Fun puzzle. So many methods to solve. No CHAINS required.

Post puzzles for others to solve here.

Fun puzzle. So many methods to solve. No CHAINS required.

Postby wapati » Mon Oct 02, 2006 7:45 pm

This puzzle can be solved by all "solvers" that I tried but all took differnet (a lot different) paths. This may be the "hardest to rate" puzzle?

It is a great illustration of 'whatever path you take' works.



Code: Select all
. . . | . . . | . . .
2 . . | . . . | . . 9
. . . | 7 5 4 | . . .
---------------------
5 . 4 | . . . | 6 . 1
. 2 . | . . . | . 5 .
. 3 1 | . . . | 4 9 .
---------------------
. . 9 | 8 . 2 | 5 . .
. 5 . | 4 . 6 | . 1 .
. 6 . | 9 7 5 | . 2 .
Last edited by wapati on Mon Oct 16, 2006 4:12 am, edited 1 time in total.
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3 types of UR

Postby wapati » Thu Oct 05, 2006 9:22 am

This fully symmetric puzzle is easy except for requiring UR1, UR4 and a Unique Closed Loop!

Code: Select all
5.9.6.1.3
.........
3..912..8
..3.7.2..
6.71.43.9
..1.8.4..
9..231..4
.........
4.5.9.6.1
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JellyFish

Postby wapati » Thu Oct 05, 2006 11:51 am

I wanted a Jelly for the effortless extremes but the only one I have generated needs an xyz. It is hard to avoid the Jelly, though forcing chains can avoid nearly any pattern, I guess?
Code: Select all
. . . | . 9 . | . . 4
. . 1 | 3 . . | 6 8 .
. 4 6 | . . . | 3 5 .
---------------------
. . . | . 7 4 | . . .
. . . | . 3 9 | . . 2
. 2 . | 8 . . | . 1 .
---------------------
1 6 . | . . . | 9 3 .
. 7 8 | 9 . . | 4 . .
. . 4 | . . . | . . .
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Postby daj95376 » Thu Oct 05, 2006 5:00 pm

I doubt if RW is accepting Jellyfish for the EE thread, but here's some examples that I believe will qualify. They definitely qualify for the Superior Plus thread.

Code: Select all
.......15.84.7..9..7.3..4..76.83.5...3.9.1.6...9.67.31..6..3.5..4..1.67.51.......
.....13.8.1...8..2..2..3.4.......7.1.8..9..3.4.9.......2.7..8..1..2...6.6.48.....
.....3..7.3.8.1..921...78........46...82.43...24........17...238..3.9.1.7..6.....
...9...1..9.14.683....6.7.......436.4...5...2.617.......3.9....159.72.3..7...6...
..2.4.....1.5.6.2...41....59.16..2..2...9...1..5..13.41....35...9.4.2.7.....1.6..
..5.2.68....6........9.72...58....7..42.7.36..3....54...72.3........9....24.6.8..
..789...5.4...6..9.597..8....4..1..7.8..2..1.9..4..2....5..418.4..6...7.1...784..
..98.2.6...8.....123...9.....64.....7...3...2.....76.....2...736.....9...4.1.38..
.3.5....98.93....5..4...16...14.....3..261..4.....86...13...9..6....24.84....3.5.
.4..28.7187.6...2............48..26...1.4.9...86..24............6...9.4313.27..9.
.5.6.98...3...7..9....4.51.8......4...3.1.7...9......6.84.7....1..9...3...94.1.8.
.7.....5.1....639.....72..1..1.9..65..2.3.1..96..5.2..3..82.....157....8.9.....2.
.816.2....69.4......39..4....8....141..894..734....6....2..37......8.14....7.983.
1...6..858..2....73.5.8.9...8.7.9.3.....1.....2.3.6.7...8.9.7.62....3..965..7...3
2....358.....2...1...4.56.....9.4.68..5.1.9..61.8.2.....15.8...3...4.....263....4
3......89.1.6.......6..72..6..34..7.9.2.7.3.8.3..96..2..72..4.......9.2.12......3
4...3.1..5..6..7..23...9....7.4..3..19..5..67..4..7.9....9...74..5..2..6..1.4...3
4..2.7.8...3..85.6.786...4.2.....61.....2.....17.....4.5...346.6.15..2...3.1.2..8
48.6....2.6.85...4..74....8......82..2..9..5..15......1....52..9...82.4.2....6.17
6..8.23..84..5....25.7.....3....1.5.5..327..4.7.4....8.....4.86....1..72..25.8..3
64..9.5.8..748..1.5.81.......58...3...6...7...7...31.......84.9.9..513..7.3.4..61
7.......1.6...38.5.8..673.....7.1...3.1.5.7.4...6.9.....417..8.5.84...3.9.......7
8.6..43.9.7.8..5.4..........2..7..4.7.3.9.2.6.4..2..8..........4.8..2.9.2.95..8.7
9.74.....3...951.7.4...3.5.6....49.............31....8.8.7...3.7.153...4.....68.1
91...427.46...1..8...6...4....1...3.1.49.78.2.8...3....9...2...7..8...29.237...84

Code: Select all
# includes X-Wing(s)
.......63..763.48...3..8..1.3...41.5.1..8..3.5.63...7.2..7..3...74.562..65.......
..3..2...7..93.1.5.1..4.2.3.2.5..9..4...1...2..7..4.5.9.4.2..6.3.1.59..7...4..5..
5......4.24..1..75..8..7.....51.48..6...5...4..76.85.....7..4..83..2..67.5......3
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Postby wapati » Fri Oct 06, 2006 9:00 am

daj95376 wrote:I doubt if RW is accepting Jellyfish for the EE thread, but here's some examples that I believe will qualify. They definitely qualify for the Superior Plus thread.

Code: Select all
8.6..43.9.7.8..5.4..........2..7..4.7.3.9.2.6.4..2..8..........4.8..2.9.2.95..8.7



This one is quite nice, it is easy except for the Jelly and the Jelly is hard to ignore. Good one!
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Postby Carcul » Fri Oct 06, 2006 10:24 am

Here's the path I used for your first puzzle:

Code: Select all
 *----------------------------------------------------*
 | 34    8     367 | 2     9     13 | 137   3467  5   |
 | 2     47    5   | 6     8     13 | 137   347   9   |
 | 9     1     36  | 7     5     4  | 2     368   368 |
 |-----------------+----------------+-----------------|
 | 5     9     4   | 3     2     78 | 6     78    1   |
 | 6     2     78  | 1     4     9  | 378   5     37  |
 | 78    3     1   | 5     6     78 | 4     9     2   |
 |-----------------+----------------+-----------------|
 | 34    47    9   | 8     1     2  | 5     367   367 |
 | 78    5     2   | 4     3     6  | 9     1     78  |
 | 1     6     38  | 9     7     5  | 38    2     4   |
 *----------------------------------------------------*

R5c7=7 or r7c9=7. But r5c7<>7 (due to the UR in cells r12c67). So r7c9=7 and the puzzle is solved.

Carcul
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Postby Carcul » Fri Oct 06, 2006 10:49 am

For your second puzzle:

Code: Select all
 *------------------------------------------------------------*
 | 5      278    9    | 478    6      78  | 1      247    3   |
 | 17     1678   2468 | 34578  45     35  | 79     4679   267 |
 | 3      67     46   | 9      1      2   | 57     4567   8   |
 |--------------------+-------------------+-------------------|
 | 8      4      3    | 56     7      9   | 2      1      56  |
 | 6      5      7    | 1      2      4   | 3      8      9   |
 | 2      9      1    | 356    8      356 | 4      67     567 |
 |--------------------+-------------------+-------------------|
 | 9      678    68   | 2      3      1   | 578    57     4   |
 | 17     1378   28   | 456    45     56  | 789    379    27  |
 | 4      23     5    | 78     9      78  | 6      23     1   |
 *------------------------------------------------------------*

Solution 1: Let's consider that r8c4 is not "4". Then we have r6c4=3 or r6c9=7, and r6c6=3 or r6c9=7: but this then means that r6c8 must be "6". Also, the UR in cells r19c46 tells us that in fact r8c4<>4. So, r6c8=6 and the puzzle is solved.

Solution 2:

[r7c7]=8|6=[r3c38]-6-[r3c2]-7-[r7c23]-8-[r8c3]-2-[r7c8|r8c9]-5,7-[r7c7],

and so r7c7=8 which solves the puzzle.

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Postby daj95376 » Fri Oct 06, 2006 11:13 am

A similar approach for the first puzzle. Carcul's UR in [r12c67] forces [r5c7]<>7 and [r12c8]<>7. Coloring on <7> then forces [r7c9]=7.

I give full credit to Carcul for spotting the UR. My solver doesn't have UR Type 2 (yet) and had to fight its way through two XY-Wings and an XYZ-Wing to reach a solution.
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Postby Carcul » Fri Oct 06, 2006 11:14 am

And for your third puzzle:

Wapati wrote:It is hard to avoid the Jelly, though forcing chains can avoid nearly any pattern, I guess?


It's quite simple to avoid that dangerous sea creature:

Code: Select all
 *---------------------------------------------------------------------------*
 | 3578     358      35 | 56       9        1568    | 12       27       4    |
 | 2579     59       1  | 3        4        25      | 6        8        79   |
 | 289      4        6  | 7        128      128     | 3        5        19   |
 |----------------------+---------------------------+------------------------|
 | 358      1        35 | 2        7        4       | 58       9        6    |
 | 6        58       7  | 1        3        9       | 58       4        2    |
 | 4        2        9  | 8        56       56      | 7        1        3    |
 |----------------------+---------------------------+------------------------|
 | 1        6        2  | 4        58       578     | 9        3        578  |
 | 35       7        8  | 9        1256     12356   | 4        26       15   |
 | 359      359      4  | 56       12568    1235678 | 12       267      1578 |
 *---------------------------------------------------------------------------*

r3c1=2 or r4c1=3. But:

[r4c1]=3|2=[r3c1]-2-[r3c56]-1,8-[r1c46]-5-[r1c3]=5=[r4c3]=3=[r4c1]

and so r4c1=3 which solves the puzzle.

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Postby Carcul » Fri Oct 06, 2006 11:21 am

Daj95376 wrote:Carcul's UR in [r12c67] forces [r5c7]<>7 and [r12c8]<>7.


That UR also forces r1c7/r2c7<>3.

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Postby daj95376 » Fri Oct 06, 2006 11:49 am

Carcul wrote:
Daj95376 wrote:Carcul's UR in [r12c67] forces [r5c7]<>7 and [r12c8]<>7.


That UR also forces r1c7/r2c7<>3.

Carcul

Does the UR force these eliminations in <3> ... or the resulting Naked Quad in [b3]?
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Postby daj95376 » Fri Oct 06, 2006 11:58 am

For your second puzzle.

Code: Select all
# SSTS, UR 1 in <78> => [r1c4]=4, Singles
 *-----------------------------------------------------------*
 | 5     278   9     | 4     6     78*   | 1     27#   3     |
 | 17*   1678  2468  | 78*   5     3     | 79    4679  267-  |
 | 3     67    46    | 9     1     2     | 57    4567  8     |
 |-------------------+-------------------+-------------------|
 | 8     4     3     | 56    7     9     | 2     1     56    |
 | 6     5     7     | 1     2     4     | 3     8     9     |
 | 2     9     1     | 3     8     56    | 4     67    567   |
 |-------------------+-------------------+-------------------|
 | 9     678   68    | 2     3     1     | 578   57    4     |
 | 17*   1378  28    | 56    4     56    | 789   379   27*   |
 | 4     23    5     | 78    9     78    | 6     23-   1     |
 *-----------------------------------------------------------*

XY-Chain 2-[r1c8]-7-[r1c6]-8-[r2c4]-7-[r2c1]-1-[r8c1]-7-[r8c9]-2 => [r2c9]<>2,[r9c8]<>2

and Naked Singles complete the solution.
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Postby Carcul » Fri Oct 06, 2006 12:44 pm

Daj95376 wrote:Does the UR force these eliminations in <3> ... or the resulting Naked Quad in [b3]?


The UR (also) force those eliminations, but you are right, the emerging naked quad does the same thing.

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Another one that has lots of patterns

Postby wapati » Sat Oct 07, 2006 9:54 am

There are: x-wing, xy-wing, xyz-wing, finned-x and Urs of 3 types in here.
No one application, or even two solves it, you need lots!

The image is somewhat like a leaning scarecrow?

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

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Re: Another one that has lots of patterns

Postby udosuk » Sat Oct 07, 2006 11:41 am

wapati wrote:There are: x-wing, xy-wing, xyz-wing, finned-x and Urs of 3 types in here.
No one application, or even two solves it, you need lots!

According to Simple Sudoku, you only need 2 x-wings plus 3 finned-x/turbot-fish/simple-color moves to solve it...
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