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Postby wapati » Sat May 19, 2007 8:19 am

I have had a rest.:)

Some large seafood in here!

Code: Select all
. . .|2 . .|3 9 .
. . .|. 7 .|4 . 1
. . .|. . 6|. 2 7
-----+-----+-----
6 . .|. 1 3|5 . .
. 8 .|6 . 5|. 3 .
. . 5|7 8 .|. . 4
-----+-----+-----
4 6 .|3 . .|. . .
8 . 3|. 5 .|. . .
. 5 2|. . 4|. . .
Last edited by wapati on Sun Jun 03, 2007 10:10 pm, edited 3 times in total.
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Postby ArkieTech » Sat May 19, 2007 11:57 pm

wapati said:

I have had a rest


Good puzzle:D

Welcome back.

dan
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Postby wapati » Sun May 20, 2007 3:28 am

There is a jellyfish, but it isn't needed. Sashimi swordfish isn't required but it lurks as well.:)

Code: Select all
. . .|6 . 3|. 5 .
. 9 .|8 . .|. 1 .
. . 8|. . .|. . 6
-----+-----+-----
. 6 7|. 9 .|. . 2
8 . .|7 . 2|. . 9
9 . .|. 8 .|7 4 .
-----+-----+-----
7 . .|. . .|6 . .
. 2 .|. . 8|. 9 .
. 8 .|3 . 4|. . .
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Postby wapati » Mon May 21, 2007 3:41 am

Thanks, ArkieTech, good to feel the energy again!


Lots of smaller fish.

Code: Select all
. . 3 | 9 . . | 6 . 5
. . 9 | 7 . . | . . .
2 7 . | . . 3 | . . .
---------------------
. 1 . | 4 3 . | . . .
. . 6 | . . . | 4 . .
. . . | . 7 5 | . 2 .
---------------------
. . . | 5 . . | . 1 3
. . . | . . 8 | 9 . .
3 . 1 | . . 9 | 5 . .
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Postby re'born » Mon May 21, 2007 9:28 am

wapati wrote:Thanks, ArkieTech, good to feel the energy again!


Lots of smaller fish.

Code: Select all
. . 3 | 9 . . | 6 . 5
. . 9 | 7 . . | . . .
2 7 . | . . 3 | . . .
---------------------
. 1 . | 4 3 . | . . .
. . 6 | . . . | 4 . .
. . . | . 7 5 | . 2 .
---------------------
. . . | 5 . . | . 1 3
. . . | . . 8 | 9 . .
3 . 1 | . . 9 | 5 . .


So here is a nice one step 3D coloring solution:

Code: Select all
 *--------------------------------------------------------------------*
 | 148    48     3      | 9      28     124    | 6      7      5      |
 | 1468   468    9      | 7      5      14     | 12c3A8 3a8A   12C8   |
 | 2      7      5      | 16     68     3      | 18     4C9c   4c9C   |
 |----------------------+----------------------+----------------------|
 | 5a8A   1      2      | 4      3      6      | 7      589C   8C9c   |
 | 7      3a5A   6      | 128    9      12     | 4      3A5a   18     |
 | 489    3A489  48     | 18     7      5      | 13a8   2      6      |
 |----------------------+----------------------+----------------------|
 | 4689   24689  48     | 5      246    7      | 2C8c   1      3      |
 | 45A6   2C45a6 7      | 3      1      8      | 9      46     2c4C   |
 | 3      2468c  1      | 26     246    9      | 5      468C   7      |
 *--------------------------------------------------------------------*


Clearly, a and C cannot both be true (see r8c2) and A and c cannot both be true (see r2c7).
It is then routine to check that r2c8<>8, r4c1<>8, r4c8<>5, r6c7<>8, r8c2<>4,6. The puzzle is now solved.

A more elementary approach is to first note the xy-wing pivoted at r7c7, eliminating 4 from r8c12. An x-wing then eliminates 1 from r2c7 and r5c4. This reveals an xyz-wing pivoted at r2c7 eliminating 8 from r3c7. Throw in a little uniqueness later on to remove 4 from r12c1 (don't forget so use the resulting naked quad) and finally you get to this BUG+2 position:

Code: Select all
 *--------------------------------------------------*
 | 18   48   3    | 9    2    14   | 6    7    5    |
 | 16   46   9    | 7    5    14   | 23+8 38-  28   |
 | 2    7    5    | 6    8    3    | 1    49   49   |
 |----------------+----------------+----------------|
 | 58   1    2    | 4    3    6    | 7    59+8 89   |
 | 7    35   6    | 8    9    2    | 4    35   1    |
 | 49   39   48   | 1    7    5    | 38-  2    6    |
 |----------------+----------------+----------------|
 | 49   29   48   | 5    6    7    | 28   1    3    |
 | 56   25   7    | 3    1    8    | 9    46   24   |
 | 3    68   1    | 2    4    9    | 5    68   7    |
 *--------------------------------------------------*


giving r2c8, r6c7<>8, solving the puzzle.

P.S. Great to have you back in the puzzle making biz wapati. I had missed your difficult, but not impossible puzzles every morning.
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Postby ronk » Mon May 21, 2007 11:27 am

rep'nA wrote:So here is a nice one step 3D coloring solution:

Code: Select all
 *--------------------------------------------------------------------*
 | 148    48     3      | 9      28     124    | 6      7      5      |
 | 1468   468    9      | 7      5      14     | 12c3A8 3a8A   12C8   |
 | 2      7      5      | 16     68     3      | 18     4C9c   4c9C   |
 |----------------------+----------------------+----------------------|
 | 5a8A   1      2      | 4      3      6      | 7      5A89C  8C9c   |
 | 7      3a5A   6      | 128    9      12     | 4      3A5a   18     |
 | 489    3A489  48     | 18     7      5      | 13a8   2      6      |
 |----------------------+----------------------+----------------------|
 | 4689   24689  48     | 5      246    7      | 2C8c   1      3      |
 | 45A6   2C45a6 7      | 3      1      8      | 9      46     2c4C   |
 | 3      2468c  1      | 26     246    9      | 5      468C   7      |
 *--------------------------------------------------------------------*


Clearly, a and C cannot both be true (see r8c2) and A and c cannot both be true (see r2c7).
It is then routine to check that r2c8<>8, r4c1<>8, r4c8<>5, r6c7<>8, r8c2<>4,6. The puzzle is now solved.

It's not clear to me, so would you please clarify? What I do see ...

In cells r4c8, r8c2, r8c9 and r3c9, respectively

9C!5A, 5a!2C, 2c!4C and 4c!9C (where 9C!5A means color 9C true excludes color 5A true)

Therefore color 9C is false

r3c9-9-r3c8=9=r4c8=5=r4c1-5-r5c2=5=r8c2=2=r8c9=4=r3c9, implies r3c9<>9
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Postby re'born » Mon May 21, 2007 2:53 pm

ronk wrote:
rep'nA wrote:So here is a nice one step 3D coloring solution:

Code: Select all
 *--------------------------------------------------------------------*
 | 148    48     3      | 9      28     124    | 6      7      5      |
 | 1468   468    9      | 7      5      14     | 12c3A8 3a8A   12C8   |
 | 2      7      5      | 16     68     3      | 18     4C9c   4c9C   |
 |----------------------+----------------------+----------------------|
 | 5a8A   1      2      | 4      3      6      | 7      5A89C  8C9c   |
 | 7      3a5A   6      | 128    9      12     | 4      3A5a   18     |
 | 489    3A489  48     | 18     7      5      | 13a8   2      6      |
 |----------------------+----------------------+----------------------|
 | 4689   24689  48     | 5      246    7      | 2C8c   1      3      |
 | 45A6   2C45a6 7      | 3      1      8      | 9      46     2c4C   |
 | 3      2468c  1      | 26     246    9      | 5      468C   7      |
 *--------------------------------------------------------------------*


Clearly, a and C cannot both be true (see r8c2) and A and c cannot both be true (see r2c7).
It is then routine to check that r2c8<>8, r4c1<>8, r4c8<>5, r6c7<>8, r8c2<>4,6. The puzzle is now solved.

It's not clear to me, so would you please clarify?


I will do my best. First, let me point out that I overlooked your more straigtforward deduction which I would phrase simply as "C sees a and A and therefore C is false."

r2c8<>8: If r2c8=8, then A is true and C is false (see r9c8). Thus, A and c are both true, a contradiction.

r4c1<>8: If r4c1=8, then A is true and C is false (see r4c9). Thus, A and c are both true, a contradiction.

The rest are of the same flavor, but anyone else reading this would be advised to follow ronk's shortcut.
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Postby ravel » Mon May 21, 2007 3:49 pm

To take from both:
r8c2 => a and C cannot both be true
r4c8 => A and C cannot both be true
Since a or A must be true => C is false, c is true, A is false (r2c7), a is true
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Postby wapati » Mon May 21, 2007 4:45 pm

Several unique-type flavors here, no big fish that I saw.:(

Code: Select all
5 2 .|. . .|. . 9
1 . .|. . 4|. . .
. . 6|2 1 .|5 . .
-----+-----+-----
3 9 .|. . .|. . .
. . .|6 . 1|. . .
. . .|. . .|. 8 2
-----+-----+-----
. . 9|. 6 5|1 . .
. . .|3 . .|. . 4
8 . .|. . .|. 2 5
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Postby wapati » Mon May 21, 2007 4:54 pm

Here is an odd one. It is trivial if you use uniqueness once.
I was going to toss it because I know that if I got stuck I would jump on the UR. Others may have more grit and find this a great puzzle?

It is quite hard and full of big fish if you use "won't power".
(Will power is a dumb phrase considering that you need to "won't", not "will" ! )

Anyways, easy UR, hard without!

Code: Select all
9 . 8 | 4 3 . | . 2 .
. . 2 | . . 8 | . 3 6
. . 3 | 9 . . | . . .
---------------------
8 . . | . 6 . | . . .
4 . . | 8 . 5 | . . 2
. . . | . 4 . | . . 3
---------------------
. . . | . . 9 | 3 . .
2 5 . | 3 . . | 4 . .
. 9 . | . 5 4 | 2 . 7
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Postby re'born » Mon May 21, 2007 7:48 pm

wapati wrote:Here is an odd one. It is trivial if you use uniqueness once.
I was going to toss it because I know that if I got stuck I would jump on the UR. Others may have more grit and find this a great puzzle?

It is quite hard and full of big fish if you use "won't power".
(Will power is a dumb phrase considering that you need to "won't", not "will" ! )

Anyways, easy UR, hard without!

Code: Select all
9 . 8 | 4 3 . | . 2 .
. . 2 | . . 8 | . 3 6
. . 3 | 9 . . | . . .
---------------------
8 . . | . 6 . | . . .
4 . . | 8 . 5 | . . 2
. . . | . 4 . | . . 3
---------------------
. . . | . . 9 | 3 . .
2 5 . | 3 . . | 4 . .
. 9 . | . 5 4 | 2 . 7


Yes, it is easy with UR, but it doesn't have to be too hard without. Doing a little 3D coloring, I found

Code: Select all
 *-----------------------------------------------------------*
 | 9     167   8     | 4     3     167   | 157   2     15    |
 | 17    4     2     | 5     17    8     | 9     3     6     |
 | 5     167   3     | 9     127   1267  | 17    4     8     |
 |-------------------+-------------------+-------------------|
 | 8     127   59    | 127   6     3     | 15    1579  4     |
 | 4     3     1A7a  | 8     9     5     | 6     1a7A  2     |
 | 6     127   59    | 127   4     127   | 8     59    3     |
 |-------------------+-------------------+-------------------|
 | 17    8     4     | 1267  127   9     | 3     156   15    |
 | 2     5     167A  | 3     8     1A7a  | 4     1-6   9     |
 | 3     9     16    | 16    5     4     | 2     8     7     |
 *-----------------------------------------------------------*


[r8c8]-1-[r8c6]-7-[r8c3]=7=[r5c3]-7-[r5c8]-1-[r8c8], which gives r8c8<>1, solving the puzzle.

Alternatively, one could notice the 'naked pair covering an xyz-wing':

Code: Select all
 *-----------------------------------------------------------*
 | 9     167   8     | 4     3     167   | 157   2     15    |
 | 17    4     2     | 5     17    8     | 9     3     6     |
 | 5     167   3     | 9     127   1267  | 17    4     8     |
 |-------------------+-------------------+-------------------|
 | 8     127   59    | 127   6     3     | 15    1579  4     |
 | 4     3     17    | 8     9     5     | 6     17    2     |
 | 6     127   59    | 127   4     127   | 8     59    3     |
 |-------------------+-------------------+-------------------|
 | 17#   8     4     | 1267- 127-  9     | 3     156*  15*   |
 | 2     5     167-  | 3     8     17#   | 4     16*   9     |
 | 3     9     16    | 16    5     4     | 2     8     7     |
 *-----------------------------------------------------------*


I suppose it is the ALS xz-rule with A={1567} on r7c189, B={167} on r8c68, x = 6, z = 7. But this is a pattern I've seen before and so recognize as an xyz-wing (or in this case even a naked triple in a box) where the arms both see a bivalue cell (with the same candidates) sharing the normal elimination candidate for the xyz-wing. More generally, it might look like:


Code: Select all
 *  .  .  | .  .  .  |  .  .  .
 *  wx .  | .  xz .  |  .  xyz .
 *  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  .  .  | .  .  .  |  .  .  .
 .  .  .  | .  .  .  |  .  .  .
 .  .  .  | .  .  .  |  .  .  .
----------+----------+----------
 .  *  .  | .  .  .  |  .  .  .
 wx *  .  | .  .  .  |  .  xy  .
 .  *  .  | .  .  .  |  .  .  .


where we can eliminate w from the *'d cells.
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Postby wapati » Mon May 21, 2007 8:15 pm

rep'nA wrote:
[r8c8]-1-[r8c6]-7-[r8c3]=7=[r5c3]-7-[r5c8]-1-[r8c8], which gives r8c8<>1, solving the puzzle.


You call this 3D coloring. I don't do colors but I am aware that fishy patterns and colors pretty much overlap.

What you posted looks like a chain, to me (who doesn't read chains).

Anyway, glad you solved it and I do welcome easy paths!
(I just don't follow most of them.):)

Nice analysis, BTW.
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Postby re'born » Mon May 21, 2007 8:30 pm

wapati wrote:
rep'nA wrote:
[r8c8]-1-[r8c6]-7-[r8c3]=7=[r5c3]-7-[r5c8]-1-[r8c8], which gives r8c8<>1, solving the puzzle.


You call this 3D coloring. I don't do colors but I am aware that fishy patterns and colors pretty much overlap.

What you posted looks like a chain, to me (who doesn't read chains).

Anyway, glad you solved it and I do welcome easy paths!
(I just don't follow most of them.):)


Yeah, so 3D coloring, as far I know, does not overlap with fishy patterns. I like it because it is a terribly easy way to spot what becomes my 'chain' solutions. I supply the chain notation for posterity and precision, but I supply the picture because that is how I see it.

You're right that it is a chain, but in a sense, I can only find the easiest of chains, or perhaps the next level above that. I rarely use more than 4 colors on a grid (this is the limit of my colored pencil collection) and usually only 2 (as was the case for this puzzle). But here is the important thing that I'm slowly getting to...with the coloring in place, my deductions are all pattern based. I'm never chasing candidates along a chain. If you like, my chains are never forced.:)
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Postby wapati » Mon May 21, 2007 8:45 pm

A puzzle would have to be way trivial if there was only one way to solve it.
I don't hold one method as superior, I just use what I like, as do all sane people!:)

I only have a mono pencil (+ eraser) so I don't do colors.
( I cheat sometimes and use + - signs though.):(
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Postby wapati » Tue May 22, 2007 5:21 am

This varies by one's path.

I found a swordfish, you may find a wombat?

Code: Select all
. . .|1 . .|8 4 .
. . 4|5 . 7|6 . .
. . .|. 8 .|. . 2
-----+-----+-----
9 . 6|. 5 .|. 1 .
. . 3|7 . 8|9 . .
. 5 .|. 1 .|3 . 4
-----+-----+-----
3 . .|. 7 .|. . .
. . 5|6 . 3|4 . .
. 6 8|. . 1|. . .
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