Gurth's Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Re: Extreme Jade

Postby Ocean » Thu Nov 09, 2006 8:43 pm

gurth wrote:I couldn't resist this Extreme Jade: my solution is posted on the Advanced Solution Techniques thread.

Thanks again!
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GB14 & GB15

Postby gurth » Wed Nov 15, 2006 9:19 am

.
GB14 : Another niner
Code: Select all
  . . 7 4 . . . . .
  . 9 . . 5 . . 1 .
  8 . . . . 6 3 . .
  4 . . . . . 7 . .
  . 5 . . . . . 8 .
  . . 6 . . . . . 9
  . . 2 7 . . . . 5
  . 3 . . 8 . . 4 .
  1 . . . . 9 2 . .    SE 9.1, Pearl 9.0, Turquoise 6.7

Just to show that I am still trying. The simplicity of the 456789 lines might lead you to guess that there's not much random generation going on here, and you will be right. I don't have the means to generate puzzles en masse, don't think I want to go in for that, but think I must realise I'm not likely to produce anything above 9.2 SE.

But maybe there is a niche for puzzles in the range 9.0 - 9.1

Carrying on next morning:
Keeping the 456789 lines, and carrying them around the corner even more symmetrically, and banishing the 123s entirely to the two non-456789 corner boxes, I arrive at GB15 below, my first 9.2 puzzle posted ( I have made a few more of 9.2 recently, but didn't bother to post them.)
Code: Select all
  . . 7 4 . . . . 2
  . 8 . . 5 . 3 . .
  9 . . . . 6 . 1 .
  4 . . . . . 7 . .
  . 5 . . . . . 8 .
  . . 6 . . . . . 9
  . 3 . 7 . . . . 4
  . . . . 8 . . 5 .
  1 . . . . 9 . . .      GB15: SE 9.2, Pearl 7.2, Turquoise 3.4

There WAS a 6k7, but I removed it as it was redundant. You can also put it back and then remove 7d7, getting a puzzle SE 9.1 but with Pearl 9.1 also.
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GB16

Postby gurth » Thu Nov 16, 2006 10:44 am

GB16 : SE 9.1, Pearl 8.3
Code: Select all
  9 . . 4 . . 1 . .
  . . 8 . 5 . . . 2
  . 7 . . . 6 . 3 .
  4 . . . . . 7 . .
  . 5 . . . . . 8 .
  . . 6 . . . . . 9
  . . . 7 . . . . .
  1 . . . 8 . 4 . .
  . . 2 . . 9 . . 6

Still keeping the 456789 lines.
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Postby JPF » Thu Nov 16, 2006 5:24 pm

Hi gurth,

I like the 456789 lines.

I propose this one, minimal, diagonal symmetric, SE = 9.0

Code: Select all
 8 . . 4 . . 1 . .
 . . 9 . 5 . . . 2
 . 7 . . . 6 . . .
 4 . . . . . 7 . .
 . 5 . . . . . 8 .
 . . 6 . . . . . 9
 1 . . 7 . . . 6 .
 . . . . 8 . 4 . .
 . 2 . . . 9 . . 5


5 mutable clues give SE = 9.1

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GB25 and GB27

Postby gurth » Mon Nov 27, 2006 9:25 am

GB25 : Another niner
Code: Select all
  . . 5 3 . . . . .
  6 . . . . 7 . . .
  . 8 . . 2 . . . .
  . . 4 1 . . 7 . .
  . 3 . . 6 . . 8 .
  9 . . . . 4 . . 5
  . . 2 . . 8 . . 9
  . 1 . 5 . . 6 . .
  7 . . . 9 . . 2 .   SE=9.0

Every time I try out a "new" idea, I end up with another niner, but I can never break the 9.2 barrier. Maybe one day I will get a better idea!

Meanwhile, I doubt whether there is any point in posting more of these rather unextraordinary puzzles. Or are they of use to someone?

In the above, 6b1 can be "touched" to 1b1, but it doesn't improve the rating.
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GB27 : A Jade Challenger

Code: Select all
  1 . . . 3 . . 4 .
  . 8 . . . . . 2 .
  . . 7 . . . . . .
  2 4 . 7 . 5 1 3 .
  . 1 . . 2 . 4 . .
  . . . 6 . . 5 . .
  . 3 . 1 . 6 . . 5
  4 2 . . . . 3 1 .
  . . . . . . . . .

One gets tired of everything, particularly diagonals. Hence the passion for Cartier. (If you don't follow me, study the " Original Rare Shapes" thread.)
Incidentally, I can't make ANY puzzle with that Cartier pattern, never mind a hard one.

Now I'm developing a more and more liking for jades. Remember, jades are easy to start, hard to finish. Minimal puzzles are definitely preferable. Here's a formula I've come up with to measure jades: Jade Rating = SE x (Number of uninterrupted singles that the puzzle starts with).

The above Jade has JR = 7.8 x 20 = 156.

Can anyone match that, either with their own or with any other puzzle?
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Postby RW » Mon Nov 27, 2006 10:12 am

gurth wrote:The above Jade has JR = 7.8 x 20 = 156.

Can anyone match that, either with their own or with any other puzzle?

7.1 x 23 = 163.3:
Code: Select all
 *-----------*
 |...|...|...|
 |5.3|...|...|
 |...|...|1.2|
 |---+---+---|
 |.1.|26.|9..|
 |.94|13.|...|
 |2..|..7|...|
 |---+---+---|
 |83.|67.|.1.|
 |...|..8|65.|
 |...|9..|...|
 *-----------*


[Edit: Oops, it's actually 21 x 7.1, the 22nd and 23rd singles require XY-wing, sorry]

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Postby RW » Mon Nov 27, 2006 3:26 pm

Here's a better one:
Code: Select all
 *-----------*
 |...|.71|32.|
 |...|...|.8.|
 |.61|5..|...|
 |---+---+---|
 |.7.|...|.9.|
 |.4.|...|.6.|
 |...|.86|51.|
 |---+---+---|
 |.2.|...|...|
 |.59|23.|...|
 |8..|...|...|
 *-----------*

7.2 x 29 = 208.8

I think the rating should be more favourable to harder puzzles. As it is now, any puzzle with 50 singles and then BUG+1 would score 280 points...

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Re: GB25 and GB27

Postby JPF » Mon Nov 27, 2006 10:32 pm

gurth wrote:A Jade Challenger

Here's one JR = 224 = 6.6 x 34

Code: Select all
 . . . | . 5 1 | 4 2 .
 . . . | . 4 . | . 8 .
 . 8 3 | 9 . . | . 1 .
-------+-------+-------
 . . . | . . . | . 9 .
 . 5 . | . . . | . 4 .
 . 7 . | . 2 9 | 5 . .
-------+-------+-------
 . 2 . | . 6 . | . . .
 . 6 5 | 4 8 . | . . .
 . . . | . . . | . . .


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Re: GB25 and GB27

Postby udosuk » Tue Nov 28, 2006 1:11 am

JPF wrote:Here's one JR = 224 = 6.6 x 34

6.6 x 34 = 224.4

IMHO for a jade to be interesting the minimum SE rating should be at least 7.5...
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Re: GB25 and GB27

Postby tarek » Tue Nov 28, 2006 1:49 am

udosuk wrote:IMHO for a jade to be interesting the minimum SE rating should be at least 7.5...

a starter.... (6*9.1=54.6)
Code: Select all
 . . 4 | 9 . . | 3 . . 
 . 6 . | . . 2 | . . . 
 5 . . | . 6 . | . . 8 
-------+-------+------
 . 7 . | . . . | . 1 . 
 . . 1 | . . . | 9 . . 
 6 . . | . . . | . . 2 
-------+-------+------
 2 . . | . 8 . | . . 5 
 . . . | . . 9 | . 8 . 
 . . 9 | 3 . . | 7 . .


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Re: GB25 and GB27

Postby JPF » Tue Nov 28, 2006 4:15 pm

udosuk wrote:IMHO for a jade to be interesting the minimum SE rating should be at least 7.5...
Where this 7.5 is coming from ? Is it a new sudoku's constant ?:)

gurth wrote:Can anyone match that, either with their own or with any other puzzle?

here’s one from the gfroyle’s list :

JR = 37 x 8.3 = 307.1

Code: Select all
 . . 6 | . 7 . | 4 5 .
 . 1 . | 8 . . | . . .
 . 2 . | . . . | . . .
-------+-------+-------
 7 . . | . 4 . | . . .
 4 . . | . . . | . 8 .
 . . . | . . . | . . 1
-------+-------+-------
 . 8 . | 2 . . | . . .
 3 . . | . . . | 7 . .
 . . . | 1 . . | . . .


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Re: GB25 and GB27

Postby udosuk » Wed Nov 29, 2006 1:39 am

JPF wrote:Where this 7.5 is coming from ? Is it a new sudoku's constant ?:)

Assuming 10 as the "full mark" (which is of course not true), 7.5 is just the 3rd quarter mark... I was originally thinking about 8.0 but that'd rule out gurth's 7.8x20 one as well...

JPF wrote:here’s one from the gfroyle’s list :

JR = 37 x 8.3 = 307.1

Excellent effort!:)
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Jade Ratings

Postby gurth » Wed Nov 29, 2006 9:26 am

JADE RATINGS

I see that my formula for rating jades needs to be revised.

My benchmark for jades must currently be Ocean's Extreme Jade(for gurth), and no known puzzle should exceed its jade rating. Unless that puzzle can gain acceptance as the new benchmark.

That means the formula must value high SE more, as RW suggested, and in practice it means also, I think, the exclusion of lower-SE puzzles from the stakes, as udosuk suggested, and tarek supported.

My new formula: JR=((SE-5)^2) * n (where n = number of uninterrupted and immediate singles from start). (SE-5) may not be negative, which excludes sub-SE 5 sudokus and cripples sub-6 ones. Puzzles should PREFERABLY be minimal, but this requirement is not as essential as it is for pearls.

Results:
Ocean's EJ(for g) ........ JR = 5.6 ^2 * 5 = 156.8
Tarek's "a starter" ...... JR = 4.1 ^2 * 6 = 100.9
Gurth's GB27 ............. JR = 2.8 ^2 *20 = 156.8
RW's "better one" ........ JR = 2.2 ^2 *29 = 140.4
JPF's "challenger" ....... JR = 1.6 ^2 *34 = 87.0

The above 5 sudokus form the nucleus of the jade family, being the ORIGINAL challengers, and will be noted in the Akashic records. (The unabridged and true history of the universe). The present formula depends on them. If we regard the constant 5 in the formula as f, then the formula can easily be adjusted to meet future demands by a simple change in f, to sustain the primacy of whatever benchmark is currently in favour.

To illustrate: if someone produces a puzzle of SE below 10 and JR above 156.8, and we don't consider it deserves to be the "benchmark', then we just raise f to the point where the new challenger fails to exceed the benchmark's rating (which will also go down). This will of course make the softer jades look even worse, but I see no way to help that. Udosuk won't mind, but I feel sorry for them.

It was merely wishful, thinking that so simple a formula as SE*n could do the trick. But a proliferation of rating systems is always advisable, so any ideas?

PS: DG Rossetti wrote "And the stars in her hair were seven" .
And the singles in your "better one" were 24, not 29 RW.
(Edit 30 November: No, RW was right, the singles WERE 29. My apologies, RW).

PPS: I've just seen the mind-blasting info about the puzzle SE 8.3 with 37 singles. Now the question becomes: which jade is better, Ocean's or this "newcomer"? What are your views? Will we have to abandon these formulae, or arrange separate categories of jade?
Last edited by gurth on Thu Nov 30, 2006 5:05 am, edited 1 time in total.
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Postby RW » Wed Nov 29, 2006 11:26 am

gurth wrote:And the singles in your "better one" were 24, not 29 RW.

Nope, there's 29. You can't use Explainer to count the singles, as it does "Direct Hidden Pair" before naked singles. After the first 24 singles there's a naked single in r6c3.

gurth wrote:What are your views? Will we have to abandon these formulae, or arrange separate categories of jade?

Maybe they should be divided into feather- (7.0+) welther- (8.0+), cruiser- (9.0+)and heavyweight (10.0+) series...

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Postby JPF » Wed Nov 29, 2006 12:36 pm

I’m not lucky.
Each time i propose a Jade, the JR definition is changing:(

Having said that :
N. Juillera wrote:More precisely, the Sudoku Explainer uses the following difficulty ratings of the solving techniques:
• 1.0: Last value in block, row or column
• 1.2: Hidden Single in block
• 1.5: Hidden Single in row or column
• 1.7: Direct Pointing
• 1.9: Direct Claiming
• 2.0: Direct Hidden Pair
• 2.3: Naked Single
• 2.5: Direct Hidden Triplet
• 2.6: Pointing
• 2.8: Claiming
• 3.0, 3.2, 3.4: Naked Pair, X-Wing, Hidden Pair
• 3.6, 3.8, 4.0: Naked Triplet, Swordfish, Hidden Triplet
• 4.2, 4.4: XY-Wing, XYZ-Wing
• 4.5 - 5.0: Unique rectangles and loops
• 5.0, 5.2, 5.4: Naked Quad, Jellyfish, Hidden Quad
• 5.6 - 6.0: Bivalue Universal Graves
• 6.2: Aligned Pair Exclusion
• 6.5 - 7.5: Bidirectioal X-Cycles and Y-Cycles
• 6.6 - 7.6: Forcing X-Chains
• 7.0 - 8.0: Forcing Chains, Bidirectional Cycles
• 7.5 - 8.5: Nishio
• 8.0 - 9.0: Cell/Region Forcing Chains
• 8.5 - 9.5: Dynamic Forcing Chains
• 9.0 - 10.0: Dynamic Forcing Chains (+)
• > 9.5: Nested Forcing Chains

It seems that the difficulties 1.2, 1.5, 1.7 and >= 2 correspond to the degrees 1, 2, 3 and 4 of some newspapers. Note that many solvers are rating Naked Singles easier than Hidden Singles (which is reasonable when candidates are always visible). According to some sources, "diabolical" Sudokus are those that are not solvable without trial and error. But there is a great controversy on what "trial and error" means.

The Sudoku generator uses the following levels:
• Easy: difficulty 1.0 to 1.2 (can be solved using Hidden Singles in blocks only)
• Medium: difficulty 1.5 (requires Hidden Singles in rows or columns)
• Hard: difficulty 1.7 to 2.5 (can be solved without writing down candidates)
• Fiendish: difficulty 2.6 to 6.0 (can only be solved by writing down candidates, but does not require Forcing Chains)
• Diabolical: difficulty 6.2 or more (can only be solved with Forcing Chains)
Note that many solvers and generators place Naked Single before Direct Pointing, Direct Claiming and Direct Hidden Pairs, unlike the Sudoku Explainer.

For me, what is fun in the “Jade” concept is that we get the impression for a long time that the puzzle is easy but, at the end, we are facing with real difficulties...

As you say :
gurth wrote:Meanwhile, I doubt whether there is any point in posting more of these rather unextraordinary puzzles. Or are they of use to someone?

We should leave the level of difficulties to The hardest sudokus thread.
For a human solver (at least for me) who cares that a Jade puzzle is SE = 6.2 ; 7 ; 8 ; 8.5 ; 9 or 20 ?

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