The New Sudoku Players' Forum

[zebedee]

Can anyone help me pse with the Very Hard puzzle shown below. I've been looking at it for several hours trying to spot the next step or any X-wing but have failed miserably to make any progress. A cryptic clue would be gratefully received.

32* | **1 | 8**
6** | 3*9 | 7**
*** | *** | 36*
------------------
5** | *13 | *2*
*38 | *7* | 5**
*6* | 59* | **3
------------------
*73 | 1** | ***
*56 | 43* | ***
**2 | 9*7 | *35

Many thanks.

Zeb

(very much a Sudoku beginner)

[zebedee]

Sorry folks. I've just realised that I shouldn't have posted my earlier question on the Times puzzle forum since the puzzle shown was not from the Times. My apologies. Too much wine tonight.

Zeb

[Sue De Coq]

This is truly a very hard puzzle - first think about which values could fill the pair of cells r4c9 and r6c8, then look for an X-Wing in the 6s.

[shakers]

That one was indeed tricky - I usually only look for pairs in rows and columns, and having to do that within a box to create the X-Wing... well, it is rated 'Very Hard'! Nice puzzle though.

[Bernard Stay]

It is a toughie; however I was eventually able to do it (deliberately not looking at the above hints). Just for fun I put it to 'Su Doku Solver' [http://www.peteshaw.com/site/] which has managed to solve everything I've thrown at it so far - but it admits defeat on this puzzle, suggesting that 'perhaps there are too few clues'!

[zebedee]

This is truly a very hard puzzle - first think about which values could fill the pair of cells r4c9 and r6c8, then look for an X-Wing in the 6s.

Thanks for the clue(s) Sue but sadly I'm none the wiser. By my reckoning, Box r4c9 can be filled with a 4,6,7,8 or 9 and and Box r6c8 with a 1,4,7 or 8 but I can't narrow things down any further. Are there any other hints you (or others) could offer pse?

Many thanks.

Zeb

[simes]

Just for fun I put it to 'Su Doku Solver' [http://www.peteshaw.com/site/] which has managed to solve everything I've thrown at it so far - but it admits defeat on this puzzle, suggesting that 'perhaps there are too few clues'!

That's funny, it solved it for me. And since it tries all possibilities, i.e. trial and error, perhaps one of us didn't enter the puzzle correctly?

[Guest]

Zeb - those two cells are the only place 7 & 8 can go in box 6... This leaves an X-wing lurking, half of which is in col 9

[Sue De Coq]

The presence of a 7 and an 8 in Row 5 and Column 7 means that the 7 and 8 in Box 6 are restricted to the cells r4c9 and r6c8. We don't know which value should go into which cell - but we are sure that no other value other than a 7 or an 8 could occupy these cells. In particular, r4c9 can't contain a 6, so the only possible positions for the 6 in Column 9 are r5c9 and r7c9. Now look for an X-Wing!

BTW, the solver at act365.com/sudoku solves the puzzle.

[zebedee]

Zeb - those two cells are the only place 7 & 8 can go in box 6... This leaves an X-wing lurking, half of which is in col 9

Thanks IJ but I can't immediately spot the X-wing. Can you, perhaps, let me know me one of the four boxes that make up the invisible (to me!) X-wing to help me on my way?

Sue.

Thanks for your response as well.

Zeb

[Guest]

r5c9 - use the force!

[Tony Williams]

Can anyone help me pse with the Very Hard puzzle shown below.

32* | **1 | 8**
6** | 3*9 | 7**
*** | *** | 36*
------------------
5** | *13 | *2*
*38 | *7* | 5**
*6* | 59* | **3
------------------
*73 | 1** | ***
*56 | 43* | ***
**2 | 9*7 | *35

Many thanks.

Zeb

(very much a Sudoku beginner)

I hope this doesn't spoil the fun - I have to admire you guys solving these manually - getting the VBA Solver to work was hard enough.

This is a 'tricky one' so don't become depressed over it. Below is the log file of the solution.

Code: Select all

 - - - - - - - - - - - - - - -
Iteration Number  1
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Digit 2 occurs only in Column 9 - Square 3
Digit  2 not allowed Cell( 7, 9)
Digit  2 not allowed Cell( 8, 9)
Digit 4 occurs only in Column 6 - Square 5
Digit  4 not allowed Cell( 3, 6)
Digit 9 occurs only in Column 1 - Square 7
Digit  9 not allowed Cell( 3, 1)
Digit  9 not allowed Cell( 5, 1)
 - - - - - - - - - - - - - - -
Iteration Number  2
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Digit 9 occurs only in Row 4 - Square 4
Digit  9 not allowed Cell( 4, 7)
Digit  9 not allowed Cell( 4, 9)
 - - - - - - - - - - - - - - -
Iteration Number  3
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Testing for Pairs/Triplets [Rows]
Testing for Pairs/Triplets [Columns]
Col  7 - Digit 9 is a Pair in the same Square ~ Rows =  7, 8
Digit  9 not allowed Cell( 7, 8)
Digit  9 not allowed Cell( 8, 8)
Digit  9 not allowed Cell( 7, 9)
Digit  9 not allowed Cell( 8, 9)
 - - - - - - - - - - - - - - -
Iteration Number  4
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Testing for Pairs/Triplets [Rows]
Testing for Pairs/Triplets [Columns]
Testing for x,y Pairs of Digits [Rows]
Testing for x,y Pairs of Digits [Columns]
Col  7 - Digits   2 & 9 are a Pair into Rows =  78
Digit  4 not allowed Cell( 7, 7)
Digit  6 not allowed Cell( 7, 7)
Digit  1 not allowed Cell( 8, 7)
 - - - - - - - - - - - - - - -
Iteration Number  5
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Testing for Pairs/Triplets [Rows]
Testing for Pairs/Triplets [Columns]
Testing for x,y Pairs of Digits [Rows]
Testing for x,y Pairs of Digits [Columns]
Testing N-Cell Candidates [Rows]
Testing N-Cell Candidates [Cols]
Testing N-Cell Candidates [SQs]
N-Cell Rule - Candidates = 1469 in  Square 6
Digit  4 not allowed Cell( 4, 9)
Digit  6 not allowed Cell( 4, 9)
Digit  1 not allowed Cell( 6, 8)
Digit  4 not allowed Cell( 6, 8)
 - - - - - - - - - - - - - - -
Iteration Number  6
 - - - - - - - - - - - - - - -
Testing for Unique Placements
Test all Digits for unique to Row/Col/Sq
Testing only Row/col in Square
Testing for Pairs/Triplets [Rows]
Testing for Pairs/Triplets [Columns]
Testing for x,y Pairs of Digits [Rows]
Testing for x,y Pairs of Digits [Columns]
Testing N-Cell Candidates [Rows]
Testing N-Cell Candidates [Cols]
Testing N-Cell Candidates [SQs]
Testing for X_Wings [Rows]
Testing for X_Wings [Columns]
X_Wing Rule - Digit   6 at Columns  6 & 9 are a Pairs into Rows =  57
Digit  6 not allowed Cell( 5, 4)
Digit  6 not allowed Cell( 7, 5)
 - - - - - - - - - - - - - - -
Iteration Number  7
 - - - - - - - - - - - - - - -
Testing for Unique Placements
 35 - Digit  2 only candidate for Cell( 5, 4)
Test all Digits for unique to Row/Col/Sq
 36 - Cell( 6, 1) = 2
 37 - Digit  7 Only position in Column( 1) is Cell( 3, 1)
 - - - - - - - - - - - - - - -
Iteration Number  8
 - - - - - - - - - - - - - - -
Testing for Unique Placements
 38 - Digit  8 only candidate for Cell( 3, 4)
 39 - Digit  6 only candidate for Cell( 4, 4)
 40 - Digit  4 only candidate for Cell( 4, 7)
 41 - Digit  4 only candidate for Cell( 5, 6)
 42 - Digit  8 only candidate for Cell( 6, 6)
 43 - Digit  1 only candidate for Cell( 6, 7)
 44 - Digit  7 only candidate for Cell( 6, 8)
 45 - Digit  2 only candidate for Cell( 8, 6)
 46 - Digit  9 only candidate for Cell( 8, 7)
 47 - Digit  6 only candidate for Cell( 9, 7)
 48 - Digit  7 only candidate for Cell( 1, 4)
 49 - Digit  5 only candidate for Cell( 3, 6)
 50 - Digit  9 only candidate for Cell( 4, 2)
 51 - Digit  7 only candidate for Cell( 4, 3)
 52 - Digit  8 only candidate for Cell( 4, 9)
 53 - Digit  1 only candidate for Cell( 5, 1)
 54 - Digit  9 only candidate for Cell( 5, 8)
 55 - Digit  6 only candidate for Cell( 5, 9)
 56 - Digit  4 only candidate for Cell( 6, 3)
 57 - Digit  6 only candidate for Cell( 7, 6)
 58 - Digit  2 only candidate for Cell( 7, 7)
 59 - Digit  4 only candidate for Cell( 7, 9)
 60 - Digit  8 only candidate for Cell( 8, 1)
 61 - Digit  1 only candidate for Cell( 8, 8)
 62 - Digit  7 only candidate for Cell( 8, 9)
All Digit =  7 allocated
 63 - Digit  4 only candidate for Cell( 9, 1)
 64 - Digit  1 only candidate for Cell( 9, 2)
 65 - Digit  8 only candidate for Cell( 9, 5)
 66 - Digit  9 only candidate for Cell( 1, 9)
 67 - Digit  4 only candidate for Cell( 3, 2)
 68 - Digit  2 only candidate for Cell( 3, 5)
 69 - Digit  1 only candidate for Cell( 3, 9)
 70 - Digit  9 only candidate for Cell( 7, 1)
 71 - Digit  5 only candidate for Cell( 7, 5)
 72 - Digit  8 only candidate for Cell( 7, 8)
 73 - Digit  5 only candidate for Cell( 1, 3)
 74 - Digit  4 only candidate for Cell( 1, 8)
 75 - Digit  8 only candidate for Cell( 2, 2)
All Digit =  8 allocated
 76 - Digit  1 only candidate for Cell( 2, 3)
All Digit =  1 allocated
 77 - Digit  4 only candidate for Cell( 2, 5)
All Digit =  4 allocated
 78 - Digit  5 only candidate for Cell( 2, 8)
All Digit =  5 allocated
 79 - Digit  2 only candidate for Cell( 2, 9)
All Digit =  2 allocated
 80 - Digit  9 only candidate for Cell( 3, 3)
All Digit =  9 allocated
 81 - Digit  6 only candidate for Cell( 1, 5)
All Digit =  6 allocated
 ====================
  Puzzle Solved
 ====================



The first 6 Iterations are purely using rules to decide where digits cannot go . Only then does the X-Wing rule eliminate Digit 6 at (5,4), (7,5) - and finally the normal placement rules of each digit once in Row/Col/SQ kick in to solve the Puzzle.

The Pairs/Triplets in SQ rule is one that can be very useful, and I guess OK manually - it should be fairly obvious from above, but if (say) in a Row there only 2 (or 3) positions that a Digit can go, AND they are in the same SQ - then within the SQ we must eliminate as candidates this digit from all other cells in he SQ. Ditto if true for Columns.

As others have said - this is not easy, and those of us who enjoy the challange of writing a 'Solver' have had to work v hard to get their solvers to this level.

They can get even harder , but once you are into swordfish rules, then you are almost out of reach by manual methods - and are into 'solver' only solutions - unless you are some kind of genius, or have somehow re-wired your brain on SuDoku patters

Good luck - don't get too hooked, it becomes an obsession

[Bernard Stay]

Just for fun I put it to 'Su Doku Solver' [http://www.peteshaw.com/site/] which has managed to solve everything I've thrown at it so far - but it admits defeat on this puzzle, suggesting that 'perhaps there are too few clues'!

That's funny, it solved it for me. And since it tries all possibilities, i.e. trial and error, perhaps one of us didn't enter the puzzle correctly?

Yes, sorry, must have mis-entered it! And sorry, Pete for maligning your program.

[Animator]

For those that still have trouble with this puzzle:

Row 5: cells that can have 6:
r5c4: possible: 2/6
r5c6: possible: 2/4/6
r5c9: possible: 1/4/6/9

Row 7: cells where 6 is possible:
r7c5: possible: 2/5/6/8
r7c6: possible: 2/5/6/8
r7c9: possible: 2/4/6/8

There are only two places in colum 6 and 9 that can have the number 6: r5c6, and r7c6, and there are only two places where column 9 can have the number 6: r5c9 and r7c9 (this is IJ'XWing).


Now if you still don't see what this means (some trial and error):

* Assume you put the number in r5c4:

If r5c4 has a 6, then r5c9 can't be 6, so r7c9 has to be 6 (else there wouldn't be a 6 in column 9),

but, now r7c6 can't be 6 (because of r7c9), and r5c6 can't be 6 either (r5c4), this means that column 6 can't have a 6, so r5c4 can't be 6.

* Assume you put the number 6 in r7c5

If r7c5 has a 6, then r7c6 can't be 6, so r5c6 has to be 6 (to ensure column 6 has the number 6), but this means that r5c9 can't have the number 6, and r7c9 can't have the number 6 either, so column 9 does not have the number 6. (which means that r7c5 can't hold the number 6)



This makes r5c4 and r7c5 invalid

[zebedee]

r5c9 - use the force!

Thanks IJ. I finally cracked the puzzle today.

Zeb