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Post puzzles for others to solve here.

Postby ravel » Tue Apr 10, 2007 2:02 pm

Nice solution again, rep'nA.
Code: Select all
.---------------.---------------.---------------.
| 129  129  6   | 5    34   34  | 7    12   8   |
| 8    5    7   | 16   9    2   |B16   3    4   |
| 12   4    3   | 7    16   8   | 9    5    126 |
:---------------+---------------+---------------:
| 3    8    12  | 4    167  5   |B126  9    1267|
| 1679 179  5   | 8    2    16  | 3    4    167 |
| 1267 127  4   | 3    167  9   | 8    1267 5   |
:---------------+---------------+---------------:
| 5   A237  8   | 16  B34   16  |B24   27   9   |
|A127  6   A12  | 9    5    34  |-124  8    1237|
| 4    13   9   | 2    8    7   | 5    16   136 |
'---------------'---------------'---------------'
You can also make the elimination with an (xy?) ALS:
The 1 in r8c7 locks the 3 in A to r7c2, in B to r7c5.
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Postby udosuk » Tue Apr 10, 2007 3:46 pm

ravel wrote:You can also make the elimination with an (xy?) ALS:
The 1 in r8c7 locks the 3 in A to r7c2, in B to r7c5.

I don't like ALSs which don't reside in a single house (like your set B here)...
It's valid logically but I feel it's less elegant than the "pure" ALS-xz...

Here is such a "pure" ALS-xz, for that elimination:
Code: Select all
 *-----------------------------------------------------------*
 | 129   129   6     | 5     34    34    | 7     12    8     |
 | 8     5     7     | 16    9     2     | 16    3     4     |
 | 12    4     3     | 7     16    8     | 9     5     126   |
 |-------------------+-------------------+-------------------|
 | 3     8     12    | 4     167   5     | 126   9     1267  |
 | 1679  179   5     | 8     2     16    | 3     4     167   |
 | 1267  127   4     | 3     167   9     | 8     1267  5     |
 |-------------------+-------------------+-------------------|
 | 5     1237  8     | 16    34    1346  | 124   127   9     |
 |A127   6    A12    | 9     5     134   |-124   8    A1237  |
 | 4     13    9     | 2     8     7     | 5    B16   B136   |
 *-----------------------------------------------------------*

A: r8c139={1237}
B: r9c89={136}
x=3
z=1

Therefore r8c7<>1.:idea:
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Postby wapati » Tue Apr 10, 2007 8:12 pm

Perhaps, too easy. Too many unique patterns. Ignore them and suffer!

Code: Select all
. . 9|1 . 2|6 . .
. 2 4|. 3 .|5 8 .
. 6 .|. 4 .|. 1 .
-----+-----+-----
. . .|4 2 3|. . .
3 . .|. . .|. . 1
. 7 5|. . .|8 3 .
-----+-----+-----
. . .|. . .|. . .
. . .|5 . 1|. . .
. 1 .|3 8 4|. 5 .
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Postby wapati » Tue Apr 10, 2007 8:17 pm

This too. Unique patterns are short cuts. (This too may be too easy.)

Well, they may be the only pattern way. You decide?

Code: Select all
8 9 .|. . .|. 6 7
. . .|. 9 .|. . .
. . 4|. . .|5 . .
-----+-----+-----
4 . .|5 . 3|. . 2
1 . .|7 . 6|. . 3
. . 3|. . .|1 . .
-----+-----+-----
. . 6|3 . 2|7 . .
. . 5|6 . 8|3 . .
. . .|. 4 .|. . .
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Postby wapati » Tue Apr 10, 2007 9:32 pm

This is harder.

Code: Select all
. . 6 | 5 . 7 | 4 . .
. . . | . . . | . . .
7 . 8 | . . . | 9 . 5
---------------------
. . 2 | 9 . 8 | 7 . .
. . . | . . . | . . .
8 7 . | . 6 . | . 3 1
---------------------
2 . 4 | . . . | 8 . 6
. 6 . | . . . | . 2 .
. . 5 | . 2 . | 3 . .
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Postby re'born » Tue Apr 10, 2007 11:10 pm

wapati wrote:This too. Unique patterns are short cuts. (This too may be too easy.)

Well, they may be the only pattern way. You decide?

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


With 3D-multicoloring from:

Code: Select all
.------------.------------.------------.
| 8   9   12 | 124 3   5  | 24  6   7  |
| 56  56  127| 124 9   147| 8   3   14 |
| 37  237 4  | 8   6   17 | 5   129 19 |
:------------+------------+------------:
| 4   678 789| 5   1   3  | 69  78  2  |
| 1   258 289| 7   28  6  | 49  45  3  |
| 56  278 3  | 49  28  49 | 1   78  56 |
:------------+------------+------------:
| 9   14  6  | 3   5   2  | 7   14  8  |
| 2   14  5  | 6   7   8  | 3   149 149|
| 37  378 78 | 19  4   19 | 26  25  56 |
'------------'------------'------------'


we get the chain:

[r5c2]=5=[r5c8]-5-[r9c8]-2-[r3c8]=2=[r3c2]-2-[r5c2]

implying r5c2<>2. Continuing with this same line of coloring, one then obtains:

[r5c3]-9-[r5c7]-4-[r1c7]-2-[r3c8]=2=[r3c2]-2-[r6c2]=2=[r5c3]

and so r5c3<>9, which solves the puzzle.:(

Alternatively, to avoid a deadly pattern in r39c12[37], one obtains r39c2<>7. Locked candidates then implies r4c3<>7. The potential deadly pattern in r46c28[78] then implies that r46c2<>8. To avoid yet another deadly pattern, this time in r56c25[28], we cannot have r5c2=8 and r6c2=2, so we get:

[r5c2]-8|2-[r6c2]-7-[r6c8]-8-[r6c5]-2-[r5c5]-8-[r5c2]

giving us r5c2<>8, which solves the puzzle.:)
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Postby Carcul » Wed Apr 11, 2007 12:35 pm

Wapati wrote:This is harder.


Code: Select all
 *------------------------------------------------------------------*
 | 139     1239    6  | 5       139     7      | 4       8       23 |
 | 45      123459  13 | 123468  13489   123469 | 16      7       23 |
 | 7       1234    8  | 12346   134     12346  | 9       16      5  |
 |--------------------+------------------------+--------------------|
 | 56      13      2  | 9       13      8      | 7       56      4  |
 | 456     45      13 | 1237    1357    1235   | 256     9       8  |
 | 8       7       9  | 24      6       245    | 25      3       1  |
 |--------------------+------------------------+--------------------|
 | 2       139     4  | 137     13579   1359   | 8       15      6  |
 | 13      6       7  | 1348    13458   1345   | 15      2       9  |
 | 19      8       5  | 16      2       169    | 3       4       7  |
 *------------------------------------------------------------------*

[r2c7]-1-[r3c8]-6-[r4c8](-5-[r7c8]-1-[r7c2]=1=[r89c1]-1-[r1c1])=6=
=[r4c1]-6-[r5c1]=6|4=[r3c2]-4-[r3c5]=4|9=[r1c5]-9-[(r1c1)]-3-[r2c3]-1-
-[r2c7], => r2c7<>1.

Then: [r4c2]-3-[r3c2]=3=[r3c46]-3-[r1c5]=3=[r4c5]-3-[r4c2], => r4c2<>3.

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Postby Carcul » Wed Apr 11, 2007 12:46 pm

Wapati wrote:This too. Unique patterns are short cuts. (This too may be too easy.) Well, they may be the only pattern way. You decide?


Code: Select all
 *--------------------------------------------------*
 | 8    9    12   | 124  3    5    | 24   6    7    |
 | 56   56   127  | 124  9    147  | 8    3    14   |
 | 37   237  4    | 8    6    17   | 5    129  19   |
 |----------------+----------------+----------------|
 | 4    678  789  | 5    1    3    | 69   78   2    |
 | 1    258  289  | 7    28   6    | 49   45   3    |
 | 56   278  3    | 49   28   49   | 1    78   56   |
 |----------------+----------------+----------------|
 | 9    14   6    | 3    5    2    | 7    14   8    |
 | 2    14   5    | 6    7    8    | 3    149  149  |
 | 37   378  78   | 19   4    19   | 26   25   56   |
 *--------------------------------------------------*

[r3c8]=2|4=[r8c9]-4-[r78c8]-1,9-[r3c8], => r3c8=2 solving the puzzle.

Carcul
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Postby Mike Barker » Wed Apr 11, 2007 1:40 pm

Carcul, I am always impressed at how briefly you solve these problems, but I have to admit when I try to go through the logic I often get lost. In this last example:
Code: Select all
[r3c8]=2|4=[r8c9]-4-[r78c8]-1,9-[r3c8], => r3c8=2

does [r3c8]=2|4=[r8c9] refer to the UR r38c89? Is there an easy way to tell when you are refering to an ALS vs a UR? After that I get really confused because if it is the UR then there are overlapping cells with r78c8 which I don't understand. I do understand if r78c8=4 then r8c8 doesn't equal 1 or 9. This isn't the first time I've had problems understanding you notation and would appreciate some help because I see your advanced nice loops as a way for me to solve even tougher problems.
TIA
Mike
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Postby tarek » Wed Apr 11, 2007 1:49 pm

ravel wrote:Nice solution again, rep'nA.
Code: Select all
.---------------.---------------.---------------.
| 129  129  6   | 5    34   34  | 7    12   8   |
| 8    5    7   | 16   9    2   |B16   3    4   |
| 12   4    3   | 7    16   8   | 9    5    126 |
:---------------+---------------+---------------:
| 3    8    12  | 4    167  5   |B126  9    1267|
| 1679 179  5   | 8    2    16  | 3    4    167 |
| 1267 127  4   | 3    167  9   | 8    1267 5   |
:---------------+---------------+---------------:
| 5   A237  8   | 16  B34   16  |B24   27   9   |
|A127  6   A12  | 9    5    34  |-124  8    1237|
| 4    13   9   | 2    8    7   | 5    16   136 |
'---------------'---------------'---------------'
You can also make the elimination with an (xy?) ALS:
The 1 in r8c7 locks the 3 in A to r7c2, in B to r7c5.

I tried to tackle this hurdle with finned fish & UR but still that "1! in r8c7 still needed an ALS-xz (the one udosuk describes) to remove..... from there there was another finned x-wing (or the skyscraper) to seal the deal.....

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Postby re'born » Wed Apr 11, 2007 2:22 pm

Carcul wrote:
Wapati wrote:This too. Unique patterns are short cuts. (This too may be too easy.) Well, they may be the only pattern way. You decide?


Code: Select all
 *--------------------------------------------------*
 | 8    9    12   | 124  3    5    | 24   6    7    |
 | 56   56   127  | 124  9    147  | 8    3    14   |
 | 37   237  4    | 8    6    17   | 5    129  19   |
 |----------------+----------------+----------------|
 | 4    678  789  | 5    1    3    | 69   78   2    |
 | 1    258  289  | 7    28   6    | 49   45   3    |
 | 56   278  3    | 49   28   49   | 1    78   56   |
 |----------------+----------------+----------------|
 | 9    14   6    | 3    5    2    | 7    14   8    |
 | 2    14   5    | 6    7    8    | 3    149  149  |
 | 37   378  78   | 19   4    19   | 26   25   56   |
 *--------------------------------------------------*

[r3c8]=2|4=[r8c9]-4-[r78c8]-1,9-[r3c8], => r3c8=2 solving the puzzle.

Carcul


Or, alternatively, UR type 1 in r78c28[14] implies r8c8=9 and then r3c9=9. Then the potential deadly pattern in r38c89[19], gives

[r3c8]=2|4=[r8c9]-4-[r2c9]-1-[r3c8]

implying r3c8=2, solving the puzzle.
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Postby Carcul » Wed Apr 11, 2007 4:08 pm

Mike Barker wrote:does [r3c8]=2|4=[r8c9] refer to the UR r38c89?


That link refers to an almost TIUR (two incompatible unique rectangles) situation. Let's suppose that r3c8 is not "2" and r8c9 is not "4": then we would have the following grid,

Code: Select all
 *--------------------------------------------------*
 | 8    9    12   | 124  3    5    | 24   6    7    |
 | 56   56   127  | 124  9    147  | 8    3    14   |
 | 37   237  4    | 8    6    17   | 5    19   19   |
 |----------------+----------------+----------------|
 | 4    678  789  | 5    1    3    | 69   78   2    |
 | 1    258  289  | 7    28   6    | 49   45   3    |
 | 56   278  3    | 49   28   49   | 1    78   56   |
 |----------------+----------------+----------------|
 | 9    14   6    | 3    5    2    | 7    14   8    |
 | 2    14   5    | 6    7    8    | 3    149  19   |
 | 37   378  78   | 19   4    19   | 26   25   56   |
 *--------------------------------------------------*

Do you see now what those two URs in r78c28 and r38c89 imply? So we must have r3c8=2 or r8c9=4.

Carcul
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Postby Carcul » Wed Apr 11, 2007 5:24 pm

Wapati wrote:I didn't see any shortcuts. Lots of patterns, swordfish or finned swordfish depending on your solving order. Some unique fun.


Code: Select all
 *------------------------------------------------------*
 | 8     35    6    | 4     2     35   | 9     1     7  |
 | 9     4     35   | 1     7     8    | 2     35    6  |
 | 12    7     12   | 35    9     6    | 8     4     35 |
 |------------------+------------------+----------------|
 | 137   9     158  | 3578  6     1357 | 15    2     4  |
 | 13    6     4    | 2     135   9    | 7     8     35 |
 | 1237  158   1258 | 3578  4     1357 | 156   356   9  |
 |------------------+------------------+----------------|
 | 6     138   1389 | 357   135   1357 | 4     59    2  |
 | 5     2     79   | 6     8     4    | 3     79    1  |
 | 4     13    137  | 9     135   2    | 56    567   8  |
 *------------------------------------------------------*

We have r6c7=5 or r7c5=5 or r9c8=5, and r6c2=1 or r6c6=1 or r6c7=1. But:

[r4c7]=5=[r5c9]-5-[r3c9]=5=[r2c8]-5-[r79c8]=5=[r9c7]-5-[r4c7], => r6c7<>5.

[r7c5]-5-[r59c5]([r6c2]-1-[r5c1]=1=[r5c5]-1-[r9c5]=1=[r9c2]-1-[r6c2])
=5=[r5c9](-5-[r4c7]-1-[r4c3|r6c7])-5-[r3c9](=5=[r3c4]-5-[r46c4])=5=
=[r2c8]-5-[r2c3]=5=[r1c2]-5-[(r6c2)]-8-[(r4c3)]-5-[r4c6]=5=[r6c6], => r7c5<>5.

The final conclusion is that r9c8=5 and the puzzle is solved.

Carcul
Last edited by Carcul on Wed Apr 11, 2007 1:25 pm, edited 1 time in total.
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Postby Carcul » Wed Apr 11, 2007 5:25 pm

Wapati wrote:There is at least one finned fish here, and some uniqueness!


Code: Select all
 *------------------------------------------------------------*
 | 8      17     9     | 567    256    27  | 4      15     3  |
 | 25     25     3     | 4      1      9   | 7      6      8  |
 | 4      6      17    | 578    3      78  | 15     9      2  |
 |---------------------+-------------------+------------------|
 | 12356  134    8     | 567    256    247 | 9      125    15 |
 | 9      25     256   | 3      256    1   | 8      7      4  |
 | 7      14     1245  | 58     9      248 | 3      125    6  |
 |---------------------+-------------------+------------------|
 | 15     8      47    | 2      47     6   | 15     3      9  |
 | 256    9      2567  | 1      8      3   | 26     4      57 |
 | 1236   1347   12467 | 9      47     5   | 26     8      17 |
 *------------------------------------------------------------*

[r8c9]-7-[r9c9](-1-[r4c9]-5-[r4c15])-1-[r7c7](-5-[r7c1]-1-[r4c1|r9c13])-5-
-[r3c7]-1-[r3c3]-7-[r789c3]=5=[r8c3](-5-[r8c1|r5c3])=3=[r9c1]-3-[r4c1]
=3|5=[r5c5]-5-[r5c2], => r8c9<>7.

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Postby wapati » Wed Apr 11, 2007 8:28 pm

The way I do this one is using big finned fish.

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