The New Sudoku Players' Forum

[daj95376]

[Edit] Deleted comments on Forcing Chain/Nets in Arabian-Star puzzle.

[claudiarabia]

Code: Select all

4 . . . . . . . 9
. . . . 7 . . . .
. . 3 4 . 2 8 . .
. . 1 . . 9 6 . .
. 8 . . 3 . . 7 .
. . 2 5 . . 4 . .
. . 5 6 . 1 3 . .
. . . . 8 . . . .
9 . . . . . . . 2     Arabian Star

A star was born - I want to make it a present for you on my birthday.

Claudia

Thanks & Happy birthday !

Here is a modest gift :

(E5 : 3->6 or B5 : 8->6) => SE 8.4 -> 8.9

JPF

Thanxx and a happy Sunday for you

[gurth]

THE SNAKE below :

Code: Select all

 *-----------*
 |...|.98|7..|
 |...|3..|.6.|
 |..7|...|..5|
 |---+---+---|
 |..4|...|..1|
 |...|237|...|
 |6..|...|3..|
 |---+---+---|
 |3..|...|9..|
 |.5.|..1|...|
 |..2|58.|...|
 *-----------*


The shape appealed to me more than any other, the 8.3 rating sounded interesting... who is the composer? excuse me, I haven't followed this thread for long.

The steps:

(1) I used SSTS to reach this figure :

Code: Select all

 *--------------------------------------------------------------------*
 | 5      1246   3      | 146    9      8      | 7      124    24     |
 | 1248   1248   18     | 3      7      5      | 1248   6      9      |
 | 1489   14689  7      | 146    1246   246    | 148    3      5      |
 |----------------------+----------------------+----------------------|
 | 27     3      4      | 68     56     69     | 25     2789   1      |
 | 18     18     59     | 2      3      7      | 456    49     46     |
 | 6      27     59     | 148    145    49     | 3      289    278    |
 |----------------------+----------------------+----------------------|
 | 3      148    168    | 7      246    246    | 9      5      248    |
 | 478    5      68     | 9      246    1      | 24     2478   3      |
 | 49     479    2      | 5      8      3      | 146    14     467    |
 *--------------------------------------------------------------------*


(2) Then looking at the 7s, seeing they were all conjugate, I chose a cell with 4 candidates to try for a nice garnet : cell h8. I put ?-7h8, then only singles were required to disprove ?-7h8 by contradiction, then 7h8 was placed and only singles were required to complete the puzzle.

Showing that -7h8 was an excellent garnet.

Armed with that experience, I now decided to try for a Ruby : by starting a net with -7h8 at the very start.


This worked fine, the Ruby now being a spectacular candidate 7 in a 5-candidate cell, in a row containing five 7s, a column containing five 7s, and a box containing six 7s.

The ruby would have been even more precious if it could have done the job using singles only, as did the garnet. But in fact one set of locked candidates and one naked pair were also needed to disprove ?-7h8.
Once 7h8 was placed, only singles remained.

Considering the 8.3 rating of this puzzle, such a Ruby seems remarkable and I will call it THE Snake Ruby, or JPF's Snake Ruby, presuming JPF is the composer.

[gurth]

re: Star of Arabia

Claudia,
Thanks for the birthday present! For the most efficient solution I could find, I had to resort to REAL bifurcation, something I did not find necessary on any of the famed 11 "insolubles" concurrently in the news, nor even on Ocean's Pearl Brooch rated 9.7, nor on Ruud's #2/50000.

And it's a most lovely Pearl. I did not get the first cell till after the bifurcation (a test within a test). I even wonder whether improving the puzzle's rating might not even make it easier to solve. Computer ratings are only one sort of guide to the real difficulty !

Solution:

Code: Select all

 *-----------*
 |4..|...|..9|
 |...|.7.|...|
 |..3|4.2|8..|
 |---+---+---|
 |..1|..9|6..|
 |.8.|.3.|.7.|
 |..2|5..|4..|
 |---+---+---|
 |..5|6.1|3..|
 |...|.8.|...|
 |9..|...|..2|
 *-----------*


Step 1: SSTS, including Swordfish and Simple Colours, leading to this picture:

Code: Select all

*-----------------------------------------------------------------------------*
 | 4       12567   678     | 138     156     3568    | 1257    12356   9       |
 | 12568   1256    689     | 1389    7       3568    | 125     123456  13456   |
 | 1567    15679   3       | 4       1569    2       | 8       156     1567    |
 |-------------------------+-------------------------+-------------------------|
 | 357     3457    1       | 78      24      9       | 6       2358    358     |
 | 56      8       469     | 12      3       46      | 1259    7       15      |
 | 367     3679    2       | 5       16      78      | 4       1389    138     |
 |-------------------------+-------------------------+-------------------------|
 | 278     247     5       | 6       29      1       | 3       489     478     |
 | 12367   123467  467     | 29      8       3457    | 1579    1456    14567   |
 | 9       13467   678     | 37      45      3457    | 157     14568   2       |
 *-----------------------------------------------------------------------------*


Step 2: ? 2e4, SSTS not enough to prove anything, so discarded step.

Step 3: All the 9s make a conjugate chain, so:
? -9c2, SSTS not enough, but tired of discarding steps, so decided to bifurcate, especially as the 7s were now looking very inviting for such a move. I will now repeat this step from beginning to end, without interrupting myself with comments:

Step 3: ? -9c2, SSTS, ( ? -7a3, singles, ?? 7a3 ), singles, ?? 9c2, singles, naked pairs and singles to End.

Comment:
Such a simple bifurcation once again underlines the enormous power of Forcing Nets as a simple, efficient, versatile method.

I am almost starting to make it a principle of mine to use nothing more advanced than SSTS in my solutions and nets.
I aim to show everybody that even the hardest puzzles can be solved easily with a very modest array of techniques.

And we don't need to use computers for anything but the elementary spadework.
Angusj's Simple Sudoku program is absolutely quite enough when it comes to solving sudokus. We don't need and shouldn't want programs to give us Nice Loops, ALS, AIC, magic cells, and the like. For composing, well, maybe more is desirable.

[daj95376]

Comment:
Such a simple bifurcation once again underlines the enormous power of Forcing Nets as a simple, efficient, versatile method.

I am almost starting to make it a principle of mine to use nothing more advanced than SSTS in my solutions and nets.
I aim to show everybody that even the hardest puzzles can be solved easily with a very modest array of techniques.

I was informed awhile back that Forcing Nets are akin to Brute Force (or whatever else you want to call it). My post above included them purely as an example of just how far-reaching a Forcing Net on one cell can propogate.

[Carcul]

I aim to show everybody that even the hardest puzzles can be solved easily with a very modest array of techniques.

I think that was already showed some time ago. Pay attention to the posts. Also, using that method you have been using every puzzle can be solved, with more or less effort.

Carcul

[gurth]

GA04 : Closed Hat and Head

Code: Select all

  . . 3 6 . . . 9 .
  . 4 . . 5 . 8 . .
  5 . . . . 4 . . .
  6 . . . . 3 . . .
  . 7 . . 2 . . . .
  . . 8 9 . . 7 2 .
  . 5 . . . 8 . . 7
  3 . . . . 9 . . 6
  . . . . . . 2 4 .


An amusing shape. Note the head will just fit nicely into the hat.

It doesn't look too hard to me, you can go a little way with SSTS but then you need more.

Note also that this sudoku is an Octopus : only 8 digits are used as clues.



Two criticisms :
(1) The hat is closed, making it difficult to get onto the head.
(2) There is no pearl in sight.

Coming attraction : Open Hat and Head (Large Pearl).

[JPF]

Code: Select all

 . . 7 8 . . . 2 .
 . 1 . . 5 . 8 . .
 3 . . . . 9 . . .
 9 . . . . . . . .
 . 4 . . . . . . .
 . . 2 . . . 5 3 .
 . 9 . . . 1 . . 7
 6 . . . . 3 . . 2
 . . . . . . 1 4 .


pure gravel

Code: Select all

 . . 2 6 . . . 9 .
 . 9 . . 1 . 8 . .
 6 . . . . 7 . . .
 2 . . . . . . . .
 . 8 . . . 3 2 . .
 . . 9 . 7 . . 3 .
 . 1 . . 6 . . 5 .
 7 . . . . 2 9 . .
 . . . . . . . . .



pure 21-stepper Octopus
not so easy to solve...

and finally :

Code: Select all

 . 6 4 . . . . . .
 8 . . 7 . . . 1 .
 2 . . 8 . . 9 . .
 . 1 5 . . 8 . . .
 . . . . 9 . . . .
 . . . 4 . . 7 9 .
 . . 9 . . 3 . . 1
 . 7 . . . 4 . . 2
 . . . . . . 5 3 .


100 % minimal

JPF

[gurth]

JPF, a brilliant riposte, within minutes !
Gravel or not, my friend Jennifer and I had a great time solving it last night, doing it the hard way for a change, without computer to manage candidates or even commit worse crimes.

Every level of sudoku has its place! And methods.

[ravel]

JPF,

your shapes are unsurpassed.
And the last above has exactly the difficulty, my friend likes - thanx.

[JPF]

gurth, ravel

I am very flattered by your compliments. Thank you.
Happy that your friends appreciate these puzzles !

JPF

[ravel]

Happy that your friends appreciate these puzzles !

Nice breakfast puzzle, she says, needs more than basics, but no pencilmarks

[ronk]

I produced a an Arabian-Star-Puzzle in which you'll find a very symmetric Jellyfish.

Code: Select all

4 . . . . . . . 9
. . . . 5 . . . .
. . 3 4 . 2 8 . .
. . 1 . . 3 6 . .
. 8 . . 7 . . 5 .
. . 2 5 . . 4 . .
. . 5 6 . 1 3 . .
. . . . 8 . . . .
9 . . . . . . . 2

Very nice puzzle ... and the jellyfish has all 16 clues too. I noticed there is also a symmetric continuous coloring chain in 9s at the start.

Code: Select all

  .  .  . |  .  .  . |  .  .  .
  . -9  c |  9  .  9 |  .  .  .
  .  A  . |  .  a  . |  .  .  .   
----------+----------+----------
  .  9  . |  9 -9  . |  .  9  . 
  .  .  C | -9  . -9 |  d  .  . 
  .  9  . |  . -9  9 |  .  9  .   
----------+----------+----------
  .  .  . |  .  B  . |  .  b  .   
  .  .  . |  9  .  9 |  D -9  .
  .  .  . |  .  .  . |  .  .  .

 -r3c2=r3c5-r7c5=r7c8-r8c7=r5c7-r5c3=r2c3-r3c2=
 ... excluding 9s from r2c2, r46c5, r5c46 and r8c8

Due to the continuous nature of the chain, colors may be equated: a=b=c=d and A=B=C=D.

[JPF]

I produced a an Arabian-Star-Puzzle in which you'll find a very symmetric Jellyfish.

Code: Select all

4 . . . . . . . 9
. . . . 5 . . . .
. . 3 4 . 2 8 . .
. . 1 . . 3 6 . .
. 8 . . 7 . . 5 .
. . 2 5 . . 4 . .
. . 5 6 . 1 3 . .
. . . . 8 . . . .
9 . . . . . . . 2

interesting mutable cell in r9c1 : 9->6

Code: Select all

 4 . . . . . . . 9
 . . . . 5 . . . .
 . . 3 4 . 2 8 . .
 . . 1 . . 3 6 . .
 . 8 . . 7 . . 5 .
 . . 2 5 . . 4 . .
 . . 5 6 . 1 3 . .
 . . . . 8 . . . .
 6 . . . . . . . 2


JPF

[ronk]

interesting mutable cell in r9c1 : 9->6

Code: Select all

 4 . . . . . . . 9
 . . . . 5 . . . .
 . . 3 4 . 2 8 . .
 . . 1 . . 3 6 . .
 . 8 . . 7 . . 5 .
 . . 2 5 . . 4 . .
 . . 5 6 . 1 3 . .
 . . . . 8 . . . .
 6 . . . . . . . 2


Good one. Boosts the SE from 8.4 to 9.2!!

Here's a non-minimal full-symmetry (I think) "arabian star of 25-clues" and a 7.2 SE rating.

Code: Select all

 8 . . . . . . . 5
 . . . . 4 . . . .
 . . 4 6 . 7 9 . .
 . . 1 3 . 5 4 . .
 . 3 . . 6 . . 2 .
 . . 9 7 . 1 3 . .
 . . 5 8 . 3 7 . .
 . . . . 1 . . . .
 6 . . . . . . . 1