Stuck on this

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Stuck on this

Postby Havard » Thu Apr 20, 2006 10:42 am

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
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Postby tarek » Thu Apr 20, 2006 11:17 am

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:D
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Postby Havard » Thu Apr 20, 2006 11:31 am

tarek wrote: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:D


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

Havard
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Postby tarek » Thu Apr 20, 2006 11:47 am

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
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Postby ravel » Thu Apr 20, 2006 3:44 pm

tarek wrote: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.
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Postby Carcul » Fri Apr 21, 2006 8:42 am

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
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Postby Havard » Fri Apr 21, 2006 9:51 am

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

Havard
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Postby Carcul » Fri Apr 21, 2006 10:35 am

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

Regards, Carcul
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