------*


Stem [67]r5c3
Petal T: [1236]r1c235 (locked by stem 6)
Petal U: [137]r15c2 (locked by stem 7) => -1 r1c7,r36c2 ; stte

Bat, Steve's original post was not AIC (Eureka).
Notated in AIC it would be something like
(123=6)r1c235-(6=7)r5c3-(7=13)r15c2
So either 123 is in r1c235, implying 1r1c2 (and 3r1c5, 2r1c3), or 13 in r15c2, implying 1r1c2 (and 3r5c2) too.

[Added]
This is the long version of the same:
(1=3)r2c1-(3=2)r1c5-(2=6)r1c3-(6=7)r5c3-(7=3)r5c2-(3=1)r1c2

My suggested ABX notation:

A=r5c2, B=r5c3, X=r1c2
A<>7: r5c2=3->r1c2=1
B<>7: r5c3=6->r1c3=2->r1c5=3->r1c2=1
=>r1c2=1

If you inverse the first line (A=>B is equivalent to (not B) => (not A)), you get
r1c2<>1 => r5c2<>3 => A=7, this implies
B<>7 => r5c3=6->r1c3=2->r1c5=3->r1c2=1
Written as AIC:
(1=3)r1c2-(3=7)r5c2-(7=6)r5c3-(6=2)r1c3-(2=3)r1c5-(3=1)r2c1
So you get the same, just read from right to left.

So we have the same logic in 4 notations.

[DonM]

The first Death Blossom that I've ever picked:

Code: Select all

 *--------------------------------------------------*
 | 4  TU13  T26   | 7   T23   5    | 6-1  8    9    |
 | 5    9    38   | 6    38   1    | 2    7    4    |
 | 168  78-1 267  | 9    28   4    | 16   3    5    |
 *----------------+----------------+----------------|
 | 18   5    189  | 3    79   6    | 4    2    17   |
 | 36  U37  S67   | 4    1    2    | 9    5    8    |
 | 2    4-1  149  | 5    79   8    | 3    6    17   |
 *----------------+----------------+----------------|
 | 13   6    13   | 8    4    7    | 5    9    2    |
 | 9    48   48   | 2    5    3    | 7    1    6    |
 | 7    2    5    | 1    6    9    | 8    4    3    |
 *--------------------------------------------------*


Stem [67]r5c3
Petal T: [1236]r1c235 (locked by stem 6)
Petal U: [137]r15c2 (locked by stem 7) => -1 r1c7,r36c2 ; stte

I don't know, what a Death Blossom is. While Andrew Stuart starts from a single "stem" cell, there is none in the example by Mike Barker, who gave the technique the name.

To me, a Death Blossom is just a special case of a Kraken cell solution in which each of the links from one of the "stem" (Kraken) cell candidates to the target is a single ALS (petal) locked if the candidate is set in the stem cell. I think that's what Mike Barker says.

In the early days of sudoku, it was typical to assign names to patterns that later turned out to be simply a subset of broader patterns. The great majority of Death Blossom patterns are nothing more than a 3 set ALS chain (aka ALS xy-chain) where the middle ALS set is a bivalue cell (ie. the simplest form of ALS). So, your solution could be notated (where the bivalue cell is underlined for clarity):

als(1=236)r1c235-(6=7)-als(7=13)r15c2 => -1r1c7, -1r36c2

That said, it was clever that you apparently saw this as a visual pattern where each digit of the bivalue cell could lock the respective ALSs giving a common result. If viewed as an ALS chain, this one is clever in that there is overlap of the 2 ALSs at r1c2.

Where the Death Blossom waters have been muddied is that very occasionally (thankfully) what is nothing more than an AAIC/Kraken cell has also been called a Death Blossom.

My own opinion is that, while the Death Blossom moniker is attractive, it gives the false impression that it is unique pattern. Fwiw: the first 3 graphics in the following thread illustrate Death Blossoms as what they are: 3-set ALS chains:

http://forum.enjoysudoku.com/advanced-als-chains-a-tutorial-asi-3b-t30098.html

[blue]

Where the Death Blossom waters have been muddied is that very occasionally (thankfully) what is nothing more than an AAIC/Kraken cell has also been called a Death Blossom.

My own opinion is that, while the Death Blossom moniker is attractive, it gives the false impression that it is unique pattern. Fwiw: the first 3 graphics in the following thread illustrate Death Blossoms as what they are: 3-set ALS chains

That's an interesting take on things.

My view is exactly the opposite -- that a DB with only two petals, is just an ALS chain, and it should be written as such.
For me, a "proper" DB, has 3+ petals, and its main feature is that it offers a pattern-based interpretation for what would otherwise be a network elimination (a Kraken-cell in particular).

Cheers,
Blue.

[eleven]

I agree with blue, that these 3+ cases are more interesting and would justify an own name.
But to call it a pattern is misleading. You cannot spot them like a UR or a swordfish. Their appearances are as different as networks. (And at least i do not test 3+ value or Kraken cells to find one - maybe the other way round could work: you could notice that a candidate locks 3 ALS's, which then kill all candidates of a cell or all possibilities of a digit in a house)

[DonM]

I'm simply pointing out (as I have for years) that, by far, the most posted Death Blossoms are nothing more than an ALS chain with a bivalue cell in the middle. That's a simple fact (see below). If I have any opinion at all on the matter, it is that giving this latter pattern a particular name (ie. Death Blossom) creates the illusion that it is a distinct pattern vs. a 3-set ALS chain. To see what is the most common definition of a DB given, take a look at almost any of the graphic examples given on a Google search. Here are 2 just for the heckofit:

http://www.sudokuwiki.org/Death_Blossom
http://www.sudoku9981.com/sudoku-solving/death-blossom.php

I agree with Blue that a 3 digit stem cell would make for a more distinctive/unique pattern, but I also agree with Eleven (or not if I'm mistaking his point) that, then, you end up potentially with other net-like constructs (eg. AAIC/Kraken cell) which could muddy the definition.

[blue]

(...) by far, the most posted Death Blossoms are nothing more than an ALS chain with a bivalue cell in the middle. That's a simple fact (see below).

No doubt about that, much to my disappointment

[ I followed eleven's link in an earlier post in this thread, and did a search for related posts from Mike Barker (today), and I was totally amazed (and disheartened) at the things that were being called Death Blossoms. ]

I've looked before, at the definitions at SudoWiki, Hodoku, and the Sudopedia Mirror.
Only one example has 3+ petals -- the 2nd Hoduko example here -- and (today) I realize that its elimination can be gotten with a very short ALS-chain (ALS-XZ): (5=9)r8c345 - (9=5)r78c6,r8c4 => -5r8c2.

For the Jan 21 puzzle, I called something a "death blossom". I don't think the elimination can be gotten with a (fairly short) chain, and it does have 3 ALS petals, and so I guess I'll stand by my call -- but it uses "stringy" ALS's, that could just as well have been XY-chains in a Kraken-cell presentation.

Best Regards,
Blue.

[Leren]

Here were two 2 petal Death Blossom's that I found in this puzzle:

Code: Select all

*--------------------------------------------------------------*
| 4    S13    26     | 7     23    5      | 16    8     9      |
| 5     9    a38     | 6     38    1      | 2     7     4      |
| 168   17-8  267    | 9     28    4      | 16    3     5      |
|--------------------+--------------------+--------------------|
| 18    5     189    | 3     79    6      | 4     2     17     |
| 36    37    67     | 4     1     2      | 9     5     8      |
| 2    b14    149    | 5     79    8      | 3     6     17     |
|--------------------+--------------------+--------------------|
| 13    6     13     | 8     4     7      | 5     9     2      |
| 9    b48    48     | 2     5     3      | 7     1     6      |
| 7     2     5      | 1     6     9      | 8     4     3      |
*--------------------------------------------------------------*

2 Petal Death Blossom: Stem Cell r1c2 {13}; (8=3) r2c3 - (3) r1c2 | (8=1) r68c2 - (1) r1c2 | => - 8 r2c2

*--------------------------------------------------------------*
| 4    S13  ba26     | 7    a23    5      | 16    8     9      |
| 5     9     38     | 6     38    1      | 2     7     4      |
| 8-6  b17   b267    | 9     28    4      | 16    3     5      |
|--------------------+--------------------+--------------------|
| 18    5     189    | 3     79    6      | 4     2     17     |
| 36    37    67     | 4     1     2      | 9     5     8      |
| 2     4     19     | 5     79    8      | 3     6     17     |
|--------------------+--------------------+--------------------|
| 13    6     13     | 8     4     7      | 5     9     2      |
| 9     8     4      | 2     5     3      | 7     1     6      |
| 7     2     5      | 1     6     9      | 8     4     3      |
*--------------------------------------------------------------*

2 Petal Death Blossom: Stem Cell r1c2 {13}; (6=3) r1c35 - (3) r1c2 | (6=1) r1c3, r3c23 - (1) r1c2 | => - 6 r3c1

but as has been said by others, a 2 petal Death Blossom is just an ALS XY Wing with the second ALS being a bi-value cell (the stem cell in the Death Blossom), so I only post 3 Petal versions. In fact, the first one is also just an XY chain.

BTW can anyone provide an example of a 4 petal Death Blossom? They must be quite rare.

Leren

[DonM]

...but as has been said by others, a 2 petal Death Blossom is just an ALS XY Wing with the second ALS being a bi-value cell (the stem cell in the Death Blossom), so I only post 3 Petal versions.

Leren

A 2 petal Death Blossom is an ALS XY Chain. The bi-value cell is also an ALS.

[eleven]

If you want, you can call that a 3-petal DB in this puzzle:

Code: Select all

*--------------------------------------------------------------*
| 4    a13    26     | 7     23    5      | 16    8     9      |
| 5     9   ab38     | 6     38    1      | 2     7     4      |
|S168   17-8  267    | 9     28    4      | 16    3     5      |
|--------------------+--------------------+--------------------|
|S18    5     189    | 3     79    6      | 4     2     17     |
|c36    37    67     | 4     1     2      | 9     5     8      |
| 2     14    149    | 5     79    8      | 3     6     17     |
|--------------------+--------------------+--------------------|
|S13    6    b13     | 8     4     7      | 5     9     2      |
| 9     48    48     | 2     5     3      | 7     1     6      |
| 7     2     5      | 1     6     9      | 8     4     3      |
*--------------------------------------------------------------*

The 1 in column 1 can be in r347:
1r3c1 - (1=38)r2c1,r2c3 - 8r3c2
1r4c1 - (1=368)r357c1 - 8r3c2
1r7c1 - (1=38)r27c3 - 8r3c2

{Edit: corrected typos]

[blue]

If you want, you can call that a 3-petal DB in this puzzle:

Some typos in that ...

The 1 in column 1 can be in r347:
1r3c1 - (1=38)r2c1,r2c3 - 8r3c2
1r4c1 - (1=368)r357c1 - 8r3c2
1r7c1 - (1=38)r27c3 - 8r3c2

Is it really a "Death Blossom", or is it a "Kraken Blossom" ?
[ The actual definitions that I've seen for Death Blossom, only allow for a stem cell. ]

You can also avoid any "issues" with 1r4c1 (regarding its interactiion with 1r35c1 in the "stem" to make the LS), by replacing the middle line with:

1r4c1 - (1=48)r68c2 - 8r3c2

Nice !

[eleven]

Thanks blue, for pointing out all the typos (oops).

I don't see an essential difference between a stem cell and Kraken cells (both provide a SIS like for old-style forcing chains). Also extra candidates of a UR would be nice for that ...
But i think it is too late to make new definitions, what a Death Blossom is or not.

Another point is, that we don't need it. It is just a special - and nice - case of AIC or Kraken chains.