Very good Very Hard

Advanced methods and approaches for solving Sudoku puzzles

Very good Very Hard

Postby Arnie » Sat Jun 18, 2005 9:51 am

I've found this puzzle the most enjoyable puzzle I've done yet....this "very hard" seems to have everything...2 xwings that appear at different times ; hidden triplts, - even the opening grid is appealling.

Haven't yet finished it but hope to do so when I need to come in from the heat of the day (mini heat wave in England!!) I've posted the opening grid below


Enjoy !

*** 526 ***
**6 9*8 1**
*8* *** *6*

4** *** **3
*6* 8*1 *9*
3** *** **1

*4* *** *8*
**5 4*2 9**
*** 657 ***

Arnie
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Postby Karyobin » Sat Jun 18, 2005 10:31 am

Yup, that was a good one - took me 21 minutes but I haven't read all the site rules so I don't know whether using pencil marks is cheating. I must admit I've stumbled across a Very Hard one that so far has kept me going for DAYS (on an' off). If anyone can offer any advice on the next logical step, I'm missing something but I can't see what. Obviously.

6 8 1 9 2 4 3 5 7
2 5 * 6 * * 9 8 *
7 9 * * * 8 6 * 2
* * 7 * * * * * *
5 6 8 * * * 4 3 *
* * 9 * * * 7 * *
1 7 5 3 * * * 9 *
8 4 6 * 1 9 5 * 3
9 3 2 8 * 5 1 * 6
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Postby paulf2127 » Sat Jun 18, 2005 12:01 pm

Karyobin,

You have indeed missed something but it's not all that obvious. There is an x-wing which will open things out. I won't tell you which number because that would spoil the fun!

Paul
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Postby Karyobin » Sat Jun 18, 2005 12:59 pm

Thanks for that. I've just searched the site and rather than spend the next God-knows-how-long trying to fathom it out - could someone let me know what an X - wing is? Within context, of course.
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Postby paulf2127 » Sat Jun 18, 2005 1:17 pm

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Postby Karyobin » Sat Jun 18, 2005 1:17 pm

Paul,

Cheers.

J
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Postby Karyobin » Sat Jun 18, 2005 1:33 pm

Paul,

Just one more for you, and thanks again for the URL.

I've only being doing these things for a few months but seem to have developed a kind of personal-pride thing about never using trial-and-error. (And I'm aware of the thesis that trial-and-error is merely another form of logic, but remain unconvinced and as such I'm sticking to my guns for the time being). I have, of course, stumbled across the 'X - wing' many moons ago but wasn't aware of its idiosyncratic existence within the world of solving sudoku, I merely perceived it as an arrangement of possiblilties. In a nutshell then (too late!), how does one set about using the existence of an X - wing to take further steps without resorting to just randomly picking a diagonal and blundering on until proven right or wrong?

J
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Postby angusj » Sat Jun 18, 2005 2:19 pm

Karyobin wrote:how does one set about using the existence of an X - wing to take further steps without resorting to just randomly picking a diagonal and blundering on until proven right or wrong?

I've tried to explain the logic behind X-Wing and it's relatives (Swordfish etc) here: http://www.angusj.com/sudoku/hints.php#x_wing

On that webpage look at my comments immediately above X-Wing as they directly address your question.

Briefly - there is a special relationship between a what I call a "reciprocal pair"* (where a row, column or 3x3 box has just two occurences of a specific candidate) - one must be the value while the other can't be. When this logic is applied across the puzzle, sometimes other occurences of a specific candidate become grouped with a reciprocal pair. When this happens, this 'non-reciprocal' candidate can safely be excluded.

*Edit: Perhaps I should call these things "conjugate pairs" as per AMcK's post in this thread: http://www.setbb.com/phpbb/viewtopic.php?t=6&mforum=sudoku
Last edited by angusj on Sat Jun 18, 2005 11:36 am, edited 2 times in total.
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Postby Karyobin » Sat Jun 18, 2005 3:19 pm

Paul & Angus,

My thanks to you both for your assistance on this hottest of days. I have now formally educated myself on the nuances of X-wings and Swordfish and shall, henceforth, be invincible. My hitherto 'unsolveable' Very Hard fell like a toddler hit with a telegraph pole with the correct application of X-wing and I anticipate much further success, now that I understand these most esoteric of strategies.

Praise be upon your heads, shoulders and buttocks. You shall sit at my right hand in the fast approaching new-world-to-be-run-by-maths-teachers. And my left, just for symmetry's sake.

J

P.s. God, I love Stella.
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Postby SteveF » Tue Jun 21, 2005 8:38 am

I'm obviously still missing something in Karobin's puzzle - I can't see an X-wing and a solver that usually manages also fails.

Further clue please?
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Postby Animator » Tue Jun 21, 2005 9:43 am

More hints: column 4; number 1 ; column 6
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Postby SteveF » Tue Jun 21, 2005 12:14 pm

Many thanks Animator, but obviously my brain is not in gear today.

I have for column 4:

{9} {6} {15} {125} {127} {125} {3} {27} {8}

and column 6:

{4} {137} {8} {1236} {127} {1236} {26} {9} {5}

Using 'conventional' techniques I cannot see any other eliminations I can make in these columns (or anywhere else) so there are too many 1's for an X-wing?

The best I have managed is a couple of 'worthless' X-wings (in 4's & 9's) that do not eliminate anything.

What am I missing?
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Postby Animator » Tue Jun 21, 2005 12:21 pm

SteveF wrote:I have for column 4:

{9} {6} {15} {125} {127} {125} {3} {27} {8}


You are missing some numbers... where is the number 4?

And where can the number 2 go in box 4? and what about box 6? what do you conclude out of that for box 5? (or atleast for column 4)

Now when you done that take a really good look at it... you might be able to divide the group of candidates into two groups...
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Postby SteveF » Tue Jun 21, 2005 1:02 pm

Oops - sorry the missing 4's was a typo.

Now that you have pointed out the 2's (and of course I am now wodering how I could have missed it) everything is very obvious.

Many thanks Animator.
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Postby little Zivvy » Tue Jun 21, 2005 5:29 pm

Many thanks Arnie, this is a wonderful puzzle.
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