The New Sudoku Players' Forum

by **rsavage65** » Thu Mar 08, 2007 5:40 am

Request For Help

This is my first posting to this forum. I hope the format is satisfactory; if it is not, please advise me as to how I can improve it.

I am seeking help in solving a puzzle generated by a SUDOKU ultimate computer from ONEWORLD Electronic Essentials. It provides puzzles of nine levels. I can solve the lower number levels but cannot this level nine puzzle:

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

I have been able to solve it to the following:

Code: Select all: 1 2 69 | 35678 78 3568 | 4 389 39 8 4 3 | 9 2 16 | 16 7 5 5 7 69 | 368 148 13468 | 1689 1389 2 ----------+--------------------+--------------- 4 5 7 | 38 189 1389 | 2 6 39 3 1 8 | 2 6 79 | 579 59 4 9 6 2 | 4 5 37 | 17 13 8 ----------+--------------------+--------------- 2 9 5 | 678 478 468 | 3 48 1 6 8 4 | 1 3 59 | 59 2 7 7 3 1 | 58 489 2 | 589 4589 6

I have looked as best I can for hidden doubles or triples and for X-Wing patterns without success. I would very much appreciate someone pointing out how to progress from here.

TIA,

rsavage65

by RW » Thu Mar 08, 2007 6:57 am

Yes that one requires some more advanced techniques. I'm not going to give away the direct answer, only some hints and leave the fun part to you

. First you could have a look at these cells:

Code: Select all: 1 2 69 | 35678 78 3568 | 4 389 39 8 4 3 | 9 2 16 | 16 7 5 5 7 69 | 368 148 13468 | 1689 1389 2 ----------+--------------------+--------------- 4 5 7 | 38 189 1389 | 2 6 39 3 1 8 | 2 6 79 | 579 59 4 9 6 2 | 4 5 37 | 17 13 8 ----------+--------------------+--------------- 2 9 5 | 678 478 468 | 3 48 1 6 8 4 | 1 3 59 |*59 2 7 7 3 1 |*58 489 2 |#589 -4589 6

Look at the cell marked '#'. What are the possibilities there, how do the different possibilities affect the '*' cells, how do all possibilities affect the '-' cell? You should be able to figure it out - it's a technique called XYZ-wing.

This alone doesn't solve the puzzle, next I would advise you to read this thread. Should give you the tools neccessary to solve the rest of the puzzle. Feel free to ask if you want more specific advice. Have Fun!

RW

by **_m_k** » Thu Mar 08, 2007 9:55 pm

You may not like this solution, but in the following cells, one candidate will lead to a contradiction and another will lead to a solution using only the hidden singles:
(1, 5), (1, 9), (2, 6), (2, 7), (4, 4), (4, 9), (5, 6), (6, 7), (6, 8), (7, 8), (8, 6), (8, 7), (9, 4).
13 solution!

M.K.

by **Carcul** » Wed Mar 14, 2007 9:58 am

Code: Select all: *-----------------------------------------------------------* | 1 2 69 | 35678 78 3568 | 4 389 39 | | 8 4 3 | 9 2 16 | 16 7 5 | | 5 7 69 | 368 148 13468 | 1689 1389 2 | |------------------+---------------------+------------------| | 4 5 7 | 38 189 1389 | 2 6 39 | | 3 1 8 | 2 6 79 | 579 59 4 | | 9 6 2 | 4 5 37 | 17 13 8 | |------------------+---------------------+------------------| | 2 9 5 | 678 478 468 | 3 48 1 | | 6 8 4 | 1 3 59 | 59 2 7 | | 7 3 1 | 58 489 2 | 589 4589 6 | *-----------------------------------------------------------*

Let’s start by noting that if r7c8=8 then we must have r3c4=3 or r3c5=1.
But [r7c8](-8-[r7c45])-8-[r9c7]=8|7=[r5c7](-7-[r6c7]-1-[r2c7]=1=[r2c6]-
-1-[r3c5])-7-[r5c6]-9-[r8c6]-5-[r9c4]-8-[r4c4]-3-[r3c4]. So, r7c8<>8 and the puzzle is solved.

Carcul

by **rsavage65** » Mon Apr 16, 2007 9:43 am

I would like to thank RW, _m_k and Carcul for their help. I basically followed the approach provided by RW. It took me a while before I learned how to find forcing chains but now know how and am impressed with how useful they can be. If you are interested in the details of how I finally solved the puzzle, they follow my signature.

Thank you again,

rsavage65

Original Givens:
[code]
. 2 . | . . . | 4 . .
8 . 3 | 9 2 . | . 7 5
5 . . | . . . | . . 2
------+-------+------
. . 7 | . . . | . 6 .
3 . . | 2 6 . | . . 4
9 . . | 4 5 . | . . 8
------+-------+------
. 9 . | . . . | 3 . .
6 . 4 | 1 3 . | . 2 7
7 . . | . . . | . . 6
[/code]

I have been able to solve it to the following:

[code]
1 2 69 | 35678 78 3568 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 69 | 368 148 13468 | 1689 1389 2
----------+--------------------+---------------
4 5 7 | 38 189 1389 | 2 6 39
3 1 8 | 2 6 79 | 579 59 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 678 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 489 2 | 589 4589 6
[/code]

As per XYZ Wing help: r9c7 is the XYZ cell (Z=5), r9c4 can be the XZ cell and r8c7 the YZ cell.
One of these 3 cells must be a 5. Now cell r9c8 containing a 5 can see
each of the XYZ Wing cells and the 5 candidate may be removed from r9c8.
Further: Since cell r5c8 now is the only cell in Col 8 with a 5, 5 is the
solution to r5c8 and the 5 candidate in r5c7 can be removed.

This leaves:

[code]
1 2 69 | 35678 78 3568 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 69 | 368 148 13468 | 1689 1389 2
----------+--------------------+---------------
4 5 7 | 38 189 1389 | 2 6 39
3 1 8 | 2 6 79 | 79 5 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 678 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 489 2 | 589 489 6
[/code]

Now using Forcing Chain logic: If r5c6 is a 9 then 9 be removed from r4c6.
And if r5c6 is a 7, then r6c6 is a 3, r4c4 is an 8, r9c4 is a 5,
r8c6 would become a 9 also allowing the removal of a 9 from r4c6

This leaves:

[code]
1 2 69 | 35678 78 3568 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 69 | 368 148 13468 | 1689 1389 2
----------+--------------------+---------------
4 5 7 | 38 189 138 | 2 6 39
3 1 8 | 2 6 79 | 79 5 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 678 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 489 2 | 589 489 6
[/code]

Now the 9s rows 5 and 8 form an X Wing pattern allowing the removal of 9s from cells r3c7 and
r9c7.

this produces a Naked Pair of 58s in r9c4 and r9c7 permitting the removal of 8s in r9c5 and r9c8.

This leaves:

[code]
1 2 69 | 35678 78 3568 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 69 | 368 148 13468 | 168 1389 2
----------+--------------------+---------------
4 5 7 | 38 189 138 | 2 6 39
3 1 8 | 2 6 79 | 79 5 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 678 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 49 2 | 58 49 6
[/code]

Using Forcing Chain logic: If r4c4 is an 8 the 8s in cells r1c4, r3c4 and r7c4 can be removed.
And if r4c4 is a 3, then r6c6 is a 7, r5c6 is a 9, r8c6 is a 5, and
r9c4 is an 8 also allowing the removal of 8s from r1c4, r3c4 and
r7c4.

Removing these 8s leaves:

[code]
1 2 69 | 3567 78 3568 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 69 | 36 148 13468 | 168 1389 2
----------+--------------------+---------------
4 5 7 | 38 189 138 | 2 6 39
3 1 8 | 2 6 79 | 79 5 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 67 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 49 2 | 58 49 6
[/code]

Forcing Chain logic: If r1c3=6 then 6 can not be a candidate in r1c4.
And if r1c3=9, r1c9=3, r4c9=9, r5c7=7, r5c6=9, r8c6=5, r9c4=8, r4c4=3,
r3c4=6 and this too precludes 6 being a candidate in r1c4.
REMOVE 6 as a candidate in r1c4!!!

AND: If r6c6=3 then 3 can not be a candidate in r1c6.
And if r6c6=7, r6c7=1, r6c8=3, r4c9=9, r1c9=3 also eliminates 3 as a
candidate in r1c6.

AND: If r3c4=6 then 6 can not be a candidate in r1c6.
And if r3c4=3, r4c4=8, r9c4=5, r8c6=9, r5c6=7, r5c7=9, r4c9=3, r1c9=9,
r1c3=6 also requires removal of candidate 6 from r1c6.

Easy eliminations: r1c3=6 (only 6 in row 1), r3c3=9 (remain of a naked pair), remove 9 from
r3c8 (row 3 has a 9 in col 3)

Removing these candidates leaves:

[code]
1 2 6 | 357 78 58 | 4 389 39
8 4 3 | 9 2 16 | 16 7 5
5 7 9 | 36 148 13468 | 168 138 2
----------+--------------------+---------------
4 5 7 | 38 189 138 | 2 6 39
3 1 8 | 2 6 79 | 79 5 4
9 6 2 | 4 5 37 | 17 13 8
----------+--------------------+---------------
2 9 5 | 67 478 468 | 3 48 1
6 8 4 | 1 3 59 | 59 2 7
7 3 1 | 58 49 2 | 58 49 6
[/code]

Forcing Chain: If r4c4=3 then r4c6 can not have a 3 candidate.
And if r4c4=8 then r9c4=5, r8c6=9, r5c6=7, r6c6=3, and again r4c6 can not have
3 as a candidate.

AND: If r1c6=5 then a 5 can be not be in r1c4.
If r1c6=8 then r4c6=1, r2c6=6, r2c7=1, r6c7=7, r5c7=9, r8c7=5, r9c7=8 and
r9c4=5 so here too r1c4 can not have 5.

Easy Solving: r1c6=5 (only 5 in row 1), r8c6=9, r5c6=7 and r8c7=5; r6c6=3 and r5c7=9, r9c7=8,
r6c8=1, r4c4=8 and delete a 3 from r3c6; r9c4=5, r7c8=4, delete an 8 from r3c7;
r9c8=9 and delete 4s from r7c5 and r7c6; r4c6=1, r4c5=9, r4c9=3; r9c5=4, r3c5=1;
r2c6=6, r3c7=6, r2c7=1 and remove a 1 and a 6 from r3c6; r3c4=3, r1c4=7, r7c4=6,
r1c5=8, r7c5=7, r3c6=4, r7c6=8; r6c7=7, r1c9=9, r1c8=3, AND FINALLY r3c8=8 !!!

The Solution:

[code]
1 2 6 | 7 8 5 | 4 3 9
8 4 3 | 9 2 6 | 1 7 5
5 7 9 | 3 1 4 | 6 8 2
------+-------+------
4 5 7 | 8 9 1 | 2 6 3
3 1 8 | 2 6 7 | 9 5 4
9 6 2 | 4 5 3 | 7 1 8
------+-------+------
2 9 5 | 6 7 8 | 3 4 1
6 8 4 | 1 3 9 | 5 2 7
7 3 1 | 5 4 2 | 8 9 6
[/code]

by **udosuk** » Tue Apr 17, 2007 9:35 am

rsavage65, bad idea about posting the "details" in your signature, as it doesn't come out properly...

Also, I think you're using way too much "forcing chain logic" to solve this... There is a more elegant solution:

After basic moves:

Code: Select all: *--------------------------------------------------------------------* | 1 2 69 | 35678 78 3568 | 4 389 39 | | 8 4 3 | 9 2 16 | 16 7 5 | | 5 7 69 | 368 148 13468 | 1689 1389 2 | |----------------------+----------------------+----------------------| | 4 5 7 | 38 189 1389 | 2 6 39 | | 3 1 8 | 2 6 79 | 579 59 4 | | 9 6 2 | 4 5 37 | 17 13 8 | |----------------------+----------------------+----------------------| | 2 9 5 | 678 478 468 | 3 48 1 | | 6 8 4 | 1 3 59 |*59 2 7 | | 7 3 1 |*58 489 2 |*589 -4589 6 | *--------------------------------------------------------------------*

XYZ-wing of {589}: one of r8c7+r9c47 must be 5 => r9c8<>5
Hidden single of {5} on c8 => r5c8=5

Code: Select all: *--------------------------------------------------------------------* | 1 2 69 | 35678 78 3568 | 4 389 39 | | 8 4 3 | 9 2 16 | 16 7 5 | | 5 7 69 | 368 148 13468 |-1689 1389 2 | |----------------------+----------------------+----------------------| | 4 5 7 | 38 189 -1389 | 2 6 39 | | 3 1 8 | 2 6 *79 |*79 5 4 | | 9 6 2 | 4 5 37 | 17 13 8 | |----------------------+----------------------+----------------------| | 2 9 5 | 678 478 468 | 3 48 1 | | 6 8 4 | 1 3 *59 |*59 2 7 | | 7 3 1 | 58 489 2 |-589 489 6 | *--------------------------------------------------------------------*

X-wing of {9} in r58c67 => r4c6, r39c7<>9
Naked pair of {58} in r9c47 => r9c58={49}

Code: Select all: *--------------------------------------------------------------------* | 1 2 69 | 35678 78 -3568 | 4 389 *39 | | 8 4 3 | 9 2 16 | 16 7 5 | | 5 7 69 | 368 148 13468 | 168 1389 2 | |----------------------+----------------------+----------------------| | 4 5 7 | 38 189 138 | 2 6 *39 | | 3 1 8 | 2 6 79 | 79 5 4 | | 9 6 2 | 4 5 *37 | 17 *13 8 | |----------------------+----------------------+----------------------| | 2 9 5 | 678 478 468 | 3 48 1 | | 6 8 4 | 1 3 59 | 59 2 7 | | 7 3 1 | 58 49 2 | 58 49 6 | *--------------------------------------------------------------------*

Turbot fish of {3} in r14c9+r6c68 => r1c6<>3

(Alternative reasoning:
Either r4c9<>3 or r6c8<>3, otherwise we'll have two 3s in block 6.
If r4c9<>3, then r1c9=3.
If r6c8<>3, then r6c6=3.
Either way, r1c6<>3.)

Code: Select all: *--------------------------------------------------------------------* | 1 2 69 | 35678 78 568 | 4 389 39 | | 8 4 3 | 9 2 16 | 16 7 5 | | 5 7 69 |C368 148 13468 | 168 1389 2 | |----------------------+----------------------+----------------------| | 4 5 7 |C38 189 138 | 2 6 39 | | 3 1 8 | 2 6 79 | 79 5 4 | | 9 6 2 | 4 5 37 | 17 13 8 | |----------------------+----------------------+----------------------| | 2 9 5 |C678 A478 -468 | 3 A48 1 | | 6 8 4 | 1 3 B59 | 59 2 7 | | 7 3 1 |C58 B49 2 | 58 49 6 | *--------------------------------------------------------------------*

ALS-xyz rule:
A: r7c58={478}
B: r8c6+r9c5={459}
C: r3479c4={35678}
Restricted common between A,C: x=7
Restricted common between B,C: y=5
Common between A,B: z=4

Therefore r7c6<>4.

(Alternative reasoning:
Either r7c4=7 or r9c4=5, otherwise we'll only have {368} for the 4 cells r3479c4.
If r7c4=7, then r7c58={48} (naked pair).
If r9c4=5, then r8c6=9, and r9c5=4.
Either way, r7c6<>4.)

Then a hidden single of {4} on c6 and a box-line elimination in r4c4 solve the puzzle.