## an elementary solution of platinium blonde

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### an elementary solution of platinium blonde

rows:a,b,..;columns:1,2,...; 3d1 means d1=3
3d1,2d5,2h4 gives a solution.
Idea: pair (2,3) in row d and block 4 suggest to try to eliminate some 2 and 3 in these two units.
d1 and d2 are in their intersection. So try 3d1 and check all the 2 in row d:
2d2 or 2d8 contradiction (denoted C)
2d7,9e9 or1e9 C
2d6,2b4 or 2h4 C
2d6,2I4,5a1 or7 a1 or 8a1 C
2d5,2b4 C
2d5, 2I4,2e8 or 3e8 C
Solution obtained by hand (trial on potentialy intersting number and elementary technics including triplets)
checked on Bob Hanson solver (which works adding 3d1) and Andrew Stuart solver (which works adding 3d1,2d5)
unicity:analogous trials eliminate d1=2
in order to eliminate d1=7 it may be intersting to show that 2 and 3 are neither in d2 (giving a triplet 349)
nor in d7 (separating 123 from 679)
jb69

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Joined: 16 February 2016

### Re: an elementary solution of platinium blonde

What you describe here is one example of the "brute force" efficiency.

Yes it works (for any puzzle).

The trick in the wording is in that question :

How long does it take to see one contradiction and how could it be explained "logically".

Years ago, on such puzzles, several players (among them "ttt" ) draw very complex nets doing the same in specific conditions.

To day, players focus on puzzles having short solutions, sometimes using more complex logical steps.

Platinium blonde is one example of such puzzles if you consider the Exocet Properties.
champagne
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### Re: an elementary solution of platinium blonde

Thank you for your comments. I believe that brute force has bad press in the sudoku community! I'll try to explain my point of view.
I solve sudokus with pencil and papers (sometimes a lot of) and had used tough to extreme strategies ( AS terminology)
but I changed my technique.Some points:
1) inference chains are hypothesis
2)the natural (and trivial) idea of "potentialy intersting number" is used in chains (where does begin the chain?). Well choosen numbers give interesting information.The difference is the tools you allow to use:
a "linear" graph in the casse of a chain; a whole graph in my case.
3)The family of graphs being larger than that of chains is a potentialy stronger tool. You may sometimes deduce from an inferences graph , even not fully developped, ideas of inferences chains.
4)so "potentialy intersting number" is not more "brute force" than "classical" techniques.
5) regarding platinium blonde (PB) plus d1=3, not solved by AS solver and solved by BH solver with a difficult step 9 not in c8 "hypothesis and disproof"
my solution uses only 13 resolutions of elementary sudokus.
6)regarding PB, if you assumes unicity luck has his part to play. In my case I found first no 2 and no 3 in d2 and tried 3 in d1...
If you want to prove that there is no other solution the total number of elementary sudokus is around 45.
I believe this point to be quite general for very hard sudokus
7) if you have a "short solution" of PB by classical means I am interested.
jb69

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Joined: 16 February 2016

### Re: an elementary solution of platinium blonde

jb69, as Champagne has mentioned there is a JExocet+ pattern in Platinum Blonde. This is an advanced pattern which is described over several posts in the JExocet Compendium thread.

This is the grid after the pattern eliminations have been made
.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... Platinum Blonde
Code: Select all
` *------------------------------*------------------------------*---------------------* | 3568       3458      3467:9. | 467.9:   568        4:58     | 79    <1>    <2>    | | 1568       1458      467:9.  | 12467.9: 12568      124:58   | 79    568    <3>    | | 1:5:6:7†8: 1.5.8.9‡  <2>     | <3>      1:5:6:8:9† 1.5.7‡8. | <4>   568    68     | *------------------------------*------------------------------*---------------------* | 2.3.7‡     2:3:4:9†  <1>     | <8>      236        2:3:4'   | 236   7†9‡   <5>    | | 235        <6>       3.4.9‡  | 124:     <7>        1234:5   | <8>   2349.  149.   | | 2358       23458     3:4:7†  | 124:6    12356      <9>      | 1236  23467: 1467:  | *------------------------------*------------------------------*---------------------* | 1236       123       <8>     | <5>      1.2.3.9‡   1:2:3:7† | 1236  47:9.  47:9.  | | <9>        123       36      | 1.2.7‡   <4>        1238     | <5>   2368   167†8  | | <4>        <7>       5       | 1:2:9†   1238       <6>      | 123   238    1.8.9‡ | *------------------------------*------------------------------*---------------------*`

Legend (digit subscripts)
†, ‡ digits equivalent to (7†9‡)r4c8 (they form a conjugate loop)
., : digits that can only be true when 7† and 9‡ are true respectively
'. " digits that must be true when 7† is and 9‡ are true respectively

When (7†)r4c8 is true (4)r5c3 must be true to stop (49)UR:r57c89
When (9‡)r4c8 is true (4)r6c23 must be true to stop (47)UR:r67c89
Therefore (4)r4c2 can never be true nor can (3)r5c3.
In box2, (4) becomes locked in r12c4 together with either (7) or (9) making 126 false in these cells and (6)r6c4 true which significantly reduces the puzzle.

In the write up I actually called the combination of the two Unique Rectangle threats the Platinum Blonde sub-pattern but used a simpler example of it.

DPB
David P Bird
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### Re: an elementary solution of platinium blonde

jb69 wrote: I believe that brute force has bad press in the sudoku community!

This is an outdated debate. Players don't use brute force as such because they find no fun in that.
In turnaments, nobody ask you how you came to a solution.

jb69 wrote:If you want to prove that there is no other solution the total number of elementary sudokus is around 45.

As many, I would not qualify "sudoku" a grid with more than one solution.

Extracting sudokus among millions of grids is a daily task for several of us, but then, the question is not "what technique do you use in your brute force", but how long did it take to the computer to answer. And to-day, the answer is considered if it is around 10 microseconds in average.

jb69 wrote:7) if you have a "short solution" of PB by classical means I am interested.

As I already answered, I think that the Jexocet pattern, lond discussed in that forum is not part of your background.
champagne
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### Re: an elementary solution of platinium blonde

Thank you David for the detailed JExocetstep on platinium blonde. I will study that (new for me).
Can all sudokus be solved by "patterns"? If yes, I suppose this is not a theorem?
Same question excluding the unicity hypothesis.
I understand in Champagne response that the community is not intersted by unicity. This is surprising for me.
In mathemetics unicity may be a very difficult question ( even with no answer as for 3D Navier-Stockes equations).
A last word on platinium blonde: what as surprised me is that a sequence of 3 choices gives the solution. I wonder
if this hapen often.
jb69

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Joined: 16 February 2016

### Re: an elementary solution of platinium blonde

jp69, Sudokus can be viewed either as a challenge for a human solver (me) or for a computer programmer (Champagne) so don't expect us to agree in every respect.

A distribution of candidates that allows an elimination to be made could be considered a pattern because it is certain to be repeated in other puzzles. However consulting a catalogue of all of them would take longer than re-proving the theorem(s) they provide from basics and shouldn't be considered as a solving method.

Remembering that Sudokus were designed for human solvers, it is more realistic to confine patterns to those that are recognisable by players who are familiar with them. The theorems they provide can then be applied without having to be demonstrated and these should be described somewhere for novices. The JExocet pattern is a very advanced one so you have jumped into the deep end of the swimming pool.

It is also reasonable to expect players who have solved a puzzle to be able to explain the logic they have used. This should enable the better approach to be judged - but there are as many opinions about that as there are players.

Invalid puzzles that have multiple solutions need one or more extra clues to limit them to a single solution. The clue sets that are required to provide unique solutions are therefore more of an interest to puzzle designers than to puzzle solvers.

The more you browse the more you will learn about these aspects.
.
David P Bird
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### Re: an elementary solution of platinium blonde

What is "platinum blonde" means ?
jb69 » Tue Feb 16, 2016 4:16 pm: wrote [an elementary solution of platinium blonde]
though, with this puzzle, there are lots of easy solutions, like
1: r1c1=8 + r1c3=9 and r3c1=7 or
2: r6c7=3 + r6c8=4 and r6c9=1 or
3: pair of r4c7=67 and r4c8=67
4: r2c8 and r3c8 = pair of 58 etc
i wonder how can be logically to find a solution, not by force bruting,
Kozo Kataya

Posts: 33
Joined: 06 July 2012

### Re: an elementary solution of platinium blonde

Platinum Blonde is a mildly famous Sudoku puzzle. {EDIT}It is known for having been used as sample puzzle for a particular variation of the Exocet technique.{/EDIT} It was originally posted by coloin.

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

.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...
Last edited by JasonLion on Sun Mar 27, 2016 12:57 am, edited 2 times in total.

JasonLion
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### Re: an elementary solution of platinium blonde

Platinium blonde is not with our common rating tool one of the hardest puzzles (but it was in an article published some years ago).

It has the extended JExocet pattern (with a locked candidate). and it has been (thanks to "abi") the first discovery of such a property.

This is now a very old topic (2013) and many discussions took place in several threads about that puzzle.

The Jexocet pattern appears in about 80% of the puzzles rated "hardest with our reference tool. so it is a key pattern.

The last and easiest approach to that pattern is in that thread

jexocet-pattern-definition-t31133.html

but although you have some reference to Platinium Blonde, I did not find a clear discussion about that puzzle in the thread, and , as often, many sharp exchanges took place here, difficult to follow for a newcomer.

What is for sure, as for most of the exocets with 3 digits, is that using the Jexocet properties, the puzzles collapses immediately.
champagne
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### Re: an elementary solution of platinium blonde

More recently (March 2015) David P Bird compiled a JExocet Compendium - a large body of work that attempts to summarize the discoveries made by himself and other contributors to this extensive topic.

It can be found here http://forum.enjoysudoku.com/jexocet-compendium-t32370.html?hilit=COMPENDIUM

Leren
Leren

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### Re: an elementary solution of platinium blonde

Code: Select all
`*--------------------------------------------------------------------------------*| 3568    3458    4679-3   | 4679    568     458      | 79      1       2        || 1568    1458    4679     | 4679-12 12568   12458    | 79      568     3        || 15678   1589    2        | 3       15689   1578     | 4       568     68       ||--------------------------+--------------------------+--------------------------|| 237     2349    1        | 8       236     234      | 236     79      5        || 235     6       349      | 124     7       1235-4   | 8       2349    149      || 2358    2358-4  347      | 1246    1235-6  9        | 123-6   23467   1467     ||--------------------------+--------------------------+--------------------------|| 1236    123     8        | 5       1239    1237     | 1236    479     479      || 9       123     36       | 127     4       1238     | 5       23678   1678     || 4       7       5        | 129     1238    6        | 123     2389    189      |*--------------------------------------------------------------------------------*`

FWIW I ran Platinum Blonde through my solver to see what would turn up.

I made the same 34 JExocet pattern eliminations that David made but not the extra UR eliminations (which I wasn't aware of).

However, after the JExocet eliminations I found a Multifish (Rank 0 SLG) :

16 Truths = { 4679C3 4679C4 4679C8 4679C9 } 16 Links = { 4r56 6r68 7r68 9r59 1n34 2n34 4n8 7n89 6b3 } => - 3r1c3, - 12 r2c4, - 4 r5c6, - 4 r6c2, - 6 r6c57.

It looks like 4 of these eliminations are covered by the extra UR eliminations but - 3r1c3, - 4 r5c6 and - 4 r6c2 are not.

Ignoring the JExocet the Multifish makes 17 eliminations.

Multifish is another huge topic and not well documented in the forum. The best place to start is the Exotoc Patterns a Resume thread that can be found here : http://forum.enjoysudoku.com/exotic-patterns-a-resume-t30508.html

Be prepared to trawl though all 55 pages of this thread if you want to learn this topic.

Leren
Leren

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### Re: an elementary solution of platinium blonde

Champagne has written:
Platinium blonde is not with our common rating tool one of the hardest puzzles (but it was in an article published some years ago).
I found platinium blonde on "The hardest sudokus" by Tarek (2009) and solved also discrepancy and cigarette with pencil, paper and elementary techniques.
Question: where is a list of the actual hardest sudokus?
jb69

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Joined: 16 February 2016

### Re: an elementary solution of platinium blonde

As we have no clear definition of the rating of a sudoku, it's not possible to tell what is the hardest one.

However, in that forum, we generally agree that the hardest should have a very high rating using Sudoku Explainer rating rules.