Patterns Game 1.0

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empty rectangle

Postby claudiarabia » Mon Jun 11, 2007 3:51 pm

re'born"][quote="claudiarabia"][quote="re'born"][quote="JPF wrote:
Code: Select all
 
 1 . . | . . . | . . 2
 . 3 . | 2 . 4 | . 5 .
 . . . | . . . | 6 . .
-------+-------+-------
 . . 6 | . . . | 1 . .
 . . . | 7 . 3 | . . .
 . . 8 | . . . | 9 . .
-------+-------+-------
 . . 1 | . . . | . . .
 . 7 . | 5 . 2 | . 3 .
 8 . . | . . . | . . 9   ER=7.6


Code: Select all
*--------------------------------------------------------------------------------------*
 | 1        45689    4579     | 3689     356789   56789    | 3478     4789     2        |
 | 679      3        79*      | 2        16789    4        | 78*      5        178      |
 | 24579    24589    24579    | 1389     135789   15789    | 6        14789    13478    |
 |----------------------------+----------------------------+----------------------------|
 | 234579   2459     6        | 489      24589    589      | 1        2478     34578    |
 | 2459     12459    2459     | 7        1245689  3        | 2458     2468     4568     |
 | 23457    1245     8        | 146      12456    156      | 9        2467     34567    |
 |----------------------------+----------------------------+----------------------------|
 | 234569   24569    1        | 34689    346789   6789     | 24578    24678    45678    |
 | 469      7        49*      | 5        14689    2        | 48*      3        1468     |
 | 8        2456     2345     | 1346     13467    167      | 2457     12467    9        |
 *--------------------------------------------------------------------------------------*


...and the only 4 bivalued cells form a bidirectional y-cycle. It seems that SE finds this y-cycle, but what drives up the ER is that SE doesn't use the empty rectangle that leads (after an xy-wing) to a BUG+1. Instead, it uses "forcing chains" and "Nishio forcing chains".


Indeed, the Sudoku-Explainers oversees this kind of turbot fish. I found this puzzle, where the Explainer is taking resort to Nishio-Forcing-Chains while missing the Empty Rectangle too.
Code: Select all
 
+------------------+---------------+------------------+
|    56   56     8 |  39    2  349 |    7   349     1 |
|    12    3     4 |   6    7   19 |    5     8    29 |
|     9   12     7 |   8    5  134 |   26   346  2346 |
+------------------+---------------+------------------+
|   148  178  *369 |   2 *369    5 |   69    14    47 |
|  3456  569     2 |   7    1  369 |    8  3456   346 |
|  1356   17  3569 |   4  369    8 |  269  1356  2367 |
+------------------+---------------+------------------+
|    28   28   369 |  39    4  369 |    1     7     5 |
|   356  569 *3569 |   1 -369    7 |    4     2     8 |
|     7    4     1 |   5    8    2 |    3    69    69 |
+------------------+---------------+------------------+

http://forum.enjoysudoku.com/viewtopic.php?t=3251&postdays=0&postorder=asc&start=0

So I will be alert if I will find an Empty rectangle, wenn the Explainer offers me nishios.:)

Claudia
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Postby JPF » Wed Jun 20, 2007 9:16 pm

Puzzles for (almost) everybody

With Mauricio's pattern, here are a list of puzzles with an Explainer rating between 1.5 and 8.9

Mauricio's pattern:
Code: Select all
 x . . | . . . | . . x
 . x . | x . x | . x .
 . . . | . . . | x . .
-------+-------+-------
 . . x | . . . | x . .
 . . . | x . x | . . .
 . . x | . . . | x . .
-------+-------+-------
 . . x | . . . | . . .
 . x . | x . x | . x .
 x . . | . . . | . . x


Code: Select all
ER  #  Puzzle

8.9 # 100000002030405010000000600006000700000302000005000400007000000080901030500000008
8.4 # 100000002030405060000000700007000600000803000005000900009000000010602030500000001
8.3 # 100000002030405010000000600006000700000803000004000500007000000010904030800000006
8.2 # 100000002030104050000000600007000800000608000002000500004000000010506030200000007
7.9 # 100000002030405010000000600006000700000308000004000500007000000080902030500000008
7.8 # 100000002030405060000000700007000200000803000009000100005000000080602030700000009
7.7 # 100000002030405060000000500007000200000803000006000100004000000080906030200000006
7.6 # 100000002030401050000000600002000700000305000008000300009000000040906030200000008
7.5 # 100000002030405010000000600007000800000603000005000200009000000050702040800000003
7.4 # 100000002030204050000000100001000600000503000007000800006000000020709030500000004
7.3 # 100000002030405060000000700002000600000308000005000900007000000040601030200000004
7.2 # 100000002030405060000000700007000200000307000006000800008000000040201030900000004
7.1 # 100000002030401050000000600002000500000307000008000100006000000040509030200000008
7.0 # 100000002030405060000000700005000600000803000007000900009000000080602040500000003
6.9 # 100000002030405060000000700002000800000309000007000600005000000090806030200000004
6.8 # 100000002030405060000000700007000500000601000002000800009000000050806030700000004
6.7 # 100000002030405010000000600006000700000703000008000200007000000020901030600000005
6.6 # 100000002030104050000000600001000700000703000006000500008000000070502040900000003
6.5 # 100000002030104050000000600007000800000603000002000500006000000010508030200000007
5.6 # 100000002030405060000000700005000600000308000007000200002000000040601030800000004
4.7 # 100000002030104050000000400006000700000308000002000500001000000080509030200000008
4.6 # 100000002030405060000000500007000100000106000002000800006000000050804030200000007
4.5 # 100000002030405060000000700002000500000803000009000600004000000080607050200000009
4.4 # 100000002030405060000000700002000800000304000007000100005000000060108040700000006
4.2 # 100000002030405060000000700007000100000803000008000400001000000060902030700000006
3.8 # 100000002030104050000000600006000700000308000002000800009000000040809030500000006
3.6 # 100000002030405010000000600007000500000308000006000200009000000040801030600000007
3.4 # 100000002030405060000000400001000700000306000002000800009000000050804030200000007
3.2 # 100000002030405060000000700005000200000703000008000100001000000070608040600000003
3.0 # 100000002030405060000000700002000800000309000007000500008000000040508030900000007
2.8 # 100000002030104050000000600007000500000803000006000900009000000040208030600000004
2.6 # 100000002030405060000000700007000800000602000005000900008000000020901030700000004
2.5 # 100000002030405060000000700007000800000309000002000100001000000050902030600000004
2.3 # 100000002030405010000000600006000700000304000008000900007000000040109030200000006
2.0 # 100000002030405060000000700007000200000301000008000100009000000050902030700000005
1.7 # 100000002030401050000000400002000600000607000008000500006000000070506010200000008
1.5 # 100000002030405060000000700007000500000801000002000600009000000050906040700000003


some interesting puzzles, according to Sudoku Explainer :
Code: Select all
7.2 # 100000002030405010000000600006000700000308000001000900009000000040107030200000004
7.1 # 100000002030405010000000500002000600000307000008000400006000000090104030800000006
4.6 # 100000002030405060000000700007000200000306000008000400002000000090801030600000009
6.6 # 100000002030104050000000600007000200000305000006000800008000000040709030600000001
4.7 # 100000002030104050000000400006000700000308000002000500001000000080509030200000008


JPF
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Postby JPF » Wed Jun 27, 2007 2:51 pm

Here's the new challenge :

Code: Select all
 
 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 3 | . . . | 5 . .
-------+-------+-------
 . 5 . | . 2 . | . 6 .
 . . . | 6 . 1 | . . .
 . 7 . | . 8 . | . 3 .
-------+-------+-------
 . . 6 | . . . | 2 . .
 . . . | 4 . 2 | . . .
 8 . . | . . . | . . 1     ER=1.5

20 clues, minimal, singles (13 steps)

New rules :
In addition to the rules given above :
  • a proposed puzzle must be minimal
  • a proposed puzzle cannot have a ER higher than ER0 + 1.5 , ER0 beeing the previous posted ER.
  • nobody can post more than 5 puzzles within one week.
  • posts with several puzzles are allowed, provided that the above rules are satisfied.
Good luck !
[edited]

JPF
Last edited by JPF on Thu Jun 28, 2007 7:24 am, edited 1 time in total.
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Postby Mauricio » Wed Jun 27, 2007 5:50 pm

JPF wrote:a proposed puzzle cannot have a ER higher than ER0 + 0.5 , ER0 beeing the previous posted ER.


Sudokus within that rule might be very hard to find. I rarely see sudokus with SE rating between 4.8 and 5.5. ER0+1.0 may be a better idea.

Code: Select all
 1 . . . . . . . 2
 . . . 1 . 3 . . .
 . . 4 . . . 5 . .
 . 6 . . 1 . . 5 .
 . . . 4 . 6 . . .
 . 7 . . 5 . . 8 .
 . . 1 . . . 4 . .
 . . . 3 . 7 . . .
 9 . . . . . . . 6    ER 2.0
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Postby JPF » Wed Jun 27, 2007 7:58 pm

Mauricio wrote:Sudokus within that rule might be very hard to find. I rarely see sudokus with SE rating between 4.8 and 5.5. ER0+1.0 may be a better idea.

You are right, Mauricio.
It was not my intention.
[edited]
Let's take ER-ER0 <= 1.5


Code: Select all
 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 2 | . . . | 5 . .
-------+-------+-------
 . 3 . | . 5 . | . 6 .
 . . . | 1 . 7 | . . .
 . 6 . | . 8 . | . 4 .
-------+-------+-------
 . . 3 | . . . | 2 . .
 . . . | 6 . 8 | . . .
 5 . . | . . . | . . 1    ER=2.6


JPF
Last edited by JPF on Thu Jun 28, 2007 7:26 am, edited 1 time in total.
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Postby Mauricio » Wed Jun 27, 2007 9:27 pm

JPF wrote:Let's take ER-ER0 >= 1.5

I suppose you wanted to say ER-ER0 <= 1.5
Code: Select all
 1 . . . . . . . 2
 . . . 1 . 3 . . .
 . . 4 . . . 5 . .
 . 6 . . 2 . . 1 .
 . . . 4 . 7 . . .
 . 8 . . 5 . . 7 .
 . . 2 . . . 4 . .
 . . . 3 . 8 . . .
 7 . . . . . . . 5    ER 3.0
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Postby m_b_metcalf » Thu Jun 28, 2007 8:41 am

JPF wrote:Here's the new challenge :


Gentlemen,
Much as I'd like to try my luck again, I'm out of the running until the end of August (but with the new rules and the smaller increment, maybe I'll still be able to participate, as the rate of progress will inevitably be smaller than before).

Regards,

Mike Metcalf
(now in Geneva)
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Postby JPF » Thu Jun 28, 2007 11:06 am

Mauricio wrote:I suppose you wanted to say ER-ER0 <= 1.5
yes, of course, thanks.

m_b_metcalf (now in Geneva) wrote:Gentlemen,
Much as I'd like to try my luck again, I'm out of the running until the end of August (but with the new rules and the smaller increment, maybe I'll still be able to participate, as the rate of progress will inevitably be smaller than before).
Hm, I'm not sure:)
In any case, have a lot of fun in Europe, Mike.

My new proposal :
Code: Select all
 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 5 | . . . | 6 . .
-------+-------+-------
 . 3 . | . 1 . | . 7 .
 . . . | 6 . 5 | . . .
 . 7 . | . 2 . | . 4 .
-------+-------+-------
 . . 8 | . . . | 4 . .
 . . . | 7 . 9 | . . .
 6 . . | . . . | . . 1    ER=3.2


Here are some missing rating values so far :

Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..2|...|5..|
 |---+---+---|
 |.4.|.3.|.6.|
 |...|1.7|...|
 |.6.|.5.|.3.|
 |---+---+---|
 |..7|...|2..|
 |...|6.8|...|
 |5..|...|..1|
 +-----------+   ER=1.5 ; 23 steps
ER=1.5 has been already proposed, but the number of steps here is interesting

Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..5|...|6..|
 |---+---+---|
 |.7.|.4.|.3.|
 |...|1.6|...|
 |.6.|.5.|.7.|
 |---+---+---|
 |..4|...|5..|
 |...|8.2|...|
 |8..|...|..1|
 +-----------+    ER=1.7

Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..5|...|6..|
 |---+---+---|
 |.3.|.7.|.5.|
 |...|2.6|...|
 |.5.|.8.|.9.|
 |---+---+---|
 |..2|...|8..|
 |...|7.9|...|
 |6..|...|..7|
 +-----------+   ER=2.3

Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..5|...|6..|
 |---+---+---|
 |.3.|.2.|.7.|
 |...|6.3|...|
 |.7.|.5.|.4.|
 |---+---+---|
 |..6|...|4..|
 |...|7.8|...|
 |2..|...|..5|
 +-----------+   ER=2.5

Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..5|...|1..|
 |---+---+---|
 |.3.|.2.|.6.|
 |...|7.5|...|
 |.6.|.8.|.4.|
 |---+---+---|
 |..7|...|5..|
 |...|6.8|...|
 |2..|...|..1|
 +-----------+   ER=2.8

JPF
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Postby JPF » Fri Jun 29, 2007 10:33 pm

Ok, proposal of the day :

Code: Select all
 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 5 | . . . | 6 . .
-------+-------+-------
 . 4 . | . 6 . | . 7 .
 . . . | 1 . 5 | . . .
 . 7 . | . 8 . | . 6 .
-------+-------+-------
 . . 2 | . . . | 5 . .
 . . . | 8 . 7 | . . .
 4 . . | . . . | . . 1     ER=3.4


JPF
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Postby JPF » Tue Jul 03, 2007 3:07 pm

slowly but surely...

Code: Select all
 1 . . | . . . | . . 2
 . . . | 3 . 4 | .  . .
 . . 5 | . . . | 6 . .
-------+-------+-------
 . 7 . | . 5 . | . 3 .
 . . . | 8 . 2 | . . .
 . 4 . | . 1 . | . 8 .
-------+-------+-------
 . . 3 | . . . | 5 . .
 . . . | 7 . 9 | . . .
 8 . . | . . . | . . 1     ER=3.6


JPF
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Postby ab » Tue Jul 03, 2007 5:38 pm

here's a 4.4:
Code: Select all
 9 . . | . . . | . . 3
 . . . | 8 . 4 | . . .
 . . 7 | . . . | 9 . .
 ------+-------+------
 . 6 . | . 5 . | . 8 .
 . . . | 3 . 7 | . . .
 . 8 . | . 2 . | . 4 .
 ------+-------+------
 . . 9 | . . . | 7 . .
 . . . | 2 . 6 | . . .
 3 . . | . . . | . . 5
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Postby ab » Tue Jul 03, 2007 5:45 pm

and a 4.5:
Code: Select all
 4 . . | . . . | . . 1
 . . . | 8 . 9 | . . .
 . . 1 | . . . | 2 . .
 ------+-------+------
 . 3 . | . 7 . | . 9 .
 . . . | 5 . 1 | . . .
 . 9 . | . 2 . | . 4 .
 ------+-------+------
 . . 5 | . . . | 3 . .
 . . . | 4 . 3 | . . .
 8 . . | . . . | . . 2
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Postby m_b_metcalf » Wed Jul 04, 2007 9:25 am

JPF wrote:In any case, have a lot of fun in Europe, Mike.


Ah, ha! It is going slowly enough for me perhaps to be able to join in later.

Regards,

Mike Metcalf
(from a wet and cold Rougemont (Doubs))
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Postby JPF » Wed Jul 04, 2007 8:14 pm

here's the next step :
Code: Select all
 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 5 | . . . | 1 . .
-------+-------+-------
 . 6 . | . 2 . | . 7 .
 . . . | 8 . 1 | . . .
 . 7 . | . 5 . | . 3 .
-------+-------+-------
 . . 2 | . . . | 5 . .
 . . . | 7 . 6 | . . .
 8 . . | . . . | . . 6       ER=4.6


for the record :
Code: Select all
 +-----------+
 |1..|...|..2|
 |...|3.4|...|
 |..4|...|5..|
 |---+---+---|
 |.5.|.6.|.7.|
 |...|8.2|...|
 |.3.|.1.|.4.|
 |---+---+---|
 |..8|...|6..|
 |...|7.3|...|
 |2..|...|..8|
 +-----------+      ER=4.2

JPF
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Postby Mauricio » Fri Jul 06, 2007 3:27 pm

Let chains begin.
Code: Select all
1 . .|. . .|. . 2
. . .|3 . 4|. . .
. . 2|. . .|5 . .
-----+-----+-----
. 3 .|. 1 .|. 6 .
. . .|2 . 7|. . .
. 8 .|. 5 .|. 4 .
-----+-----+-----
. . 5|. . .|1 . .
. . .|9 . 3|. . .
4 . .|. . .|. . 7     ER 5.6
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