How hard is this puzzle?

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How hard is this puzzle?

Postby 999_Springs » Fri Feb 09, 2007 9:52 pm

How hard is this puzzle? Is it possible to solve it without using forcing chains?

Code: Select all
.5.|.29|...
.29|..1|.5.
...|..6|4..
---+---+---
1.5|..8|.6.
4..|53.|...
.9.|...|..4
---+---+---
...|...|..7
..8|7..|..1
21.|..3|9..

(This puzzle was created by me so I am not looking to solve it, only to see how hard it can get.)
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Postby ArkieTech » Sat Feb 10, 2007 12:08 am

999_Springs said
How hard is this puzzle? Is it possible to solve it without using forcing chains?


A good puzzle but not a hard one. Found a swordfish, xy-wing and a turbot

Did not need chains.

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Postby daj95376 » Sat Feb 10, 2007 12:21 am

ArkieTech,

Please post solution not needing chains. TIA!
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Postby re'born » Sat Feb 10, 2007 1:19 am

If one uses Unique Rectangles, it isn't too bad. After basic techniques:

Code: Select all
 *-----------------------------------------------------------*
 | 368   5     4     | 38    2     9     | 17*   17*   368   |
 | 368   2     9     | 4     7     1     | 38    5     368   |
 | 378   378   1     | 38    5     6     | 4     29    29    |
 |-------------------+-------------------+-------------------|
 | 1     37    5     | 9     4     8     | 237   6     23    |
 | 4     678-  26    | 5     3     27    | 178*  1789* 89#   |
 | 378   9     23    | 1     6     27    | 5     378-  4     |
 |-------------------+-------------------+-------------------|
 | 9     4     36    | 2     1     5     | 368   38    7     |
 | 5     36    8     | 7     9     4     | 236   23    1     |
 | 2     1     7     | 6     8     3     | 9     4     5     |
 *-----------------------------------------------------------*


the potential deadly pattern in r15c78, along with r5c9 implies r5c2<>8 (as well as r6c8<>8). After a few more singles, we get to:

Code: Select all
 *-----------------------------------------------------------*
 | 36*   5     4     | 8     2     9     | 17    17    36*   |
 | 36*   2     9     | 4     7     1     | 38    5     368*  |
 | 7     8     1     | 3     5     6     | 4     29    29    |
 |-------------------+-------------------+-------------------|
 | 1     37    5     | 9     4     8     | 237   6     23    |
 | 4     67    26    | 5     3     27    | 178   1789  89    |
 | 8     9     23    | 1     6     27    | 5     37    4     |
 |-------------------+-------------------+-------------------|
 | 9     4     36    | 2     1     5     | 368   38    7     |
 | 5     36    8     | 7     9     4     | 236   23    1     |
 | 2     1     7     | 6     8     3     | 9     4     5     |
 *-----------------------------------------------------------*


The potential deadly pattern in r12c19 implies that r2c9=8, and the puzzle then solves with singles.
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Postby udosuk » Sat Feb 10, 2007 9:59 am

rep'nA, your first UR doesn't need the help from r5c9:
Code: Select all
 *-----------------------------------------------------------*
 | 368   5     4     | 38    2     9     |*17   *17    368   |
 | 368   2     9     | 4     7     1     | 38    5     368   |
 | 378  #378   1     | 38    5     6     | 4     29    29    |
 |-------------------+-------------------+-------------------|
 | 1    @37    5     | 9     4     8     | 237   6     23    |
 | 4     678   26    | 5     3     27    |-178  -1789  89    |
 |#378   9    @23    | 1     6     27    | 5    @378   4     |
 |-------------------+-------------------+-------------------|
 | 9     4     36    | 2     1     5     | 368   38    7     |
 | 5    @36    8     | 7     9     4     | 236  -23    1     |
 | 2     1     7     | 6     8     3     | 9     4     5     |
 *-----------------------------------------------------------*

Strong link of 1s in r5c78 => UR-type 4 => r5c78<>7
=> Naked triple of {189} in r5c789 => r6c1=8 => r3c2=8

And then there is a turbot fish of 3s:
Strong links in r48c2 & r6c38 => r8c8<>3

And the rest are all singles...
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Postby re'born » Sat Feb 10, 2007 12:02 pm

udosuk wrote:rep'nA, your first UR doesn't need the help from r5c9


...and yet to get my exclusions that is exactly what you use

udosuk wrote:=> Naked triple of {189} in r5c789 => r6c1=8 => r3c2=8


I believe my UR was originally called a Type 3 UR, but the terminology police can correct me.
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Postby Carcul » Mon Feb 12, 2007 11:06 am

999_Springs wrote:How hard is this puzzle? Is it possible to solve it without using forcing chains?


Code: Select all
 *---------------------------------------------------*
 | 368   5     4  | 38    2     9  | 17    17    368 |
 | 368   2     9  | 4     7     1  | 38    5     368 |
 | 378   378   1  | 38    5     6  | 4     29    29  |
 |----------------+----------------+-----------------|
 | 1     37    5  | 9     4     8  | 237   6     23  |
 | 4     678   26 | 5     3     27 | 178   1789  89  |
 | 378   9     23 | 1     6     27 | 5     378   4   |
 |----------------+----------------+-----------------|
 | 9     4     36 | 2     1     5  | 368   38    7   |
 | 5     36    8  | 7     9     4  | 236   23    1   |
 | 2     1     7  | 6     8     3  | 9     4     5   |
 *---------------------------------------------------*

[r2c7]-8-[r12c9]=8=[r12c1]-8-[r6c1]=8=[r6c8]-8-[r7c8]=8=[r7c7]-8-
-[r2c7], => r2c7<>8 solving the puzzle.

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Postby ravel » Mon Feb 12, 2007 1:04 pm

Carcul wrote:[r2c7]-8-[r12c9]=8=[r12c1]-8-[r6c1]=8=[r6c8]-8-[r7c8]=8=[r7c7]-8-
-[r2c7], => r2c7<>8 solving the puzzle.
I dont see the link [r12c9]=8=[r12c1], please explain.
In fact there is a nishio for 8 in r2c7, so the fishermen again are invited to identify the creature.
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Postby re'born » Mon Feb 12, 2007 2:28 pm

ravel wrote:
Carcul wrote:[r2c7]-8-[r12c9]=8=[r12c1]-8-[r6c1]=8=[r6c8]-8-[r7c8]=8=[r7c7]-8-
-[r2c7], => r2c7<>8 solving the puzzle.
I dont see the link [r12c9]=8=[r12c1], please explain.


It follows easily from noting the potential deadly pattern in r12c19<36>. One of those four cells must be an 8.

Perhaps this is an even shorter solution using the same observation:

[r5c9]-8-[r12c9]=8=[r12c1]-8-[r6c1]=8=[r6c8]-8-[r5c9], => r5c9<>8, solving the puzzle.
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Postby ronk » Mon Feb 12, 2007 2:42 pm

ravel wrote:In fact there is a nishio for 8 in r2c7, so the fishermen again are invited to identify the creature.

Based on just the 8s in Carcul's grid, the following is possible ...
Code: Select all
 .  .  . |  8  .  . |  .  .  .
 .  .  . |  .  .  . |  8  .  .
 .  8  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  8 |  .  .  .
 .  .  . |  .  .  . |  .  .  8
 8  .  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  8  .
 .  .  8 |  .  .  . |  .  .  .
 .  .  . |  .  8  . |  .  .  .

... so the Nishio must be for different pencilmarks. Would you please post them?
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Postby ravel » Mon Feb 12, 2007 3:14 pm

Thanks rep'nA and Ron, so i was both blind and wrong:)
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Postby 999_Springs » Tue Feb 13, 2007 12:57 pm

Does removing the 1 in r4c1 make any difference to the techniques used in solving the puzzle?
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Postby udosuk » Tue Feb 13, 2007 1:20 pm

AFAIS, just a little bit of difference...

This is the sticking point without the clue at r4c1:
Code: Select all
 *-----------------------------------------------------------*
 | 368   5     4     | 38    2     9     | 17    17    368   |
 | 368   2     9     | 4     7     1     | 38    5     368   |
 | 1378  378   13    | 38    5     6     | 4     29    29    |
 |-------------------+-------------------+-------------------|
 | 137   37    5     | 9     4     8     | 1237  6     23    |
 | 4     678   126   | 5     3     27    | 178   1789  89    |
 | 378   9     23    | 1     6     27    | 5     378   4     |
 |-------------------+-------------------+-------------------|
 | 9     4     36    | 2     1     5     | 368   38    7     |
 | 5     36    8     | 7     9     4     | 236   23    1     |
 | 2     1     7     | 6     8     3     | 9     4     5     |
 *-----------------------------------------------------------*

As you can see, all the URs and chains from rep'nA, Carcul still hold, but my UR-type 4 (making use of the strong link in r5c78) doesn't work anymore... (Thanks ravel for pointing that out...:) )

Meanwhile ArkieTech still hasn't demonstrated to us his mysterious "swordfish, xy-wing and a turbot" solution...:?:
Last edited by udosuk on Tue Feb 13, 2007 12:44 pm, edited 1 time in total.
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Postby ravel » Tue Feb 13, 2007 1:39 pm

udosuk wrote:As you can see, all the URs and chains from rep'nA, Carcul & me still hold...
To be more precise, the "Strong link of 1s in r5c78 => UR-type 4" doesn't exist here.
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Postby ravel » Tue Feb 13, 2007 2:09 pm

999_Springs wrote:Does removing the 1 in r4c1 make any difference to the techniques used in solving the puzzle?
If you remove the 2 in r9c1 instead, you get a harder one:
Code: Select all
 +-------+-------+-------+
 | . 5 . | . 2 . | . . . |
 | . 2 9 | . . 1 | . 5 . |
 | . . . | . . 6 | 4 . . |
 +-------+-------+-------+
 | 1 . 5 | . . 8 | . 6 . |
 | 4 . . | 5 3 . | . . . |
 | . 9 . | . . . | . . 4 |
 +-------+-------+-------+
 | . . . | . . . | . . 7 |
 | . . 8 | 7 . . | . . 1 |
 | . 1 . | . . 3 | 9 . . |
 +-------+-------+-------+
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