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 Post subject: Setdoku (Set-Do-Ku)
PostPosted: Sat Jan 15, 2011 2:15 pm 
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This idea was brough up originally by dukuso at http://forum.enjoysudoku.com/setoku-t30070.html#p206123.

Set as described in wikipedia was invented a while back. See http://en.wikipedia.org/wiki/Set_(game) Also See http://www.setgame.com/set/rules_set.htm

It has 81 cards each with a unique symbol .... Each symbol has 4 features common to all symbols. Each features however exists in 3 possible states (e.g shading or colour) & the diffiernt combinations of the 4 features gives us the 81 symbols. The Set cards have a Unique (Shape, Number, Colour & Shading). There is a possibility of 3 Shapes, 3 numbers, 3 colours & 3 shadng styles.

A set is formed by 3 cards. Looking at each feature in all 3 symbols. They have to be in the same state or in a completely different state. So you need the 3 cards to have a feature in similar state or the 3 have to be different. 3 cards which can be described as having 2 of something and 1 of something else DO NOT form a set.

This allows you to know what the 3rd card when you know any 2 in the set.

because of the 81 symbols, dukuso suggested a Sudoku twist.

Arrange the 81 symbols on a sudoku grid so that each:

Mini-Row, Mini-Column, Maxi-Row, Maxi-column forms a set.
if you combine 2 features together ... you can have 9 groups of cards that have the same 9 possibilities allowing you to convert them into sudoku digits.

You can have 1-6 valid sudoku grids which are the combinations of the 4 features(attributes). The possible constraint choices are huge. You need to make sure what of these have been declared by the puzzle maker before attempting to solve.

In theory you can choose whatever attributes to represent the symbols. The originals have Shape, Number, Colour and Shade. simon_blow_snow has privided new visuals for the symbols. He created the following special Setdoku grid.

Image

I then wrote a conversion table based on the above & to show the transformation to sudoku
Code:
Attr           Graphic Symbol                S   12 13 14 23 24 34
------------------------------------------------------------------
0     None    None     None       None       .   .  .  .  .  .  .
1111  1 Sq    No X     Black Out  White In   1   1  1  1  1  1  1
1112  1 Sq    No X     Black Out  Yellow In  2   1  1  2  1  2  2
1113  1 Sq    No X     Black Out  Green In   3   1  1  3  1  3  3
1121  1 Sq    No X     Blue Out   White In   4   1  2  1  2  1  4
1122  1 Sq    No X     Blue Out   Yellow In  5   1  2  2  2  2  5
1123  1 Sq    No X     Blue Out   Green In   6   1  2  3  2  3  6
1131  1 Sq    No X     Red Out    White In   7   1  3  1  3  1  7
1132  1 Sq    No X     Red Out    Yellow In  8   1  3  2  3  2  8
1133  1 Sq    No X     Red Out    Green In   9   1  3  3  3  3  9
1211  1 Sq    Small X  Black Out  White In   A   2  1  1  4  4  1
1212  1 Sq    Small X  Black Out  Yellow In  B   2  1  2  4  5  2
1213  1 Sq    Small X  Black Out  Green In   C   2  1  3  4  6  3
1221  1 Sq    Small X  Blue Out   White In   D   2  2  1  5  4  4
1222  1 Sq    Small X  Blue Out   Yellow In  E   2  2  2  5  5  5
1223  1 Sq    Small X  Blue Out   Green In   F   2  2  3  5  6  6
1231  1 Sq    Small X  Red Out    White In   G   2  3  1  6  4  7
1232  1 Sq    Small X  Red Out    Yellow In  H   2  3  2  6  5  8
1233  1 Sq    Small X  Red Out    Green In   I   2  3  3  6  6  9
1311  1 Sq    Big X    Black Out  White In   J   3  1  1  7  7  1
1312  1 Sq    Big X    Black Out  Yellow In  K   3  1  2  7  8  2
1313  1 Sq    Big X    Black Out  Green In   L   3  1  3  7  9  3
1321  1 Sq    Big X    Blue Out   White In   M   3  2  1  8  7  4
1322  1 Sq    Big X    Blue Out   Yellow In  N   3  2  2  8  8  5
1323  1 Sq    Big X    Blue Out   Green In   O   3  2  3  8  9  6
1331  1 Sq    Big X    Red Out    White In   P   3  3  1  9  7  7
1332  1 Sq    Big X    Red Out    Yellow In  Q   3  3  2  9  8  8
1333  1 Sq    Big X    Red Out    Green In   R   3  3  3  9  9  9
2111  2 Sq    No X     Black Out  White In   S   4  4  4  1  1  1
2112  2 Sq    No X     Black Out  Yellow In  T   4  4  5  1  2  2
2113  2 Sq    No X     Black Out  Green In   U   4  4  6  1  3  3
2121  2 Sq    No X     Blue Out   White In   V   4  5  4  2  1  4
2122  2 Sq    No X     Blue Out   Yellow In  W   4  5  5  2  2  5
2123  2 Sq    No X     Blue Out   Green In   X   4  5  6  2  3  6
2131  2 Sq    No X     Red Out    White In   Y   4  6  4  3  1  7
2132  2 Sq    No X     Red Out    Yellow In  Z   4  6  5  3  2  8
2133  2 Sq    No X     Red Out    Green In   [   4  6  6  3  3  9
2211  2 Sq    Small X  Black Out  White In   ]   5  4  4  4  4  1
2212  2 Sq    Small X  Black Out  Yellow In  {   5  4  5  4  5  2
2213  2 Sq    Small X  Black Out  Green In   }   5  4  6  4  6  3
2221  2 Sq    Small X  Blue Out   White In   ~   5  5  4  5  4  4
2222  2 Sq    Small X  Blue Out   Yellow In  ¢   5  5  5  5  5  5
2223  2 Sq    Small X  Blue Out   Green In   £   5  5  6  5  6  6
2231  2 Sq    Small X  Red Out    White In   ¥   5  6  4  6  4  7
2232  2 Sq    Small X  Red Out    Yellow In  ¬   5  6  5  6  5  8
2233  2 Sq    Small X  Red Out    Green In   µ   5  6  6  6  6  9
2311  2 Sq    Big X    Black Out  White In   À   6  4  4  7  7  1
2312  2 Sq    Big X    Black Out  Yellow In  Á   6  4  5  7  8  2
2313  2 Sq    Big X    Black Out  Green In   Â   6  4  6  7  9  3
2321  2 Sq    Big X    Blue Out   White In   Ã   6  5  4  8  7  4
2322  2 Sq    Big X    Blue Out   Yellow In  Ä   6  5  5  8  8  5
2323  2 Sq    Big X    Blue Out   Green In   Å   6  5  6  8  9  6
2331  2 Sq    Big X    Red Out    White In   Æ   6  6  4  9  7  7
2332  2 Sq    Big X    Red Out    Yellow In  Ç   6  6  5  9  8  8
2333  2 Sq    Big X    Red Out    Green In   È   6  6  6  9  9  9
3111  3x3 Sq  No X     Black Out  White In   É   7  7  7  1  1  1
3112  3x3 Sq  No X     Black Out  Yellow In  Ê   7  7  8  1  2  2
3113  3x3 Sq  No X     Black Out  Green In   Ë   7  7  9  1  3  3
3121  3x3 Sq  No X     Blue Out   White In   Ì   7  8  7  2  1  4
3122  3x3 Sq  No X     Blue Out   Yellow In  Í   7  8  8  2  2  5
3123  3x3 Sq  No X     Blue Out   Green In   Î   7  8  9  2  3  6
3131  3x3 Sq  No X     Red Out    White In   Ï   7  9  7  3  1  7
3132  3x3 Sq  No X     Red Out    Yellow In  Р  7  9  8  3  2  8
3133  3x3 Sq  No X     Red Out    Green In   Ñ   7  9  9  3  3  9
3211  3x3 Sq  Small X  Black Out  White In   Ò   8  7  7  4  4  1
3212  3x3 Sq  Small X  Black Out  Yellow In  Ó   8  7  8  4  5  2
3213  3x3 Sq  Small X  Black Out  Green In   Ô   8  7  9  4  6  3
3221  3x3 Sq  Small X  Blue Out   White In   Õ   8  8  7  5  4  4
3222  3x3 Sq  Small X  Blue Out   Yellow In  Ö   8  8  8  5  5  5
3223  3x3 Sq  Small X  Blue Out   Green In   Ø   8  8  9  5  6  6
3231  3x3 Sq  Small X  Red Out    White In   Ù   8  9  7  6  4  7
3232  3x3 Sq  Small X  Red Out    Yellow In  Ú   8  9  8  6  5  8
3233  3x3 Sq  Small X  Red Out    Green In   Û   8  9  9  6  6  9
3311  3x3 Sq  Big X    Black Out  White In   Ü   9  7  7  7  7  1
3312  3x3 Sq  Big X    Black Out  Yellow In  Ý   9  7  8  7  8  2
3313  3x3 Sq  Big X    Black Out  Green In   Þ   9  7  9  7  9  3
3321  3x3 Sq  Big X    Blue Out   White In   ß   9  8  7  8  7  4
3322  3x3 Sq  Big X    Blue Out   Yellow In  Œ   9  8  8  8  8  5
3323  3x3 Sq  Big X    Blue Out   Green In   Š   9  8  9  8  9  6
3331  3x3 Sq  Big X    Red Out    White In   Ÿ   9  9  7  9  7  7
3332  3x3 Sq  Big X    Red Out    Yellow In  Ž   9  9  8  9  8  8
3333  3x3 Sq  Big X    Red Out    Green In   ƒ   9  9  9  9  9  9


Puzzles & solving techniques to follow.

tarek
[EDIT: Line notation symbols revised for technical reasons]


Last edited by tarek on Mon Jan 24, 2011 12:54 am, edited 1 time in total.

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 Post subject: Re: Setdoku (Set-Do-Ku)
PostPosted: Sun Jan 23, 2011 6:11 pm 
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tarek

Been playing around with them a bit - interesting. Someting like four separate disjoint group sudoku on 1,2,3 but with interactions and more freedom.

For notation consider using: +£1a, -$2b, *€3c, not as pretty as Simon's or as visual.

Maurice


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 Post subject: Re: Setdoku (Set-Do-Ku)
PostPosted: Mon Jan 24, 2011 12:52 am 
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Hatman,

These are the formats that I have been using.

Code:
Set rules for Mini/Maxi Row/Column
Attributes 1,2 & 3,4 respectively form 2 valid vanilla sudoku grids

Line format:
1.......Z....S......È...Ù............Â.....Ÿ............U...Ü......Û....Í.......O

123456789ABC format:
147A .... ....  .... .... ....  .... .... 249B 
.... .... ....  .... 247A ....  .... .... .... 
.... .... 269C  .... .... ....  359A .... .... 

.... .... ....  .... .... ....  .... .... .... 
.... 267C ....  .... .... ....  .... 369A .... 
.... .... ....  .... .... ....  .... .... .... 

.... .... 247C  .... .... ....  367A .... .... 
.... .... ....  .... 359C ....  .... .... .... 
348B .... ....  .... .... ....  .... .... 168C 

123123123123 format:
1111 .... ....  .... .... ....  .... .... 2132 
.... .... ....  .... 2111 ....  .... .... .... 
.... .... 2333  .... .... ....  3231 .... .... 

.... .... ....  .... .... ....  .... .... .... 
.... 2313 ....  .... .... ....  .... 3331 .... 
.... .... ....  .... .... ....  .... .... .... 

.... .... 2113  .... .... ....  3311 .... .... 
.... .... ....  .... 3233 ....  .... .... .... 
3122 .... ....  .... .... ....  .... .... 1323 

Sudoku grids (12 & 34)
1.......4....4......6...8............6.....9............4...9......8....7.......3
1.......8....1......9...7............3.....7............3...1......9....5.......6

You are suggesting a +-*£$€123abc format. This the solution to the above puzzle in this format
Code:
+£1a +€2a +$3a  *$1c *£2c *€3c  -€1b -$2b -£3b 
*€1b *$2b *£3b  -$3a -£1a -€2a  +£2c +€3c +$1c 
-$1c -£2c -€3c  +$2b +£3b +€1b  *$3a *£1a *€2a 

*$3b *£1b *€2b  -£2a -€3a -$1a  +€1c +$2c +£3c 
-£3c -€1c -$2c  +£1b +€2b +$3b  *£2a *€3a *$1a 
+€3a +$1a +£2a  *£3c *€1c *$2c  -$3b -£1b -€2b 

-€2c -$3c -£1c  +€3b +$1b +£2b  *€1a *$2a *£3a 
+$2a +£3a +€1a  *€2c *$3c *£1c  -£2b -€3b -$1b 
*£2b *€3b *$1b  -€1a -$2a -£3a  +$3c +£1c +€2c

I had to revise the line notation though several times for technical reasons.

the 2 corresponding sudokus will make sure that a certain attribute can't appear more than 3 times in a sudoku constraint ... This will allow players to solve at symbol level as well. I'm hoping to demostrate soon practical solving techniques.

tarek


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 Post subject: Setdoku 05
PostPosted: Sun Jan 30, 2011 9:22 pm 
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I have a puzzle & a walkthrough ....
It should be solvable using Set Rules & singles. This one however does not have MAXI column/row Set rules.
Code:
Setdoku puzzle 05
Set Rules in Mini row/column only
Attributes 1&2 form a valid vanilla sudoku grid
Attributes 3&4 form a valid vanilla sudoku grid

Line format:
.H..Ã.....W.Î.Ž.R...........Â.....Y.¬.......N.6V....A...........J.8.~.Á.....I..Ú.

Hatman Symbols:
.... +$3b ....  .... -€2a ....  .... .... .... 
.... -£2b ....  *£2c .... *€3b  .... +€3c .... 
.... .... ....  .... .... ....  .... .... .... 

.... -€1c ....  .... .... ....  .... -£3a .... 
-$3b .... ....  .... .... ....  .... .... +€2b 
.... +£2c -£2a  .... .... ....  .... +$1a .... 

.... .... ....  .... .... ....  .... .... .... 
.... +€1a ....  +£3b .... -$2a  .... -€1b .... 
.... .... ....  .... +$3c ....  .... *$3b .... 

Original Symbols:
.... 1232 ....  .... 2321 ....  .... .... .... 
.... 2122 ....  3123 .... 3332  .... 1333 .... 
.... .... ....  .... .... ....  .... .... .... 

.... 2313 ....  .... .... ....  .... 2131 .... 
2232 .... ....  .... .... ....  .... .... 1322 
.... 1123 2121  .... .... ....  .... 1211 .... 

.... .... ....  .... .... ....  .... .... .... 
.... 1311 ....  1132 .... 2221  .... 2312 .... 
.... .... ....  .... 1233 ....  .... 3232 .... 

Sudoku Grid 1 (Attributes 1&2)
.2..6.....4.7.9.3...........6.....4.5.......3.14....2...........3.1.5.6.....2..8.
. 2 .|. 6 .|. . .
. 4 .|7 . 9|. 3 .
. . .|. . .|. . .
-----+-----+-----
. 6 .|. . .|. 4 .
5 . .|. . .|. . 3
. 1 4|. . .|. 2 .
-----+-----+-----
. . .|. . .|. . .
. 3 .|1 . 5|. 6 .
. . .|. 2 .|. 8 .

Sudoku grid 2 (Attributes 3&4)
.8..4.....5.6.8.9...........3.....7.8.......5.64....1...........1.8.4.2.....9..8.
. 8 .|. 4 .|. . .
. 5 .|6 . 8|. 9 .
. . .|. . .|. . .
-----+-----+-----
. 3 .|. . .|. 7 .
8 . .|. . .|. . 5
. 6 4|. . .|. 1 .
-----+-----+-----
. . .|. . .|. . .
. 1 .|8 . 4|. 2 .
. . .|. 9 .|. 8 .

Solution:
Hidden Text:
1HOµÃTŒËÙÆW}ÎÒŽBR4ÕÝÑL7EZ£ÀKÂÜD¢Ø9YЬÛGSÊ3ÅßNÍ6VŸQÈÔA{CÌÇÓXP]5ƒ[JÖ8Þ~ÏÁFŠ¥2ÄIÉMÚU

+£1a +$3b +€2c -$3c -€2a -£1b *€2b *£1c *$3a
-€3a -£2b -$1c *£2c *$1a *€3b +$1b +€3c +£2a
*$2a *€1b *£3c +€1c +£3a +$2b -£3b -$2c -€1a

+€1b -€1c *€1a +$2a -$2b *$2c +£3c -£3a *£3b
-$3b *$3c +$3a -£1a *£1b +£1c -€2c *€2a +€2b
*£2b +£2c -£2a *€3a +€3b -€3c *$1c +$1a -$1b

+$1c *£2a -€3b *$1b -£2c +€3a -$1a +£2b *€3c
-£3c +€1a *$2b +£3b *€1c -$2a *£3a -€1b +$2c
*€2c -$3a +£1b -€2b +$3c *£1a +€2a *$3b -£1c


1111 1232 1323 2233 2321 2112 3322 3113 3231
2331 2122 2213 3123 3211 3332 1212 1333 1121
3221 3312 3133 1313 1131 1222 2132 2223 2311

1312 2313 3311 1221 2222 3223 1133 2131 3132
2232 3233 1231 2111 3112 1113 2323 3321 1322
3122 1123 2121 3331 1332 2333 3213 1211 2212

1213 3121 2332 3212 2123 1331 2211 1122 3333
2133 1311 3222 1132 3313 2221 3131 2312 1223
3323 2231 1112 2322 1233 3111 1321 3232 2113


123564978645789231897312456369258147582471693714936825276843519438195762951627384
186942537753618294429375861231456978897123645564789312348267159915834726672591483


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 Post subject: Re: Setdoku (Set-Do-Ku)
PostPosted: Sun Jan 30, 2011 9:28 pm 
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Here is the Walkthrough which is detailed & shows some trivial things just to demonstrate how manual solving / PM aided solving would work:
Hidden Text:
.H..Ã.....W.Î.Ž.R...........Â.....Y.¬.......N.6V....A...........J.8.~.Á.....I..Ú.

Code:
.... +$3b .... .... -€2a .... .... .... ....
.... -£2b .... *£2c .... *€3b .... +€3c ....
.... .... .... .... .... .... .... .... ....

.... -€1c .... .... .... .... .... -£3a ....
-$3b .... .... .... .... .... .... .... +€2b
.... +£2c -£2a .... .... .... .... +$1a ....

.... .... .... .... .... .... .... .... ....
.... +€1a .... +£3b .... -$2a .... -€1b ....
.... .... .... .... +$3c .... .... *$3b ....


In a Setdoku puzzle there are 81 different symbols, if a symbol is uncovered
then no other cell can house that symbol.


+$3b is a given clue in r1c2
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +$3b
-€2a is a given clue in r1c5
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -€2a
-£2b is a given clue in r2c2
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -£2b
*£2c is a given clue in r2c4
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> *£2c
*€3b is a given clue in r2c6
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> *€3b
+€3c is a given clue in r2c8
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +€3c
-€1c is a given clue in r4c2
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -€1c
-£3a is a given clue in r4c8
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -£3a
-$3b is a given clue in r5c1
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -$3b
+€2b is a given clue in r5c9
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +€2b
+£2c is a given clue in r6c2
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +£2c
-£2a is a given clue in r6c3
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -£2a
+$1a is a given clue in r6c8
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +$1a
+€1a is a given clue in r8c2
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +€1a
+£3b is a given clue in r8c4
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +£3b
-$2a is a given clue in r8c6
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -$2a
-€1b is a given clue in r8c8
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> -€1b
+$3c is a given clue in r9c5
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> +$3c
*$3b is a given clue in r9c8
[r1c1346789][r28c13579][r37c123456789][r4c1345679][r5c2345678][r6c145679][r9c1234679]<> *$3b

Using Set Rules:
If you know 2 symbols from a set then there is only one symbol that can complete the set
(Remeber: The attribute are either all the same or all different)


*$1a in r2c5 is the only symbol to make *£2c & *€3b a set in the [r2c456] Mini Line
*£2b in r6c1 is the only symbol to make +£2c & -£2a a set in the [r6c123] Mini Line
*€1c in r8c5 is the only symbol to make +£3b & -$2a a set in the [r8c456] Mini Line
*€1b in r3c2 is the only symbol to make +$3b & -£2b a set in the [r123c2] Mini Line
*$3c in r5c2 is the only symbol to make -€1c & +£2c a set in the [r456c2] Mini Line
*€2a in r5c8 is the only symbol to make -£3a & +$1a a set in the [r456c8] Mini Line
+£2b in r7c8 is the only symbol to make -€1b & *$3b a set in the [r789c8] Mini Line

And back to the eliminations:
(These eliminations are only important for more complex techniques & useful when transferring
into sudoku grids)


[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *$1a
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *€1b
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *$3c
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *€2a
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *£2b
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> +£2b
[r1c1346789][r28c1379][r3c13456789][r4c1345679][r5c34567][r6c45679][r7c12345679][r9c1234679]<> *€1c

Continue until you can uncover no more

+$3a in r5c3 is the only symbol to make -$3b & *$3c a set in the [r5c123] Mini Line
-€2c in r5c7 is the only symbol to make *€2a & +€2b a set in the [r5c789] Mini Line
+£3a in r3c5 is the only symbol to make -€2a & *$1a a set in the [r123c5] Mini Line
+€1b in r4c1 is the only symbol to make -$3b & *£2b a set in the [r456c1] Mini Line
-£2c in r7c5 is the only symbol to make *€1c & +$3c a set in the [r789c5] Mini Line
[r13c1346789][r28c1379][r4c345679][r5c456][r6c45679][r79c1234679]<> +£3a
[r13c1346789][r28c1379][r4c345679][r5c456][r6c45679][r79c1234679]<> +€1b
[r13c1346789][r28c1379][r4c345679][r5c456][r6c45679][r79c1234679]<> +$3a
[r13c1346789][r28c1379][r4c345679][r5c456][r6c45679][r79c1234679]<> -€2c
[r13c1346789][r28c1379][r4c345679][r5c456][r6c45679][r79c1234679]<> -£2c
*€1a in r4c3 is the only symbol to make +€1b & -€1c a set in the [r4c123] Mini Line
*€1a in r4c3 is the only symbol to make +$3a & -£2a a set in the [r456c3] Mini Line
[r13c1346789][r28c1379][r46c45679][r5c456][r79c1234679]<> *€1a

Now you can uncover no more symbols in the trivial manner mentioned above
Using the conversion table (or if you can visualize the attribute combination as
a unque symbol) convert the Setdoku grid into 2 Sudoku grids.
(attribute 1 & 2 are grid 12 in the table & attribute 3 & 4 are grid 34 in the table)

Do a preliminary cleanup


Looking at Sudoku Grid 12:
Code:
+-------------------------+-------------------------+-------------------------+
| 18 2 13578 | 345 6 34 | 145789 57 145789 |
| 16 4 156 | 7 8 9 | 125 3 1256 |
| 68 9 35678 | 2345 1 234 | 24578 57 245678 |
+-------------------------+-------------------------+-------------------------+
| 3 6 9 | 258 57 1278 | 1578 4 1578 |
| 5 8 2 | 4 7 147 | 6 9 3 |
| 7 1 4 | 35689 35 368 | 58 2 58 |
+-------------------------+-------------------------+-------------------------+
| 2689 57 5678 | 368 4 3678 | 23579 1 2579 |
| 248 3 78 | 1 9 5 | 247 6 247 |
| 1469 57 1567 | 36 2 367 | 34579 8 4579 |
+-------------------------+-------------------------+-------------------------+
Looking at Sudoku Grid 34:
Code:
+----------------------+----------------------+----------------------+
| 13679 8 369 | 2359 4 2359 | 12357 36 12367 |
| 347 5 3 | 6 1 8 | 2347 9 2347 |
| 13469 2 369 | 359 7 359 | 13458 36 13468 |
+----------------------+----------------------+----------------------+
| 2 3 1 | 459 58 569 | 89 7 89 |
| 8 9 7 | 123 2 123 | 6 4 5 |
| 5 6 4 | 2379 28 2379 | 2389 1 2389 |
+----------------------+----------------------+----------------------+
| 3479 47 2389 | 127 6 127 | 13479 5 13479 |
| 679 1 569 | 8 3 4 | 79 2 679 |
| 3467 47 2356 | 1257 9 1257 | 1347 8 13467 |
+----------------------+----------------------+----------------------+


You can clearly see that r5c5 in both grids has only one candidate

Transferring back into a setdoku grid:


*£1b in r5c5 is a Naked single
[r1c79][r579c6][r79c3]<> *£1b

The above procedures can now be used to advance the puzzle as follows:

Looking at Sudoku Grid 12:
[r13c4][r5c6]<>4
[r4c56][r5c6]<>7
Looking at Sudoku Grid 34:
[r13c13][r2c179][r79c3]<>3
[r5c46][r6c456]<>2
-$2b in r4c5 is a Naked single
[r13c47][r4c4][r9c3]<> -$2b
+€3b in r6c5 is the only symbol to make -$2b & *£1b a set in the [r456c5] Mini Line
.H..Ã.....W.ÎÒŽ.R..Ý..7....KÂÜ.¢..Y.¬ÛG.Ê.ÅßNÍ6V.Q..A.....X..5..J.8Þ~.Á.....I..Ú.
.2..6.....4.789.3..9..1....369.5..4.582471693714.3..2.....4..1..3.195.6.....2..8.
.8..4.....53618.9..2..7....231.5..7.897.2.645564.8..1.....6..5..1.834.2.....9..8.
Looking at Sudoku Grid 12:
[r4c479][r6c4]<>5
[r4c6]<>1
[r6c46]<>3
Looking at Sudoku Grid 34:
[r4c46]<>5

You need to apply your sudoku solving skills to advance the puzzle now:

Looking at Sudoku Grid 12:
9 in r6c4 is a hidden single in more than one sector
Looking at Sudoku Grid 34:
8 in r7c3 is a hidden single in more than one sector

Hidden Singles (Or Hidden & Naked singles if you do not use the PM) is the maximum you
will need to advance this puzzle towards solution as follows:


Looking at Sudoku Grid 12:
6 in r6c6 is a hidden single in more than one sector
Looking at Sudoku Grid 34:
2 in r9c3 is a hidden single in more than one sector
Looking at Sudoku Grid 12:
[r79c6]<>6
Looking at Sudoku Grid 34:
5 in r8c3 is a hidden single in more than one sector
*$2b in r8c3 is a Naked single
[r13c7]<> *$2b
-£3c in r8c1 is the only symbol to make +€1a & *$2b a set in the [r8c123] Mini Line
[r13c6][r8c79]<> -£3c
Looking at Sudoku Grid 12:
[r9c1]<>4
[r13c3][r7c1]<>8
[r13479c7][r789c9]<>7
Looking at Sudoku Grid 34:
[r137c1][r8c79]<>9
+£3c in r4c7 is a Naked single
[r1c3][r4c9]<> +£3c
*£3b in r4c9 is the only symbol to make +£3c & -£3a a set in the [r4c789] Mini Line
*$1c in r6c7 is the only symbol to make +£3c & -€2c a set in the [r456c7] Mini Line
[r3c9][r7c3]<> *£3b
[r13c79][r6c9]<> *$1c
-$1b in r6c9 is the only symbol to make *$1c & +$1a a set in the [r6c789] Mini Line
-$1b in r6c9 is the only symbol to make *£3b & +€2b a set in the [r456c9] Mini Line
[r1c479][r2c79][r9c3]<> -$1b
-€3b in r7c3 is a Naked single
[r3c9]<> -€3b
+£1b in r9c3 is the only symbol to make -€3b & *$2b a set in the [r789c3] Mini Line
[r12c79]<> +£1b
*£3a in r8c7 is a Naked single
[r1c9][r79c26]<> *£3a
+$2c in r8c9 is the only symbol to make *£3a & -€1b a set in the [r8c789] Mini Line
[r3c9][r4c6]<> +$2c
*$2c in r4c6 is a Naked single
[r13c19]<> *$2c
+$2a in r4c4 is the only symbol to make -$2b & *$2c a set in the [r4c456] Mini Line
[r23c79][r7c179]<> +$2a
Looking at Sudoku Grid 12:
[r3c4]<>2
[r7c6]<>8
[r12c7]<>1
[r13c9]<>7
[r13c7]<>8
[r12379c9]<>5
[r3c3][r7c14][r9c1]<>6
[r237c9][r7c7]<>2
[r2c3][r9c1]<>1
Looking at Sudoku Grid 34:
[r7c7]<>9
[r3c9]<>8
[r1379c7]<>3
[r12c9]<>2
[r1279c7][r79c9]<>7
[r139c9]<>6
-$1c in r2c3 is a Naked single
[r13c48]<> -$1c
-€3a in r2c1 is the only symbol to make -£2b & -$1c a set in the [r2c123] Mini Line
[r2c9][r6c6][r9c4]<> -€3a
+$1b in r2c7 is a Naked single
+£2a in r2c9 is the only symbol to make +$1b & +€3c a set in the [r2c789] Mini Line
-€3c in r6c6 is a Naked single
*€3a in r6c4 is the only symbol to make +€3b & -€3c a set in the [r6c456] Mini Line
+£1c in r5c6 is the only symbol to make *$2c & -€3c a set in the [r456c6] Mini Line
[r1c9]<> +£1c
[r1c9][r79c1]<> *€3a
-£1a in r5c4 is the only symbol to make *£1b & +£1c a set in the [r5c456] Mini Line
-£1a in r5c4 is the only symbol to make +$2a & *€3a a set in the [r456c4] Mini Line
[r139c79]<> -£1a
+$1c in r7c1 is a Naked single
[r3c6]<> +$1c
*£2a in r7c2 is the only symbol to make +$1c & -€3b a set in the [r7c123] Mini Line
*€2c in r9c1 is the only symbol to make +$1c & -£3c a set in the [r789c1] Mini Line
[r9c2]<> *£2a
-$3a in r9c2 is the only symbol to make *€2c & +£1b a set in the [r9c123] Mini Line
-$3a in r9c2 is the only symbol to make *£2a & +€1a a set in the [r789c2] Mini Line
*€3c in r7c9 is a Naked single
-$1a in r7c7 is the only symbol to make +£2b & *€3c a set in the [r7c789] Mini Line
-£1c in r9c9 is the only symbol to make *€3c & +$2c a set in the [r789c9] Mini Line
[r139c7]<> -$1a
[r13c69]<> -£1c
+€2a in r9c7 is the only symbol to make *$3b & -£1c a set in the [r9c789] Mini Line
+€2a in r9c7 is the only symbol to make -$1a & *£3a a set in the [r789c7] Mini Line
Looking at Sudoku Grid 12:
[r3c1]<>6
[r13c3]<>5
[r3c7]<>2
[r1c9]<>1
[r7c6]<>7
[r9c46]<>3
Looking at Sudoku Grid 34:
[r1c1]<>7
[r1c7]<>2
[r3c9]<>4
[r9c4]<>1
[r13c6]<>3
[r79c4]<>7
[r7c6]<>1
[r9c6]<>7
+£1a in r1c1 is a Naked single
+€2c in r1c3 is the only symbol to make +£1a & +$3b a set in the [r1c123] Mini Line
*$2a in r3c1 is the only symbol to make +£1a & -€3a a set in the [r123c1] Mini Line
[r3c3]<> +€2c
*£3c in r3c3 is the only symbol to make *$2a & *€1b a set in the [r3c123] Mini Line
*£3c in r3c3 is the only symbol to make +€2c & -$1c a set in the [r123c3] Mini Line
-£1b in r1c6 is a Naked single
-$3c in r1c4 is the only symbol to make -€2a & -£1b a set in the [r1c456] Mini Line
+$2b in r3c6 is the only symbol to make -£1b & *€3b a set in the [r123c6] Mini Line
[r3c4]<> -$3c
+€1c in r3c4 is the only symbol to make +£3a & +$2b a set in the [r3c456] Mini Line
+€1c in r3c4 is the only symbol to make -$3c & *£2c a set in the [r123c4] Mini Line
*€2b in r1c7 is a Naked single
-£3b in r3c7 is the only symbol to make *€2b & +$1b a set in the [r123c7] Mini Line
*$3a in r1c9 is a Naked single
*£1c in r1c8 is the only symbol to make *€2b & *$3a a set in the [r1c789] Mini Line
-€1a in r3c9 is the only symbol to make *$3a & +£2a a set in the [r123c9] Mini Line
[r3c8]<> *£1c
-$2c in r3c8 is the only symbol to make -£3b & -€1a a set in the [r3c789] Mini Line
-$2c in r3c8 is the only symbol to make *£1c & +€3c a set in the [r123c8] Mini Line
*$1b in r7c4 is a Naked single
+€3a in r7c6 is the only symbol to make *$1b & -£2c a set in the [r7c456] Mini Line
-€2b in r9c4 is the only symbol to make *$1b & +£3b a set in the [r789c4] Mini Line
*£1a in r9c6 is the only symbol to make -€2b & +$3c a set in the [r9c456] Mini Line
*£1a in r9c6 is the only symbol to make +€3a & -$2a a set in the [r789c6] Mini Line
Puzzle Solved
1HOµÃTŒËÙÆW}ÎÒŽBR4ÕÝÑL7EZ£ÀKÂÜD¢Ø9YЬÛGSÊ3ÅßNÍ6VŸQÈÔA{CÌÇÓXP]5ƒ[JÖ8Þ~ÏÁFŠ¥2ÄIÉMÚU
123564978645789231897312456369258147582471693714936825276843519438195762951627384
186942537753618294429375861231456978897123645564789312348267159915834726672591483

There are more complex Setdoku & Sudoku techniques which can be used. The above puzzle is an easy example.

This level should satisfy variants enthusiasts. PM enthusiasts can obviosly advance puzzles by dissecting the symbols & solving at attribute level.

A few more examples in the next few weeks. Then, puzzles will be posted if there is a public demand (That is why I'm quite relaxed ;) ). I will be posting this Walkthrough on the sudokuSolver & programmers forums.

tarek


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