Sudokus with an original rare shape

Everything about Sudoku that doesn't fit in one of the other sections

Postby daj95376 » Sun Jul 30, 2006 6:19 am

Code: Select all
9...1.......2.3.8...8...7...2.....3.4...6...1.6.....5...3...6...1.8.7.......4...5

r1c6    =  8     Hidden Single
r4c9    =  6     Hidden Single
    b8  -  6     Locked Candidate (1)
r2      -  6     Locked Candidate (2)
  c9    -  2349  Naked  Quad
    b6  -  4     Locked Candidate (1)
r7c2    <> 8     Templates -- Pass C   (Multi-Colors in Simple Sudoku)

I get this far with Basic Techniques.

Code: Select all
 *--------------------------------------------------------------------*
 | 9      3457   2457   | 4567   1      8      | 235    246    234    |
 | 1567   457    14567  | 2      579    3      | 159    8      49     |
 | 1235   345    8      | 4569   59     4569   | 7      12469  2349   |
 |----------------------+----------------------+----------------------|
 | 1578   2      1579   | 14579  5789   1459   | 489    3      6      |
 | 4      35789  579    | 3579   6      259    | 289    279    1      |
 | 1378   6      179    | 13479  23789  1249   | 2489   5      78     |
 |----------------------+----------------------+----------------------|
 | 2578   4579   3      | 159    259    1259   | 6      12479  78     |
 | 256    1      24569  | 8      2359   7      | 239    249    2349   |
 | 278    789    279    | 1369   4      1269   | 12389  1279   5      |
 *--------------------------------------------------------------------*

At this point, I want to show that [r1c3]=2 using the chain below.

Code: Select all
[r1c3]=2=[r3c1]=1=[r3c8]-1-[r79c8]
               =3=[r6c1]-3-[r6c45]=3=[r5c4]-3-[r9c4]=3=[r9c7]

This results in [b9]=INVALID (no 1s) and I get the contradiction I need.

Is there a simple way to show this chain and the resulting contradiction?
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Postby ravel » Sun Jul 30, 2006 12:06 pm

A bit simpler is to write it in a closed chain:
r3c1=2 => r3c8=1 => r2c7<>1 => r9c7=1 => r9c4=3 => r8c5<>3 => r6c5=3 => r6c1<>3 => r3c1=3
ravel
 
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A fully symmetrical diamond puzzle

Postby claudiarabia » Sun Jul 30, 2006 2:02 pm

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

Claudia
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Postby daj95376 » Sun Jul 30, 2006 4:13 pm

ravel wrote:A bit simpler is to write it in a closed chain:
r3c1=2 => r3c8=1 => r2c7<>1 => r9c7=1 => r9c4=3 => r8c5<>3 => r6c5=3 => r6c1<>3 => r3c1=3

Thanks ravel !!! I'll study this and use it in the future.
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Postby udosuk » Sun Jul 30, 2006 5:12 pm

Code: Select all
 *--------------------------------------------------------------------*
 | 9      3457   2      | 4567   1      8      | 35     46     34     |
 | 1567   457    46     | 2      579    3      | 159    8      49     |
 | 135    345    8      | 4569   59     4569   | 7      12469  2349   |
 |----------------------+----------------------+----------------------|
 | 78     2      1579   | 14579  5789   1459   | 489    3      6      |
 | 4      3789   579    | 3579   6      259    | 289    279    1      |
 | 378    6      179    | 13479  23789  1249   | 2489   5      78     |
 |----------------------+----------------------+----------------------|
 | 2578   4579   3      | 159    259    1259   | 6      12479  78     |
 | 256    1      46     | 8      2359   7      | 239    249    2349   |
 | 278    789    79     | 1369   4      1269   | 12389  1279   5      |
 *--------------------------------------------------------------------*

r7c2=9 => r9c3=7 => r9c2=8 => r9c1=2 => r7c1=5
       => r7c456={125}

How to represent this nicely?
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Postby ronk » Sun Jul 30, 2006 6:54 pm

udosuk wrote:How to represent this nicely?

Using the ALS xz-rule:
Code: Select all
 Sets: A = {r7c1,r9c123} = {25789}
       B = {r7c456} = {1259}
       x = 5, z = 9 implies r7c2<>9, r9c46<>9
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Postby udosuk » Mon Jul 31, 2006 4:18 am

Thanks ronk (#1)!:) Will try to learn this technique... Are there simpler methods for this puzzle?

Just realised it's like a "grouped wxyz-wing":

r7c2=9 or r9c46=9 => r7c456={125} & r9c123={278} => nothing left for r7c1
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faces

Postby ravel » Mon Jul 31, 2006 2:18 pm

I dont know, if someone here plays my p&p puzzles, which need a bit more than basics, but are not harder, if you know x-, xy-, xyz-wing, UR type 1,2,4 and turbot fish (all easier to spot than some naked triples).
But my friend, who is pure p&p solver (and much faster than me), likes them, because she does not need much pencilmarks. So i continue with some faces:


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


 . . . . . . . . .       . . . . . . . . .       . . . . . . . . .
 . 4 1 . . . 2 6 .     . 4 7 . . . 2 6 .     . 1 7 . . . 6 5 .
 2 . . 6 . 1 . . 5     6 . . 4 . 8 . . 5     2 . . 3 . 9 . . 7
 5 . . 2 . 9 . . 3     1 . . 6 . 2 . . 9     7 . . 1 . 2 . . 6
 . 6 4 . . . 8 5 .     . 3 9 . . . 8 7 .     . 2 3 . . . 4 9 .
 . . . . . . . . .     . . . . . . . . .     . . . . . . . . .
 . . . 3 9 4 . . .     . . . 3 7 9 . . .     1 . . . . . . . 9
 . . 2 . . . 9 . .     . . 5 . . . 4 . .     . 4 . . . . . 7 .
 . . 8 . 6 . 1 . .     . . . 5 6 4 . . .     . . . 4 2 3 . . .

For copying:
Code: Select all
..........63...21.4..6.8..91..5.2..6.47...18..............1.....56...43....369...
..........41...79.2..9.8..61..5.7..2.29...63.....................54619...9.....5.
..........61...39.2..9.8..11..5.7..2.24...97............9.6.7....8...1.....743...
..........41...26.2..6.1..55..2.9..3.64...85.............394.....2...9....8.6.1..
..........47...26.6..4.8..51..6.2..9.39...87.............379.....5...4.....564...
..........17...65.2..3.9..77..1.2..6.23...49..........1.......9.4.....7....423...

With 2x BUG lite:
Code: Select all
..........31...78.4..5.6..29..3.1..8.68...15.............875.....5...3.....693...
With UR3:
Code: Select all
..........39...46.4..7.5..33..8.6..4.92...75.............183.....1...9.....469...
ravel
 
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Postby JPF » Tue Aug 01, 2006 1:30 pm

How many solutions ?

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


:)
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Postby udosuk » Tue Aug 01, 2006 3:01 pm

(Classical) Sudoku is a puzzle about:
Code: Select all
. # # # # # # # .
# # # # # # # # #
# # . . . . . # #
# # . . . . . # #
# # # # # # # # #
. # # # # # # # #
. . . . . . . # #
# # # # # # # # #
. # # # # # # # .

Anyone?:D
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Postby JPF » Tue Aug 01, 2006 10:34 pm

udosuk wrote:(Classical) Sudoku is a puzzle about:
Code: Select all
. # # # # # # # .
# # # # # # # # #
# # . . . . . # #
# # . . . . . # #
# # # # # # # # #
. # # # # # # # #
. . . . . . . # #
# # # # # # # # #
. # # # # # # # .

Anyone?:D


You mean : the boss ?

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Postby udosuk » Wed Aug 02, 2006 5:01 am

I don't think the boss will take up this challenge... It's you I'm counting on...:)

With so many filled cells, is it hard to construct a puzzle with that number of solutions?:?:
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Postby JPF » Wed Aug 02, 2006 7:27 am

udosuk wrote:With so many filled cells, is it hard to construct a puzzle with that number of solutions?:?:

Yes it is.
With your proposed shape, 4 solutions seems to be the maximum.

JPF
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Postby ravel » Wed Aug 02, 2006 11:24 am

Three patterns:

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

The last one is a bit harder (BUG lite, UR type3).
ravel
 
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a rotational symmetry

Postby claudiarabia » Sun Aug 06, 2006 7:00 pm

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


Claudia
Last edited by claudiarabia on Sun Aug 06, 2006 3:08 pm, edited 1 time in total.
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