setoku

Notes on possible new logic puzzles

Re: setoku

Postby simon_blow_snow » Sun Jan 16, 2011 6:14 pm

tarek

I tried to convert my 2 solution grids into your 2 canonical grids via "isomorph transformation" (band/stack/row/column swapping etc). But I cannot get the first one (the one I used for my avatar) to match either of yours. It seems neither of your 2 grids covers one feature of my 1st solution grid: FOUR out of 6 pairing of attributes produce a Sudoku grid (SQ-X, in-out, SQ-out, in-X).

Perhaps your software can generate a canonical grid with that feature?


I think my 2nd solution grid can be converted into your 1st canonical grid, but am too busy to do it manually. Do you have a program to "canonicalize" any given setdoku grid? If so could you canonicalize both my solution grids and tell me the results? Thanks!
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Re: setoku

Postby tarek » Sun Jan 16, 2011 7:55 pm

I tried 2
simon_blow_snow wrote:It seems neither of your 2 grids covers one feature of my 1st solution grid: FOUR out of 6 pairing of attributes produce a Sudoku grid (SQ-X, in-out, SQ-out, in-X).
Perhaps your software can generate a canonical grid with that feature

i have made Setdokus with 2 sudoku grids & 6 grids & not 4 (This should be easy to do). The 6 sudokus version will always have 1 of the attributes matching with the rest all different. So there is No all different sets version from it.

The canonicalizer is on the agenda. If you are canonicalizing remember the relabelling issue you have 4 attributes that can be relabelled to produce a "1111" symbol.

The sudoku grids canicalizing is a good idea? You have to canonicalize each grid Isolate the most canonical of these canonical grids. if 2 solution grids do non identical most canonical grid then they are not isomorphic.

will produce some results later.

tarek
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Most Canonical grids

Postby tarek » Sun Jan 16, 2011 10:27 pm

Here the results for the most canonical grids. I've included all 6 sudoku grids. The 2 sudokus version should be line 1 & 6, the 4 sudokus version should be lines 1,2,5 & 6
The most canonical grid is the same even if you remove the Maxi row/column set restriction
Code: Select all
Most Canonical No Maxi Row/Column 2 sudoku grids

147A 157B 167C  248A 258B 268C  349A 359B 369C 
248B 258C 268A  349B 359C 369A  147B 157C 167A 
349C 359A 369B  147C 157A 167B  248C 258A 268B 

158A 168B 148C  259A 269B 249C  357A 367B 347C 
259B 269C 249A  357B 367C 347A  158B 168C 148A 
357C 367A 347B  158C 168A 148B  259C 269A 249B 

169A 149B 159C  267A 247B 257C  368A 348B 358C 
267B 247C 257A  368B 348C 358A  169B 149C 159A 
368C 348A 358B  169C 149A 159B  267C 247A 257B 


1111 1212 1313  2121 2222 2323  3131 3232 3333 
2122 2223 2321  3132 3233 3331  1112 1213 1311 
3133 3231 3332  1113 1211 1312  2123 2221 2322 

1221 1322 1123  2231 2332 2133  3211 3312 3113 
2232 2333 2131  3212 3313 3111  1222 1323 1121 
3213 3311 3112  1223 1321 1122  2233 2331 2132 

1331 1132 1233  2311 2112 2213  3321 3122 3223 
2312 2113 2211  3322 3123 3221  1332 1133 1231 
3323 3121 3222  1333 1131 1232  2313 2111 2212 


123456789456789123789123456231564897564897231897231564312645978645978312978312645
111555999555999111999111555222666777666777222777222666333444888444888333888333444
123456789564897231978312645123456789564897231978312645123456789564897231978312645
147258369258369147369147258582693471693471582471582693936714825714825936825936714
159159159267267267348348348483483483591591591672672672726726726834834834915915915
123456789564897231978312645456789123897231564312645978789123456231564897645978312

Most Canonical with Maxi Row/Column 2 sudoku grids

147A 157B 167C  248A 258B 268C  349A 359B 369C 
248B 258C 268A  349B 359C 369A  147B 157C 167A 
349C 359A 369B  147C 157A 167B  248C 258A 268B 

158A 168B 148C  259A 269B 249C  357A 367B 347C 
259B 269C 249A  357B 367C 347A  158B 168C 148A 
357C 367A 347B  158C 168A 148B  259C 269A 249B 

169A 149B 159C  267A 247B 257C  368A 348B 358C 
267B 247C 257A  368B 348C 358A  169B 149C 159A 
368C 348A 358B  169C 149A 159B  267C 247A 257B 


1111 1212 1313  2121 2222 2323  3131 3232 3333 
2122 2223 2321  3132 3233 3331  1112 1213 1311 
3133 3231 3332  1113 1211 1312  2123 2221 2322 

1221 1322 1123  2231 2332 2133  3211 3312 3113 
2232 2333 2131  3212 3313 3111  1222 1323 1121 
3213 3311 3112  1223 1321 1122  2233 2331 2132 

1331 1132 1233  2311 2112 2213  3321 3122 3223 
2312 2113 2211  3322 3123 3221  1332 1133 1231 
3323 3121 3222  1333 1131 1232  2313 2111 2212 


123456789456789123789123456231564897564897231897231564312645978645978312978312645
111555999555999111999111555222666777666777222777222666333444888444888333888333444
123456789564897231978312645123456789564897231978312645123456789564897231978312645
147258369258369147369147258582693471693471582471582693936714825714825936825936714
159159159267267267348348348483483483591591591672672672726726726834834834915915915
123456789564897231978312645456789123897231564312645978789123456231564897645978312


Most Canonical No Maxi Row/Column 4 sudoku grids

147A 158A 169A  247B 258B 269B  347C 358C 369C 
247C 258C 269C  347A 358A 369A  147B 158B 169B 
347B 358B 369B  147C 158C 169C  247A 258A 269A 

159A 167A 148A  259B 267B 248B  359C 367C 348C 
259C 267C 248C  359A 367A 348A  159B 167B 148B 
359B 367B 348B  159C 167C 148C  259A 267A 248A 

168A 149A 157A  268B 249B 257B  368C 349C 357C 
268C 249C 257C  368A 349A 357A  168B 149B 157B 
368B 349B 357B  168C 149C 157C  268A 249A 257A 


1111 1221 1331  2112 2222 2332  3113 3223 3333 
2113 2223 2333  3111 3221 3331  1112 1222 1332 
3112 3222 3332  1113 1223 1333  2111 2221 2331 

1231 1311 1121  2232 2312 2122  3233 3313 3123 
2233 2313 2123  3231 3311 3121  1232 1312 1122 
3232 3312 3122  1233 1313 1123  2231 2311 2121 

1321 1131 1211  2322 2132 2212  3323 3133 3213 
2323 2133 2213  3321 3131 3211  1322 1132 1212 
3322 3132 3212  1323 1133 1213  2321 2131 2211 


123456789456789123789123456231564897564897231897231564312645978645978312978312645
123456789456789123789123456312645978645978312978312645231564897564897231897231564
111555999666777222888333444111555999666777222888333444111555999666777222888333444
159159159159159159159159159672672672672672672672672672834834834834834834834834834
147258369369147258258369147471582693693471582582693471714825936936714825825936714
147258369369147258258369147714825936936714825825936714471582693693471582582693471

Most Canonical With Maxi Row/Column 4 sudoku grids

147A 158A 169A  247B 258B 269B  347C 358C 369C 
247C 258C 269C  347A 358A 369A  147B 158B 169B 
347B 358B 369B  147C 158C 169C  247A 258A 269A 

159A 167A 148A  259B 267B 248B  359C 367C 348C 
259C 267C 248C  359A 367A 348A  159B 167B 148B 
359B 367B 348B  159C 167C 148C  259A 267A 248A 

168A 149A 157A  268B 249B 257B  368C 349C 357C 
268C 249C 257C  368A 349A 357A  168B 149B 157B 
368B 349B 357B  168C 149C 157C  268A 249A 257A 


1111 1221 1331  2112 2222 2332  3113 3223 3333 
2113 2223 2333  3111 3221 3331  1112 1222 1332 
3112 3222 3332  1113 1223 1333  2111 2221 2331 

1231 1311 1121  2232 2312 2122  3233 3313 3123 
2233 2313 2123  3231 3311 3121  1232 1312 1122 
3232 3312 3122  1233 1313 1123  2231 2311 2121 

1321 1131 1211  2322 2132 2212  3323 3133 3213 
2323 2133 2213  3321 3131 3211  1322 1132 1212 
3322 3132 3212  1323 1133 1213  2321 2131 2211 


123456789456789123789123456231564897564897231897231564312645978645978312978312645
123456789456789123789123456312645978645978312978312645231564897564897231897231564
111555999666777222888333444111555999666777222888333444111555999666777222888333444
159159159159159159159159159672672672672672672672672672834834834834834834834834834
147258369369147258258369147471582693693471582582693471714825936936714825825936714
147258369369147258258369147714825936936714825825936714471582693693471582582693471
Last edited by tarek on Sat Jan 22, 2011 10:37 am, edited 1 time in total.
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Special Setdoku grid

Postby tarek » Tue Jan 18, 2011 2:02 am

Here is another Most canonical grid with a special feature (Closer to your 2nd grid simon)

Code: Select all
Set Rules in Mini row/column, Maxi row/column & All Mini box diagonals
All possible combinations of attributes form 6 X-Sudoku grids.
 
147A 158B 169C  248C 259A 267B  349B 357C 368A 
249B 257C 268A  347A 358B 369C  148C 159A 167B 
348C 359A 367B  149B 157C 168A  247A 258B 269C 

168B 149C 157A  269A 247B 258C  367C 348A 359B 
267C 248A 259B  368B 349C 357A  169A 147B 158C 
369A 347B 358C  167C 148A 159B  268B 249C 257A 

159C 167A 148B  257B 268C 249A  358A 369B 347C 
258A 269B 247C  359C 367A 348B  157B 168C 149A 
357B 368C 349A  158A 169B 147C  259C 267A 248B 

123456789456789123789123456312645978645978312978312645231564897564897231897231564
123564978645789231897312456231645789456897312978123564312456897564978123789231645
123645897564789312978231456231456978645897123789312564312564789456978231897123645
159267348348159267267348159834915726726834915915726834672483591591672483483591672
159348267267159348348267159834726915915834726726915834672591483483672591591483672
159672834834159672672834159591726348348591726726348591915267483483915267267483915


I will focus now on solving techniques for players.

tarek
Last edited by tarek on Sat Jan 22, 2011 10:38 am, edited 1 time in total.
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Re: setoku

Postby tarek » Sat Jan 22, 2011 10:35 am

Here are 2 puzzles that explit these constraints, They are Symmetrically minimal. Difficulty has not been tested, so for the time being it should be a machine excerceise only
Code: Select all
Setdoku puzzle 03
Set Rules in Mini row/column, Maxi row/column & All Mini box diagonals
All possible combinations of attributes form 6 X-Sudoku grids.

............................¢.....S.Æ.......Þ.Û.....Í............................

.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 

.... 258B ....  .... .... ....  .... 247A .... 
269A .... ....  .... .... ....  .... .... 367C 
.... 359C ....  .... .... ....  .... 348B .... 

.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 


.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 

.... 2222 ....  .... .... ....  .... 2111 .... 
2331 .... ....  .... .... ....  .... .... 3313 
.... 3233 ....  .... .... ....  .... 3122 .... 

.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 


............................5.....4.6.......9.8.....7............................
............................5.....4.6.......7.9.....8............................
............................5.....4.4.......9.9.....8............................
............................5.....1.9.......7.6.....2............................
............................5.....1.7.......9.6.....2............................
............................5.....1.7.......3.9.....5............................

Code: Select all
Setdoku puzzle 04
Set Rules in Mini row/column, Maxi row/column & All Mini box diagonals
All possible combinations of attributes form 6 X-Sudoku grids.

......................3.........C.....Ì...£.....7.........G......................

.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... 147C ....  .... .... .... 

.... .... ....  .... .... 157C  .... .... .... 
.... .... 348A  .... .... ....  258C .... .... 
.... .... ....  149A .... ....  .... .... .... 

.... .... ....  .... 159A ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 


.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... 1113 ....  .... .... .... 

.... .... ....  .... .... 1213  .... .... .... 
.... .... 3121  .... .... ....  2223 .... .... 
.... .... ....  1131 .... ....  .... .... .... 

.... .... ....  .... 1231 ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 
.... .... ....  .... .... ....  .... .... .... 


......................1.........2.....7...5.....1.........2......................
......................1.........1.....8...5.....3.........3......................
......................3.........3.....7...6.....1.........1......................
......................1.........4.....2...5.....3.........6......................
......................3.........6.....1...6.....1.........4......................
......................3.........3.....4...6.....7.........7......................
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Re: setoku

Postby tarek » Sat Jan 22, 2011 11:07 am

I found a way to utilise the corresponding sudoku grids for Canonicalization. It is a bit tedious.

Superimpose the 2 grids (G12 & G34). Each cell would have 2 symbols (G12 Symbol 1st then G34 symbol 2nd) . Perform the canonicalization process (Row Normal or Box normal) for Vanilla sudokus (648 transformations). Repeat the process but swapping symbols. The most lexographic result would show (G12 & G34 in that order) & a Setdoku grid can be generated. If we have 4 grids or 6 grids then this can be done as well for each 2 different grid combinations so possibly (G12 & G34, G13 & G24, G14 & G23). The most lexographic would be G12 & G34 & the setdoku grid can be generated. I'm sure there is a more effecient way, but this is what came to my mind.

tarek
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Setdoku 05

Postby tarek » Thu Jan 27, 2011 11:50 pm

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: Select all
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: Show
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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Re: setoku

Postby tarek » Sun Jan 30, 2011 6:15 pm

Here is the Walkthrough which is detailed & shows some trivial things just to demonstrate how manual solving / PM aided solving would work:

Setdoku 05 Solution Walkthrough: Show
.H..Ã.....W.Î.Ž.R...........Â.....Y.¬.......N.6V....A...........J.8.~.Á.....I..Ú.

Code: Select all
.... +$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: Select all
+-------------------------+-------------------------+-------------------------+
| 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: Select all
+----------------------+----------------------+----------------------+
| 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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tarek
 
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