The New Sudoku Players' Forum

[wychwood]

Hi all

I've been absent for quite a while, but now have got totally stuck on this one, at the following position:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 9       56      47      | 238     26      2368    | 138     4578    1457    |
 | 56      2       47      | 389     1       3689    | 38      4578    457     |
 | 8       13      13      | 5       4       7       | 6       2       9       |
 |-------------------------+-------------------------+-------------------------|
 | 2457    1458    6       | 123478  257     12358   | 9       3578    157     |
 | 3       45      18      | 47      9       56      | 18      567     2       |
 | 257     1589    1289    | 12378   2567    123568  | 4       35678   1567    |
 |-------------------------+-------------------------+-------------------------|
 | 1       7       5       | 6       8       4       | 2       9       3       |
 | 246     4689    289     | 279     3       259     | 57      1       46      |
 | 246     3469    239     | 1279    257     1259    | 57      46      8       |
 *-----------------------------------------------------------------------------*

I am sure there will be an ALS in there somewhere, but I am blowed if I can see it.

Cheers
Neil (wychwood)

[tarek]

Very difficult one........

Had to feed it to my solver ........ heavy on ALS-XY rule eliminations.

what was the original source of this puzzle wychwood ?


tarek

[udosuk]

A simple ALS-xz from that position:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 9       56      47      | 238    @26      2368    | 138     4578    1457    |
 | 56      2       47      | 389     1       3689    | 38      4578    457     |
 | 8       13      13      | 5       4       7       | 6       2       9       |
 |-------------------------+-------------------------+-------------------------|
 | 2457    1458    6       | 123478 @257     12358   | 9       3578    157     |
 | 3      #45      18      |#47      9      -56      | 18      567     2       |
 | 257     1589    1289    | 12378  @2567    123568  | 4       35678   1567    |
 |-------------------------+-------------------------+-------------------------|
 | 1       7       5       | 6       8       4       | 2       9       3       |
 | 246     4689    289     | 279     3       259     | 57      1       46      |
 | 246     3469    239     | 1279    257     1259    | 57      46      8       |
 *-----------------------------------------------------------------------------*

ALS-xz:
A: r146c5={2567}
B: r5c24={457}
x=7, z=5

Therefore r5c6 can't be 5, r5c6=6.

After singles, pairs and triples:

Code: Select all

 *--------------------------------------------------*
 | 9    5    47   | 238  6    238  | 138  478  147  |
 | 6    2    47   | 389  1    389  | 38   47   5    |
 | 8    13   13   | 5    4    7    | 6    2    9    |
 |----------------+----------------+----------------|
 | 5    18   6    | 4    2    138  | 9    378  17   |
 | 3    4   -18   | 7    9    6    |@18   5    2    |
 | 7    9    2    | 138  5    138  | 4    368 @16   |
 |----------------+----------------+----------------|
 | 1    7    5    | 6    8    4    | 2    9    3    |
 |#24   68  #89   |#29   3    5    | 7    1   #46   |
 | 24   36   39   | 129  7    129  | 5    46   8    |
 *--------------------------------------------------*

A: r5c7+r6c9={168}
B: r8c1349={24689}
x=6, z=8

Therefore r5c3 can't be 8, r5c3=1.

And singles solve the rest.

I hope 2 ALS-xz moves are not too hard for you.

[JPF]

what was the original source of this puzzle wychwood ?

flashback ; guess :

Code: Select all

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



JPF

[re'born]

A simple ALS-xz from that position:

Code: Select all

 *--------------------------------------------------------------------------*
 | 9       56      47     | 238    @26      2368   | 138     4578    1457   |
 | 56      2       47     | 389     1       3689   | 38      4578    457    |
 | 8       13      13     | 5       4       7      | 6       2       9      |
 |------------------------+------------------------+------------------------|
 | 2457    1458    6      | 123478 @257     12358  | 9       3578    157    |
 | 3      #45      18     |#47      9      -56     | 18      567     2      |
 | 257     1589    1289   | 12378  @2567    123568 | 4       35678   1567   |
 |------------------------+------------------------+------------------------|
 | 1       7       5      | 6       8       4      | 2       9       3      |
 | 246     4689    289    | 279     3       259    | 57      1       46     |
 | 246     3469    239    | 1279    257     1259   | 57      46      8      |
 *--------------------------------------------------------------------------*

ALS-xz:
A: r146c5={2567}
B: r5c24={457}
x=7, z=5

Therefore r5c6 can't be 5, r5c6=6.

An alternative way to see this same elimination is the (4-color) nice loop:

r5c6 - 5 - {r8c6 = 5 = r8c7 = 7 = r8c4 - 7 - r5c4 - 4 - r5c2} - 5 - r5c6, => r5c6 <> 5.

Instead of applying the 2nd ALS above, I then noticed the UR-single r1c8 = 8, using r12c38<47>.

[Steve R]

If you wish, you can also dodge the first ALS by using the W-wing represented by the pairs (56) in r1c2 and r5c6.

These are linked by the conjugate 6s in the fifth column, so at least one wing contains 5 and it may therefore be eliminated from r5c2.

Steve

[wychwood]

Thanks folks, composite response to various replies:

1. Source grid is exactly as 'guessed' by JPF ["how do they do that??"]. It comes from a book called 1,000 Sudoku Puzzles complied by Tom Melhuish and published by Lagoon Books. Three grades in this - the easy and medium are very easy - but the hard has some gems in, like this one, plus some that are relatively straight forward. It also has a dozen labelled XXX.

2. I should be ale to cope with two ALS-xzs, once I know where they are, but I am very inexperienced in spotting them. Also, I do not spend much time on puzzles, and do not have the chance to sit and go throguh every possible permutation in each puzzle - hence I turn to the Board!!

3 I have absolutely no idea what Steve R is takling about with a W wing - X wings and XY wings are fine, but W......? Nor for that matter does re'born's loop mena anything to me.

Thanks again for all replies so far.

Wychwood

[re'born]

3 I have absolutely no idea what Steve R is takling about with a W wing - X wings and XY wings are fine, but W......? Nor for that matter does re'born's loop mena anything to me.

Look at the thread Y-wing styles for answers (W-wing is a synonym for Y-wing style and semi-remote naked pair).
As for my loop, I won't explain the terminology, but my methodology. Start from r8c6. Color the 5 blue. There is a strong link on 5 with r8c7, so we color that 5 green. Since r8c7 is a bivalue cell, we can color the 7 blue. The strong link on 7 with r8c4 then lets us color the 7 in r8c4 green. Now we have to switch colors. Our previous 7 is weakly linked to the 7 in r5c4, so we color it pink. r5c4 is a bivalue cell, so we color the 4 in it amber. Ths strong link on 4 in row 5 allows us to color the 4 in r5c2 pink and hence the 5 in r5c2 amber. Now as green sees pink, we can eliminate any placement that sees both blue and amber. In particular, r5c6<>5 since it sees the amber 5 in r5c2 and the blue 5 in r8c6. I hope this helps a little.

[udosuk]

Wychwood, here is a detailed explanation of Steve R's W-wing move:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 9      *56      47      | 238     26      2368    | 138     4578    1457    |
 |#56      2       47      | 389     1      #3689    | 38      4578    457     |
 | 8       13      13      | 5       4       7       | 6       2       9       |
 |-------------------------+-------------------------+-------------------------|
 | 2457    1458    6       | 123478  257     12358   | 9       3578    157     |
 | 3      -45      18      | 47      9      *56      | 18      567     2       |
 | 257     1589    1289    | 12378   2567    123568  | 4       35678   1567    |
 |-------------------------+-------------------------+-------------------------|
 | 1       7       5       | 6       8       4       | 2       9       3       |
 | 246     4689    289     | 279     3       259     | 57      1       46      |
 | 246     3469    239     | 1279    257     1259    | 57      46      8       |
 *-----------------------------------------------------------------------------*

r2c16 are the only possible cells to have 6 on r2. One of these 2 cells must be 6.
If r2c1=6, r1c2 can't be 6, must be 5.
If r2c6=6, r5c6 can't be 6, must be 5.
Thus one of r1c2 & r5c6 must be 5.
Hence, r5c2, seeing both these 2 cells, can't be 5, and must be 4.

Hope it's clearer for you this time.

The method to spot this move is:

1. Find 2 bivalue cells containing the same 2 candidates not connecting to each other. (In this case r1c2=r5c6={56}.)

2. Try to search for a strong link involving one of these 2 candidates, with each end connecting to a separate bivalue cell above. (In this case the strong link of 6 in r2c16.)



Edited: typos fixed

[wychwood]

udosuk (and others)

Any tips as to where to go for practice in SPOTTING ALSs? I understand why and how they work, but it is just spotting them that is the difficult bit.
Are there any particular patterns that you need to look for?

Thanks for the explanation of W wing - no way I will be able to spot those!!

Not too sure about loops - seem a bit like colours (in Simple Sudoku) and I sometimes find those a bit close to 'trial and error' which I don't like using if I cna avoid it. All chains and, I guess, loops seem to start with "what if" and I am not too happy about that as a principle in solving. Just my personal preference, of course.

Wychwood

[udosuk]

Any tips as to where to go for practice in SPOTTING ALSs? I understand why and how they work, but it is just spotting them that is the difficult bit.
Are there any particular patterns that you need to look for?

Thanks for the explanation of W wing - no way I will be able to spot those!!

IMHO W-wings (aka Y-wings, semi-remote-pairs) are easier to spot than ALSs. So if you find it hard to spot W-wings then ALSs are definitely harder. Mind you, spotting moves is a highly intuitive talent depending on your observation ability, attention to details, stamina to stay highly focused, as well as perservance and will power. It's not something that can be taught. You either have it or you don't.

If you do Killer Sudokus and other variants you'll find it much more challenging to spot moves than solving vanilla (i.e. normal) Sudokus. For the really insane (or "ruudiculous", a term we use in tribute of my fellow respected moderator/webmaster/puzzle-creator to describe the ultimate mind-bogglers) puzzles sometimes we have to spend hours (or even days) staring at the grid to spot a single critical move that will crack the puzzle wide open.

Not too sure about loops - seem a bit like colours (in Simple Sudoku) and I sometimes find those a bit close to 'trial and error' which I don't like using if I cna avoid it. All chains and, I guess, loops seem to start with "what if" and I am not too happy about that as a principle in solving. Just my personal preference, of course.

For this I share your feeling. That's why I much prefer ALSs and wings etc than loops/chains interpretation, albeit in most case the logic is identical.

[Para]

Thanks for the explanation of W wing - no way I will be able to spot those!!

Actually this move was also pointed out in an earlier request for help.

http://forum.enjoysudoku.com/viewtopic.php?p=42206#p42206

greetings

Para