## Stuck on this

Post the puzzle or solving technique that's causing you trouble and someone will help

### Stuck on this

Hi.

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

original:
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`. 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:
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`3     9     4     | 78    678   1     | 5     267   2672     57    8     | 3     567   4     | 9     67    157    1     6     | 279   2579  59    | 8     4     3------------------+-------------------+------------------45    3     7     | 248   258   56    | 124   126   99     6     125   | 1247  12457 57    | 3     8     248     24    12    | 1249  12349 369   | 7     5     46------------------+-------------------+------------------6     8     25    | 1479  13479 379   | 124   1279  24571     47    3     | 5     479   2     | 6     79    8457   2457  9     | 6     147   8     | 124   3     2457`

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

Posts: 377
Joined: 25 December 2005

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

tarek

Posts: 2650
Joined: 05 January 2006

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

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
Havard

Posts: 377
Joined: 25 December 2005

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

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`Candidates in r2c8 will force r8c8 to have only 9 as valid Candidatesr2c8=7 => r8c8=9r2c8=6 => (r2c5<>6,r2c8=6 => r4c8<>6 => r6c9=6 => r6c6<>6 => r4c6=6) => r1c5=6 => r4c5=8 => r4c1=5 => r6c2=4 => r8c2=7 => r8c8=9Therefore r8c8=9`

& this one too......
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`Candidates in r2c8 will force r2c2 to have only 5 as valid Candidatesr2c8=7 => r2c2=5r2c8=6 => (r2c5<>6,r2c8=6 => r4c8<>6 => r6c9=6 => r6c6<>6 => r4c6=6) => r1c5=6 => r4c5=8 => r4c1=5 => r3c1<>5 => r2c2=5Therefore r2c2=5`

so definitely a tough one...
tarek

tarek

Posts: 2650
Joined: 05 January 2006

tarek wrote:so definitely a tough one...

So i dare to post a rather complicated solution, starting where tarek stopped above.
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`3     9     4     | 78    678   1     | 5     267   2672     5     8     | 3     67    4     | 9     67    17     1     6     | 29    259   59    | 8     4     3------------------+-------------------+------------------45    3     7     | 248   258   56    | 124   126   99     6     125   | 1247  12457 57    | 3     8     248     24    12    | 1249  12349 369   | 7     5     46------------------+-------------------+------------------6     8     25    | 1479  13479 379   | 124   127   24571     47    3     | 5     47    2     | 6     9     845    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.
ravel

Posts: 998
Joined: 21 February 2006

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

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` *-----------------------------------------------------* | 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
Carcul

Posts: 724
Joined: 04 November 2005

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

Havard
Havard

Posts: 377
Joined: 25 December 2005

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

Regards, Carcul
Carcul

Posts: 724
Joined: 04 November 2005

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