Cylindrical Stairstep Sudoku

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Cylindrical Stairstep Sudoku

Postby Pyrrhon » Fri Jun 16, 2006 5:56 pm

The grid is joined at the outermost columns as if it were a cylindrical grid. Fill in the grid so that every row, every column, and every marked region contains the digits 1 through 9.

Image

I hope you like it ...

Pyrrhon
Last edited by Pyrrhon on Sat Jun 17, 2006 1:32 am, edited 1 time in total.
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Postby r.e.s. » Sat Jun 17, 2006 2:19 am

There seem to be 4 solutions (found using Ruud's software) ...

Image

The following will paste directly into SumoCue:

SumoCueV1
=0J0=0J1=7J1=0J1=2J2=0J2=8J2=0J0=0J0
=2J1=0J1=0J1=0J2=0J2=0J2=0J0=0J0=9J0
=0J1=0J1=1J2=0J2=0J2=0J0=3J0=0J0=0J1
=0J3=0J3=0J3=6J4=0J4=8J4=0J5=0J5=0J5
=7J3=0J3=9J4=0J4=3J4=0J5=6J5=0J5=4J3
=0J3=0J4=0J4=2J4=0J5=3J5=0J5=0J3=0J3
=0J6=0J6=8J7=0J7=0J7=0J8=5J8=0J8=0J6
=8J6=0J7=0J7=0J7=0J8=0J8=0J8=0J6=3J6
=0J7=0J7=2J7=0J8=6J8=0J8=9J6=0J6=0J6
r.e.s.
 
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Joined: 31 August 2005

Postby Pyrrhon » Sat Jun 17, 2006 3:38 am

Sorry, I made two mistakes using Finned X-Wings. Some trouble in my thought.

Pyrrhon
Last edited by Pyrrhon on Sat Jun 17, 2006 12:32 am, edited 2 times in total.
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Postby r.e.s. » Sat Jun 17, 2006 4:14 am

If the 6 in the bottom row is changed to a 4, then there's a unique solution.:)
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Postby Pyrrhon » Sat Jun 17, 2006 4:35 am

Thank you again, I will check your correction for its difficulty.

The grid now is:

Image

Pyrrhon
Last edited by Pyrrhon on Sun Jun 18, 2006 2:12 am, edited 1 time in total.
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Postby r.e.s. » Sat Jun 17, 2006 7:04 pm

Here's a solution-path for your puzzle when r9c5 is set to 4 ...

After hidden singles on digits 3,8,2,9,4, the candidate grid is
Code: Select all
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
  1456   | 3        7        1459   | 2        4569     8      | 1456     156     
+--------+                 +--------+                 +--------+                 +
| 2        1456     456    | 3        567 A    4567 F | 17 E     8        9      |
+                 +--------+                 +--------+                 +--------+
  456      4569   | 1        4579     5679   | 24567    3        24567  | 8   
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 15       2        3      | 6        157 B    8      | 4        9        157 C  |
+                 +--------+                 +--------+                 +--------+
  7        8      | 9        15       3      | 125      6        125    | 4
         +--------+                 +--------+                 +--------+
  9      | 1457     45       2      | 8        3        17 D   | 156      156
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
  146      1467   | 8        1479     1679   | 1679 G   5        3      | 2 
         +--------+                 +--------+                 +--------+ 
  8      | 145679   456      14579  | 1679 H   1679 G   2      | 14567    3
+--------+                 +--------+                 +--------+                 +
| 3        1567     2      | 8        4        167  G | 9        1567     1567   |
+--------+--------+--------+--------+--------+--------+--------+--------+--------+

and now there are two nice eliminations using Alternating Inference Chains ...

Code: Select all
AIC #1:  7A--7B==7C--7D==7E--7A           =>   7A is False
AIC #2:  7B--7C==7D--7E==7A--7G==7H--7B   =>   7B is False

The rest is solved with only hidden & naked singles.

EDIT: Some typos have been corrected in the candidate grid.
r.e.s.
 
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Joined: 31 August 2005

Postby Pyrrhon » Sun Jun 18, 2006 6:46 am

Your first AIC, a turbot fish, I saw. The second one I had not spotted. This conclusion is sometimes also called a turbot chain.

My improvement of the original puzzle is (again with full symmetry of digits):

Image

Pyrrhon
Last edited by Pyrrhon on Tue Jun 20, 2006 1:32 am, edited 1 time in total.
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Postby r.e.s. » Mon Jun 19, 2006 10:21 pm

That's a beautiful symmetry in your last version. Here's the grid after basic moves, where candidates are shown only in five cells A,B,C,D,E ...
Code: Select all
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
         |                   4      |          9               |                 
+--------+                 +--------+                 +--------+                 +
|          1               |                          |          8               |
+                 +--------+                 +--------+                 +--------+
                  |                   7      |                          |     
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| 1                        | 6        35+4 A   8      |                   7      |
+                 +--------+                 +--------+                 +--------+
  7               | 9        35+1 C   35+4 B |          6               | 
         +--------+                 +--------+                 +--------+
  9      | 7        14 E     2      | 48   D   3               | 6        5 
+--------+--------+--------+--------+--------+--------+--------+--------+--------+
  4               |                   1      |                          |   
         +--------+                 +--------+                 +--------+
         | 4                        |                          | 5         
+--------+                 +--------+                 +--------+                 +
|                          | 8                 4      |                          |
+--------+--------+--------+--------+--------+--------+--------+--------+--------+


To avoid an impossible pattern 35-35-35 in A,B,C, there must be a strong link between 1C and 8D:
NOT(1C) => (4A OR 4B) => NOT(4D) => 8D.

So we have this Alternating Inference Chain:
8D==4D--4E==1E--1C==8D
=> 8D is True.

After basic moves there is then another AIC:
4[29]--4[25]==4[33]--4[43]==4[59]--4[29]
=> 4[29] is False.

And finally one more AIC leaves only basic moves to finish:
4[27]--4[25]==4[33]--4[63]==4[67]--4[27]
=> 4[27] is False.

(There may well be good alternatives to this solution-path, but I wanted practice in recognising AICs:) )

This will paste the puzzle directly into SumoCue:

SumoCueV1
=0J0=0J1=0J1=4J1=0J2=9J2=0J2=0J0=0J0
=0J1=1J1=0J1=0J2=0J2=0J2=0J0=8J0=0J0
=0J1=0J1=0J2=0J2=7J2=0J0=0J0=0J0=0J1
=1J3=0J3=0J3=6J4=0J4=8J4=0J5=0J5=7J5
=0J3=0J3=9J4=0J4=0J4=0J5=6J5=0J5=0J3
=9J3=0J4=0J4=2J4=0J5=3J5=0J5=0J3=5J3
=0J6=0J6=0J7=0J7=1J7=0J8=0J8=0J8=0J6
=0J6=4J7=0J7=0J7=0J8=0J8=0J8=5J6=0J6
=0J7=0J7=0J7=8J8=0J8=4J8=0J6=0J6=0J6
r.e.s.
 
Posts: 337
Joined: 31 August 2005

Postby Pyrrhon » Tue Jun 20, 2006 6:13 am

By the way, your picture with the 4 grids gives a good idea for a multi grid variant of sudoku. The upstairs should be shift 2 columns into left for this. The idea could also be possible with a Moebius strip. (Twist befor connecting the ends). In this case the upstairs must be made correct with respect to the moebius strip laws and the nonets 4-6 must be symmetrical with respect to row 5 to get a correct picture. It seems that both variants are hard to construct.

Pyrrhon
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Posts: 240
Joined: 26 April 2006

Postby comocomocomocomo » Mon Jul 10, 2006 9:18 am

I also made a sudoku moebius, but with ordinary grids:
http://sudoku-sensei.sourceforge.net/examples.html#moebius
I think it would look better with your "stair" blocks. Hummm... it would require some tweaking for making it with my software:(
Anyway, if you want to make a moebius strip, you need about 10 grids or more.
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