The New Sudoku Players' Forum

[Havard]

Hi.

I have thrown everything I got against this puzzle, and I can't seem to advance it any further... Any suggestions?

original:

Code: Select all

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


Where I am up to:

Code: Select all

3     9     4     | 78    678   1     | 5     267   267
2     57    8     | 3     567   4     | 9     67    1
57    1     6     | 279   2579  59    | 8     4     3
------------------+-------------------+------------------
45    3     7     | 248   258   56    | 124   126   9
9     6     125   | 1247  12457 57    | 3     8     24
8     24    12    | 1249  12349 369   | 7     5     46
------------------+-------------------+------------------
6     8     25    | 1479  13479 379   | 124   1279  2457
1     47    3     | 5     479   2     | 6     79    8
457   2457  9     | 6     147   8     | 124   3     2457


now I know there is a nishio here (can anyone find that one in some way?)

Code: Select all

. . 4 | . . . | . . .
. . . | . . 4 | . . .
. . . | . . . | . 4 .
------+-------+------
4 . . | 4 . . | 4 . .
. . . | 4 4 . | . . 4
. 4 . | 4 4 . | . . 4
------+-------+------
. . . | 4 4 . | 4 . 4
. 4 . | . 4 . | . . .
4 4 . | . 4 . | 4 . *


but that does not seem to help much...


any help appreciated!

Havard

[tarek]

why do it via Nishio Havard if you have the Finned X-wing in columns 1 & 7.........You have missed drinking your mug of cofee this morning

[Havard]

why do it via Nishio Havard if you have the Finned X-wing in columns 1 & 7.........You have missed drinking your mug of cofee this morning

whops... you got me! But what about solving that damn thing? Has that escaped me just as easily, or is this a though one?

Havard

[tarek]

this should advance it a bit....
I'm not sure if something simpler is there

Code: Select all

Candidates in r2c8 will force r8c8 to have only 9 as valid Candidates
r2c8=7 => r8c8=9
r2c8=6 => (r2c5<>6,r2c8=6 => r4c8<>6 => r6c9=6 => r6c6<>6 => r4c6=6) => r1c5=6 => r4c5=8 => r4c1=5 => r6c2=4 => r8c2=7 => r8c8=9
Therefore r8c8=9

& this one too......

Code: Select all

Candidates in r2c8 will force r2c2 to have only 5 as valid Candidates
r2c8=7 => r2c2=5
r2c8=6 => (r2c5<>6,r2c8=6 => r4c8<>6 => r6c9=6 => r6c6<>6 => r4c6=6) => r1c5=6 => r4c5=8 => r4c1=5 => r3c1<>5 => r2c2=5
Therefore r2c2=5

so definitely a tough one...
tarek

[ravel]

so definitely a tough one...

So i dare to post a rather complicated solution, starting where tarek stopped above.

Code: Select all

3     9     4     | 78    678   1     | 5     267   267
2     5     8     | 3     67    4     | 9     67    1
7     1     6     | 29    259   59    | 8     4     3
------------------+-------------------+------------------
45    3     7     | 248   258   56    | 124   126   9
9     6     125   | 1247  12457 57    | 3     8     24
8     24    12    | 1249  12349 369   | 7     5     46
------------------+-------------------+------------------
6     8     25    | 1479  13479 379   | 124   127   2457
1     47    3     | 5     47    2     | 6     9     8
45    247   9     | 6     147   8     | 124   3     2457


If r9c1=4:
r4c1=5, r4c5<>5
r6c2=4, r8c2=7, r9c2<>7
(r9c1=4) r9c9=5, r9c5=7, r2c5=6, r1c5=8, r4c5<>8
(r9c5=7) r9c7=1, r7c78<>1
(r2c5=6) r2c8=7, r7c8=2, r7c7=4, r4c7=2, r4c5<>2
=>r9c1=5

An xy-chain then solves the puzzle.

[Carcul]

This puzzle provides two excellent examples of application of Almost Nice Loops (ANL):

Code: Select all

 *-----------------------------------------------------*
 | 3    9     4   | 78    678    1   | 5    267   267  |
 | 2    57    8   | 3     567    4   | 9    67    1    |
 | 57   1     6   | 279   2579   579 | 8    4     3    |
 |----------------+------------------+-----------------|
 | 45   3     7   | 248   258    568 | 124  126   9    |
 | 9    6     125 | 1247  12457  57  | 3    8     24   |
 | 8    24    12  | 1249  12349  369 | 7    5     246  |
 |----------------+------------------+-----------------|
 | 6    8     25  | 1479  13479  379 | 124  1279  2457 |
 | 1    47    3   | 5     479    2   | 6    79    8    |
 | 457  2457  9   | 6     1478   78  | 124  3     2457 |
 *-----------------------------------------------------*


1. [r9c6]=8=[r9c5]=1=[r9c7]-1-[r7c8]=1=[r4c8]=6=[r4c6]=8=[r9c6], => r9c6=8.

2. [r9c9]-4-[r56c9]=4=[r4c7]-4-[r4c1]=4=[r9c1]-4-[r9c9], => r9c9<>4.

3. We have an ANL in the set of cells {r2c2/r3c1/r9c1/r4c1568/r2c8} where a Nice Loop sets up if r4c5 is not "5":

[r2c5]-5-[r4c5]-{Nice Loop: [r2c2]-7-[r3c1]=7=[r9c1]=4=[r4c1]=5=[r4c6]=6=[r4c8]-6-[r2c8]-7-[r2c2]}-7-[r2c2]-5-[r2c5], => r2c5<>5.

4. [r7c8]-7-[r7c456]=7=[r89c5]-7-[r2c5]=7=[r2c8]-7-[r7c8], => r7c8<>7.

5. Now we have an ANL in cells {r4c1/r9c1/r8c28/r1c8/r2c8/r4c68} where a Nice Loop arises if r1c8 is not "6" nor "7":

[r4c4]=8=[r1c4]-8-[r1c5]=(AUR: r12c57)=8|2=[r1c8]-{Nice Loop: [r4c1]=4=[r9c1]-4-[r8c2]-7-[r8c8]=7=[r2c8]=6=[r4c8]-6-[r4c6]-5-[r4c1]}-5-[r4c1]-4-[r4c4], => r4c4<>4.

6. [r7c9]=5=[r7c3]=2=[r9c2]=7=[r8c2]-7-[r8c8]-9-[r7c78|r9c7]-2,4-[r7c9], => r7c9<>2,4.

7. [r4c4]-2-[r3c4]-9-[r3c6]-5-[r4c6]-6-[r4c78]-2-[r4c4],

which implies r4c4<>2 and that solves the puzzle.

Carcul

[Havard]

thanks Carcul, that is very interesting! I will sit down with a jug of coffee and go through your loops.

Havard

[Carcul]

Thanks Havard. If you like, read also this post and make another jug of coffee.

Regards, Carcul