X-treme 23 October - stuck

Welcome to the world of the unknown. Each day you need to solve <a href="http://www.sudocue.net/xfile.php">two mysteries</a>.<br>Take the X-R-Size or solve the X-Treme problem. Stuck? Found a nice solution? Tell us about it.
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia

X-treme 23 October - stuck

Great puzzles Ruud. Love being able to use lots of cross-over moves - but not enough this time. Any suggestions anyone? Thanks.

Code: Select all

``````.------------------.------------------.------------------.
| 349   467   3467 | 2     3459  3457 | 3457  1     8    |
| 348   479   2    | 14578 6     1457 | 3459  3457  4579 |
| 348   5     1    | 3478  349   347  | 3479  2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 34567 345   13457| 2     4567  4579 |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 12459 12467 45679| 1457  8     457  | 45679 4567  3    |
&#58;------------------+------------------+------------------&#58;
| 12345 124   45   | 9     1345  8    | 34567 34567 457  |
| 7     49    3459 | 345   1345  6    | 1345  8     2    |
| 6     14    8    | 345   7     2    | 1345  9     45   |
'------------------'------------------'------------------'
``````
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
This X-Treme is much harder than others I've posted.

Here is a hint on how to proceed:

r1c1=3 => r2c2=9 => r8c2=4 => r8c3=9 => r1c3=1 => r1c1<>3

This chain proves that r1c1 cannot be 3.

After a series of steps, you need another tough move.

I'll see you when you get there...

Ruud
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Ruud wrote: I'll see you when you get there...
So, we meet again! Great hints Ruud. OK - so this is where I'm at this time - another contradiction chain? Have been staring at all the cells with two candidates - but nothing showing. Do I really have to go up to the 3 candidates cells? This is a ripper!

Code: Select all

``````.------------------.------------------.------------------.
| 49    467   346  | 2     459   3457 | 457   1     8    |
| 348   479   2    | 14578 6     145  | 459   345   459  |
| 348   5     1    | 478   49    347  | 3479  2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  4579 |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 12459 1246  45679| 1457  8     457  | 4569  4567  3    |
&#58;------------------+------------------+------------------&#58;
| 12345 124   45   | 9     1345  8    | 36    34567 457  |
| 7     49    3459 | 345   1345  6    | 1345  8     2    |
| 6     14    8    | 345   7     2    | 1345  9     45   |
'------------------'------------------'------------------'``````
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
The next move is a skewed X-Wing that you will only find in a Sudoku-X

Code: Select all

``````.------------------.------------------.------------------.
| 49    467   346  | 2     459   3457 | 457   1     8    |
| 348   479   2    | 14578 6     145  | 459   345   459  |
| 348   5     1    | 478   49    347  |-3479  2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679|*36    345   1457 | 2     4567  4579 |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 12459 1246  45679| 1457  8     457  | 4569  4567  3    |
&#58;------------------+------------------+------------------&#58;
| 12345 124   45   | 9     1345  8    |*36    34567 457  |
| 7     49    3459 |-345   1345  6    |-1345  8     2    |
| 6     14    8    |*345   7     2    |*1345  9     45   |
'------------------'------------------'------------------'``````
Row 9 and the \ diagonal have all candidates confined to 2 columns. Like a straight X-Wing, you can eliminate the remaining candidates from these 2 columns.
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Nice one - love the name too. Is that a positive or negative skewed X-Wing?

Now - next day - next spot. Next hint?

Code: Select all

``````.------------------.------------------.------------------.
| 49    467   346  | 2     459   3457 | 457   1     8    |
| 48    479   2    | 14578 6     145  | 459   3     459  |
| 348   5     1    | 478   49    347  | 479   2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  479  |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 12459 1246  45679| 1457  8     457  | 469   4567  3    |
&#58;------------------+------------------+------------------&#58;
| 12345 124   45   | 9     1345  8    | 36    467   47   |
| 7     49    3459 | 45    1345  6    | 145   8     2    |
| 6     14    8    | 345   7     2    | 1345  9     45   |
'------------------'------------------'------------------'``````
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
sudokuEd wrote:Is that a positive or negative skewed X-Wing?
I had a very positive experience when I found it.

The next step is X-tremely tough. It is an ALS-xz step.

Column 1 has an Almost Locked Set in cells r123457c1 with digits 1234589. That's 7 digits for 6 cells.
Box 7 has an Almost Locked Set in cells r7c23, r8c2 & r9c2 with digits 12459. That's 5 digits for 4 cells.

Digit 2 can only appear in one of these 2 sets, because it will either be in r7c1 or r7c2. As a result, one of these sets will eventually be locked for the remaining digits.

Scenario 1: r7c1=2 => (Locked Set in box 7) => r8c2=9
Scenario 2: r7c2=2 => (Locked Set in column 1) => r1c1=9

r2c2 can see both these cells and you can eliminate digit 9 from this cell.

There are a few more of these ALS steps ahead. Ready to throw in the towel?
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
That is a very clever move Ruud. Very worthy of Mr

Now - just have to work out how to find one for myself. No luck so far - but will study up your solving guide on the w-end and try again. So the towel can stay nicely tucked in the corner for a bit longer yet - though it is getting pretty sweaty!

BTW - So good to be able to save a puzzle with SudoCue - and paste in marks. Any chance of making SumoCue be as clever?
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Getting the towel out... Just can't see any more ALS - or anything for that matter

Code: Select all

``````.------------------.------------------.------------------.
| 9     467   346  | 2     45    3457 | 457   1     8    |
| 48    47    2    | 14578 6     145  | 459   3     459  |
| 348   5     1    | 478   9     347  | 47    2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  479  |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 1245  1246  45679| 1457  8     457  | 469   4567  3    |
&#58;------------------+------------------+------------------&#58;
| 12345 124   45   | 9     1345  8    | 36    467   47   |
| 7     9     345  | 45    1345  6    | 145   8     2    |
| 6     14    8    | 345   7     2    | 1345  9     45   |
'------------------'------------------'------------------'
``````
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Just threw in the towel and resorted to "hints". Alas - NMH

Does that mean another contradiction chain Ruud? Have looked at all the two candidate cells - but nothing.

Actually, maybe I should download the Beta version - it might do better Will edit this if successful.

 Just found this
Change and save the Solver Options to enable the new solving techniques.
So beta does find NLS eliminations (maybe the earlier one did too but didn't have enabled).

Gotta go now - but will study later and ask for help if needed.

emm
Hooked
Posts: 34
Joined: Wed Oct 11, 2006 6:01 pm
I bet this is not the smartest next move, Ed, but it gets you a little way further on.

I really tried to find an ALS - I'm hoping this is a valid contradiction chain.

r9c2=4 => r9c9=5

r9c2=4 => r2c2=7 => r1c2=6 => r1c3=4 => r1c5=5 => r1c7=7 => r3c7=4 => r8c7=5

=> r9c2<>4 which gets you to here

Code: Select all

``````.------------------.------------------.------------------.
| 9     467   346  | 2     45    3457 | 457   1     8    |
| 48    47    2    | 14578 6     145  | 459   3     459  |
| 348   5     1    | 478   9     347  | 47    2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  479  |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 1245  246   45679| 1457  8     457  | 469   4567  3    |
&#58;------------------+------------------+------------------&#58;
| 2345  24    45   | 9     1     8    | 36    467   47   |
| 7     9     34   | 45    345   6    | 1     8     2    |
| 6     1     8    | 34    7     2    | 345   9     45   |
'------------------'------------------'------------------'``````
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Aarggh - Ruud and emm - you're messing with my head.

emm doing it I can understand and forgive since we beat you in netball (if you are the emm with the nice round vowels ).

Ruud doing it I can understand - because that's what coaches do.

But why are you both doing it at the same time Must be some sort of complex, sinister plot - perhaps
sinister riddler wrote:NLS . . ALS
OK. Now getting serious.
emm wrote:I'm hoping this is a valid contradiction chain.
Don't think so unfortunately. I think the second chain still has r89c7 with {135} available. So, not sure how you can lock in the 5 there. But I could be wrong 'cause I find it very tough to 'see' that many steps ahead. BTW - I think you missed a step also to be able to show that r1c3=4 ( r78c3 = [53])
SudoCue wrote:Two Almost Locked Sets sharing digit 7 eliminate candidate(s) for digit 5
I can't understand how the two ALS's share digit 7. This is the way it looks to me

1. One ALS in r45689c4 with digits 134567. 6 digits, 5 cells.
2. One ALS in r23c7 + r2c9 with digits 4579. 4 digits, 3 cells.
The only way those two ALS see each other is through D/.

But how they "share digit 7". Why can't 7 be in r5c4 when 7 is in r3c7? If 7 can be in both spots, then 7 is not "restricted common".

There must be another way of interpreting SudoCue I can't see yet. Can anyone clarify? Thanks.
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
Actually, I found a more appropriate ALS-xz pattern in your grid, which can only be found in a Sudoku-X.

Here it is:

Isn't it a beauty? Digit 3 is shared on a diagonal...
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
Now that I can understand - it is a beauty. It made perfect sense as soon as you pointed it out .

I really like this ALS technique - just can't find them for myself yet.

Mind you, eliminating that 5 doesn't seem to get us any further - just also lose a 5 from r8c7. Can't see anything from there - unless I'm missing something. emm's contradiction idea still doesn't seem to help

The "hints" again points out the ALS move which I can't understand. When all the solver options are enabled it gets really scary with "Medusa" something. So....totally out of my depth there.

But have something to improve in that looks really promising. Time to practice on some friendlier X-tremes - perhaps the ones that don't say "unfair"! Thanks coach
emm
Hooked
Posts: 34
Joined: Wed Oct 11, 2006 6:01 pm
Ruud, you're a wizard at making things clear. Your coloured dots light the ALS up like a runway strip!

Ed, my moves weren’t so much missing as implied !

r9c2 = 4 -> r9c7 = 1 -> r8c7 <> 1
r9c2 = 4 -> r1c3 = 3 -> r8c3 = 5 -> r8c7 <> 5
If I’d been able, I’d have done a nice loop but it was too complicated.

Thanks for the hint about the other ALS - I see what you’re saying about the 7s.
If 7 is restricted common because of the diagonal, then is this also true?

Code: Select all

``````.------------------.------------------.------------------.
| 9     467   346  | 2     45    3457 | 457   1     8    |
| 48    47    2    | 14578 6     145  | 459   3     459  |
| 348   5     1    | 478   9     347  | 47    2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  479  |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 1245  246   45679| 1457  8     457  | 469   4567  3    |
&#58;------------------+------------------+------------------&#58;
| 2345  24    45   | 9     1     8    | 36    467   47   |
| 7     9     34   | 45    345   6    | 1     8     2    |
| 6     1     8    | 34    7     2    | 345   9     45   |
'------------------'------------------'------------------'``````
A = r1c2 r2c12
B = r6c3678
X = 7 ( D\ r2c2 and r6c6)
Y = 6
=> r6c2 <> 6

So now we have

Code: Select all

``````.------------------.------------------.------------------.
| 9     6     34   | 2     45    3457 | 457   1     8    |
| 48    7     2    | 1458  6     145  | 459   3     459  |
| 348   5     1    | 478   9     347  | 47    2     6    |
&#58;------------------+------------------+------------------&#58;
| 145   8     45679| 36    345   1457 | 2     4567  479  |
| 45    3     4567 | 4567  2     9    | 8     457   1    |
| 1245  24    45679| 1457  8     457  | 469   4567  3    |
&#58;------------------+------------------+------------------&#58;
| 2345  24    45   | 9     1     8    | 36    467   47   |
| 7     9     34   | 45    345   6    | 1     8     2    |
| 6     1     8    | 34    7     2    | 345   9     45   |
'------------------'------------------'------------------'``````

PPS : Do I know you from another persona or are you a lurker in the other forum?
sudokuEd
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia
emm wrote:Ed, my moves weren’t so much missing as implied !
Thanks for pointing that out. I've only ever been a Killerholic - this is my first foray into any Killer variants - so not familiar with the syntax etc.

I've finally been able to convince myself that r9c2<>4 (using SudoCue rather than my head).
r9c2=4 => r9c9=5 => r9c7=1 =>r8c7=4

r9c2=4 => r2c2=7 => r1c2=6 => r1c3=4 => r1c5=5 => r1c7=7 => r3c7=4

= two 4's in c7=> r9c2<>4.

I'm still not sure of the way you did it - but at least we agree on the result now - and with your marks pic. So - at least we're making some progress.
emm wrote:Thanks for the hint about the other ALS - I see what you’re saying about the 7s.
If 7 is restricted common because of the diagonal, then is this also true?
I don't understand the other hint about the 7's. It may be true - but it seems to be a different pattern than Ruud's ALSxz and I can't understand how it works.

I have the same problem with your suggestion of the 7's on D\ . To me the 7 is not "restricted common" because 7 could be in both ALS at the same time eg. if r6c6 was 7, could have 7 in r1c2. So the 6 is not forced to be in r1c2. Similarly, when r6c6 = 7, the other 3 cells in ALS B have {4569} available - so 6 is not forced to be there either.

Please try again if I havn't got this right.

PS. lurker