The New Sudoku Players' Forum

[bat999]

Hi
Please can somebody give me a *hint*, how to move forward with this puzzle.

The puzzle came from sudokuisland.com.
Described as "Extreme".


Original.

Code: Select all

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

Stuck here.

Code: Select all

246  5   246  | 3   1    9    | 46   8  7
1    8   46   | 24  267  267  | 3    9  5
7    9   3    | 45  56   8    | 1    46 2
--------------+---------------+-------------
469  124 2469 | 129 3    5    | 8    7  1469
259  12  7    | 6   8    4    | 259  3  19
4569 3   8    | 7   29   12   | 2569 26 1469
--------------+---------------+-------------
3    24  249  | 129 267  1267 | 279  5  8
8    6   1    | 59  2579 27   | 2479 24 3
29   7   5    | 8   4    3    | 269  1  69

Solution.

Code: Select all

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

[daj95376]

My solver needed to use chains to finish your puzzle. You may wish to consider another, easier puzzle.

_

[Leren]

The puzzle can be finished off in 2 moves

Code: Select all

*--------------------------------------------------------------*
| 246   5     246    | 3     1     9      | 46    8     7      |
| 1     8     46     | 24   a267   267    | 3     9     5      |
| 7     9     3      | 45   b56    8      | 1    c46    2      |
|--------------------+--------------------+--------------------|
| 469   124   2469   | 129   3     5      | 8     7     1469   |
| 259   12    7      | 6     8     4      | 259   3     19     |
| 4569  3     8      | 7     9-2   12     | 2569 d26    1469   |
|--------------------+--------------------+--------------------|
| 3     24    249    | 129  a267   1267   | 279   5     8      |
| 8     6     1      | 59    2579  27     | 2479  24    3      |
| 29    7     5      | 8     4     3      | 269   1     69     |
*--------------------------------------------------------------*

(2=6) r27c5 - r3c5 = r3c8 - (6=2) r6c8 => - 2 r6c5;

Code: Select all

*--------------------------------------------------------------*
| 246   5     246    | 3     1     9      | 46    8     7      |
| 1     8     46     |d24    267   267    | 3     9     5      |
| 7     9     3      |c45    56    8      | 1    b46    2      |
|--------------------+--------------------+--------------------|
| 469   124   2469   |e12    3     5      | 8     7     1469   |
| 259   12    7      | 6     8     4      | 259   3     19     |
| 456   3     8      | 7     9    f12     | 256   6-2   146    |
|--------------------+--------------------+--------------------|
| 3     24    249    | 129   267   1267   | 279   5     8      |
| 8     6     1      | 59    257   7-2    | 2479 a24    3      |
| 29    7     5      | 8     4     3      | 269   1     69     |
*--------------------------------------------------------------*

(2=4) r8c8 - r3c8 = r3c4 - (4=2) r2c4 - r4c4 = (2) r6c6 => - 2 r6c8, r8c6;

The puzzle is then solved via a cascade of singles.

Leren

[JC Van Hay]

Hint : look at what you can do from the cells in R3 anc C8.

A short analysis as an example :

Code: Select all

+------------------+-------------------+-------------------+
| 246    5    246  | 3      1     9    | 46    8      7    |
| 1      8    46   | (24)   267   267  | 3     9      5    |
| 7      9    3    | 5(4)   56    8    | 1     -6(4)  2    |
+------------------+-------------------+-------------------+
| 2469   124  2469 | 19(2)  3     5    | 8     7      1469 |
| 259    12   7    | 6      8     4    | 259   3      19   |
| 24569  3    8    | 7      9(2)  1(2) | 2569  (26)   1469 |
+------------------+-------------------+-------------------+
| 3      24   249  | 129    2679  1267 | 279   5      8    |
| 8      6    1    | 259    2579  27   | 2479  24     3    |
| 29     7    5    | 8      4     3    | 269   1      69   |
+------------------+-------------------+-------------------+


r3c8=6 -> r3c4=4 and r6c8=2=r4c4; r2c4 is empty :=> r3c8=4 and singles to the end.

[bat999]

The puzzle can be finished off in 2 moves...

Hi Leren, thanks for your reply.
I don't really understand the notation yet.

Please will you explain that first move (in words).
(2=6) r27c5 - r3c5 = r3c8 - (6=2) r6c8 => - 2 r6c5;

I can see that you have eliminated the 2 from r6c5.
How?

[bat999]

Hint : look at what you can do from the cells in R3 anc C8...

Hi JC Van Hay, thanks for your reply.

If r3c8 was 6
then r3c4 would be 4 and r2c4 would be 2.

But if r3c8 was 6
then r6c8 would be 2 and r6c56 would both be not 2.
So r4c4 would be 2 and r2c4 would be 4.

It's a contradiction, r2c4 can't be both 2 and 4.
I understand that.

"r3c8=6 -> r3c4=4 and r6c8=2=r4c4; r2c4 is empty :=> r3c8=4"

I will eliminate the 6 from r3c8 to make it 4 then take it from there.

[bat999]

I will eliminate the 6 from r3c8 to make it 4 then take it from there...

Update
It has worked out OK
Thanks.

[Leren]

bat999 wrote:
Please will you explain that first move (in words).
(2=6) r27c5 - r3c5 = r3c8 - (6=2) r6c8 => - 2 r6c5;

Notice that r2c5 and r7c5 form an Almost Locked Set (ALS). That's N different digits in N-1 cells, where N=2 here.

Now suppose that neither of the 2's in r2c5 and r7c5 were True. Then the other 2 digits, 6 and 7 would have to be True in these cells, the important digit here being 6.

Since r3c5 sees both r2c5 and r7c5 the 6 there must be False, and since there are only 2 6's in Row 3 the 6 in r3c8 must be True.

So the 6 in r6c8 must be False and so the 2 in that cell must be True.

The net result of all this is that at least one of r2c5, r7c5 and r6c8 must be 2. Since r6c5 can see all of these cells it can't be 2.

It's customary to leave out repeated or unimportant digits in chain notation so that it doesn't get too cluttered. I could have written the chain as (2=76) r27c5 - (6) r3c5 = (6) r3c8 - (6=2) r6c8 and it might be clearer for a beginner.

Notice also that the chain can be read from right to left as well as from left to right. That's why I've written the digits in parentheses - the True/False status of the digits depends on which direction you are reading the chain.

If you read it from right to left you start by assuming that 2 in r6c8 is False and conclude that one of the 2's in r2c5 and r7c5 must be True, so again r6c5 can't be 2.

Leren

[bat999]

Notice that r2c5 and r7c5 form an Almost Locked Set (ALS)....

The net result of all this is that at least one of r2c5, r7c5 and r6c8 must be 2. Since r6c5 can see all of these cells it can't be 2.

OK thanks, I can follow that logic now.

As for the second move...
If r8c8 is 2 then r8c6 is not 2.

If r8c8 is 4 then r3c8 is 6 and r3c5 is 5 and r3c4 is 4 and r2c4 is 2 and r4c4 is 1 and r6c6 is 2, so again r8c6 is not 2.

From there...
r8c6 is 6. This eliminates the 6 from r3c8 and puzzle will solve same as with JC Van Hay's suggestion.

[bat999]

... You may wish to consider another, easier puzzle.

Hi
I am currently solving the puzzles from extremesudoku.info without too much trouble.

It's a neat website but I'd like to try something *slightly* more difficult.

That's why I tried sudokisland.com.

There are several websites listed at sudopedia.enjoysudoku.com/Sudoku_Websites.html

Any recommendations?

[Leren]

bat999 wrote: Any recommendations?

Try this site http://hodoku.sourceforge.net/en/index.php

Leren

[bat999]

Try this site http://hodoku.sourceforge.net/en/index.php

Hi
This HoDoKu seems to be an impressive piece of kit.
The Sudoku programs that I have used before would solve problems, but would not show me how.
That's why I asked in the forum.

When I entered the sudokisland.com puzzle...
It first found a finned swordfish to remove 2 from r4c3.
I should have been able to find that myself, but I missed it.
2 r159 c137 fr5c2 => r4c3<>2

Then various other moves, some I would have managed OK, and some that I would not.

JC Van Hay's solution seems to be the most elegant.
It relies on being able to spot the contradiction if r3c8 was 6.
I suppose this skill comes with practice.

So far, I have been using HoDoKu to generate "medium" puzzles, but I will increase the difficulty level in stages.
Perhaps I will evolve into a Sudoku maven.