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Difference between revisions of "Sudoku/Puzzles/Inkala's Maze/Solution process"

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Inkala's Maze [https://www.sudokuwiki.org/sudoku.htm?bd=800000000003600000070090200050007000000045700000100030001000068008500010090000400 in SW Solver] has relatively few bifurcation seeds, but more than some "unsolvables." There is a bivalue cell display in SW Solver, and it shows seven chains and one cell pair. One chain connects three cells, so for a Bivalue Ariadne's Thread (BAT) process, a pair in that is an optimal choice, it would appear. We can choose the next bifurcation pair as a reasonable choice among what has become available.  
+
Inkala's Maze ([https://www.sudokuwiki.org/sudoku.htm?bd=800000000003600000070090200050007000000045700000100030001000068008500010090000400 in SW Solver]) has relatively few bifurcation seeds, but more than some "unsolvables." There is a bivalue cell display in SW Solver, and it shows seven chains and one cell pair. One chain connects three cells, so for a Bivalue Ariadne's Thread (BAT) process, a pair in that is an optimal choice, it would appear. We can choose the next bifurcation pair as a reasonable choice among what has become available.  
  
 
*1. 61=7 [https://www.sudokuwiki.org/sudoku.htm?bd=800000000003600000070090200050007000000045700700100030001000068008500010090000400 link]
 
*1. 61=7 [https://www.sudokuwiki.org/sudoku.htm?bd=800000000003600000070090200050007000000045700700100030001000068008500010090000400 link]
Line 37: Line 37:
 
*-----20 72=3 contrad.
 
*-----20 72=3 contrad.
 
*-----20 72=4* contrad.
 
*-----20 72=4* contrad.
*----19 82=4* BSNs 72={23}, <>2 72=3 etc. contrad.
+
*----19 82=4* SBNs 72={23}, <>2 72=3 etc. contrad.
 
*---8 87=9*
 
*---8 87=9*
 
*----21 27=1
 
*----21 27=1
 +
*-----22 22=2
 +
*------23 26=4 contrad.
 +
*------23 26=8*
 +
*-------24 72=3
 +
*--------25 82=4 SBN 12={16} => 6 => contrad.
 +
*--------25 82=6* SBN 12={14) => 1 => contrad.
 +
*-------24 72=4* SBN 12={16} => 1 => contrad.
 +
*-----22 22=4* contrad.
 +
*----21 27=8* SBN 65={28} => 8 => contrad.
 +
*---7 71=5
 +
*----26 77=3
 +
*-----27 75=2 SBN 89={27} => 2 => contrad.
 +
*-----27 75=7*
 +
*------28 93=2
 +
*-------29 94=3 contrad.
 +
*-------29 94=8* SBN 38={58} => 8 => SBN 36={13} => 3; SBN 22={12} => 2 => SBN 12={16} => 6 => contrad.
 +
*------28 93=6*
 +
*-------30 33=4 SBN 31={16} => 6 => contrad.
 +
*----26 77=9* SBN 72={23} => 3
 +
*-----31 82=2 contrad.
 +
*-----31 82=4*
 +
*------32 81=2
 +
*-------33 65=2 SBN 45={38} => contrad.
 +
*-------33 65=8 SBN 45={23} => 2 => contrad.
 +
*------32 81=7*
 +
*-------34 65=2 SBN 38={58} => 8 => contrad.
 +
*-------34 65=8*
 +
*--------35 75=2 contrad.
 +
*--------35 75=7* contrad.
 +
*---7 71=7*contrad. (check this!) incorrect savepoint 7, should have been
 +
*7 71=5* [resolved]
 +
*-36 77=3
 +
*--37 72=2
 +
*---38 89=2 contrad.
 +
*---38 89=7* SBN 62={68} => 8 => [full solution]
 +
uniqueness proof:
 +
*--37 72=4*
 +
*---39 76=2
 +
*----40 89=2 contrad.
 +
*----40 89=7* contrad.
 +
*---39 76=9*

Revision as of 03:16, 3 December 2019

Inkala's Maze (in SW Solver) has relatively few bifurcation seeds, but more than some "unsolvables." There is a bivalue cell display in SW Solver, and it shows seven chains and one cell pair. One chain connects three cells, so for a Bivalue Ariadne's Thread (BAT) process, a pair in that is an optimal choice, it would appear. We can choose the next bifurcation pair as a reasonable choice among what has become available.

  • 1. 61=7 link
  • -2 77=5
  • --3 27=1
  • ---4 31=1 contrad.
  • ---4 36=1* contrad.
  • --3 27=8* contrad.
  • -2 71=5*
  • --5 91=3
  • ---6 72=2 contrad.
  • ---6 72=4* contrad.
  • 1 63=7* [resolved]
  • -7 77=5
  • --8 87=3
  • ---9 93=5
  • ----10 33=4 contrad.
  • ----10 33=6*
  • -----11 91=3
  • ------12 72=2
  • ------12 72=4* contrad.
  • -----11 91=6*
  • ------13 82=2 contrad.
  • ------13 82=4*
  • -------14 13=4
  • --------15 27=1
  • ---------16 74=4 contrad.
  • ---------16 74=9* contrad.
  • --------15 27=8*
  • ---------17 12=1 contrad.
  • ---------17 12=2* contrad.
  • -------14 13=9*
  • --------18 74=4 contrad.
  • --------18 74=9* contrad.
  • ---9 93=6*
  • ----19 82=2
  • -----20 72=3 contrad.
  • -----20 72=4* contrad.
  • ----19 82=4* SBNs 72={23}, <>2 72=3 etc. contrad.
  • ---8 87=9*
  • ----21 27=1
  • -----22 22=2
  • ------23 26=4 contrad.
  • ------23 26=8*
  • -------24 72=3
  • --------25 82=4 SBN 12={16} => 6 => contrad.
  • --------25 82=6* SBN 12={14) => 1 => contrad.
  • -------24 72=4* SBN 12={16} => 1 => contrad.
  • -----22 22=4* contrad.
  • ----21 27=8* SBN 65={28} => 8 => contrad.
  • ---7 71=5
  • ----26 77=3
  • -----27 75=2 SBN 89={27} => 2 => contrad.
  • -----27 75=7*
  • ------28 93=2
  • -------29 94=3 contrad.
  • -------29 94=8* SBN 38={58} => 8 => SBN 36={13} => 3; SBN 22={12} => 2 => SBN 12={16} => 6 => contrad.
  • ------28 93=6*
  • -------30 33=4 SBN 31={16} => 6 => contrad.
  • ----26 77=9* SBN 72={23} => 3
  • -----31 82=2 contrad.
  • -----31 82=4*
  • ------32 81=2
  • -------33 65=2 SBN 45={38} => contrad.
  • -------33 65=8 SBN 45={23} => 2 => contrad.
  • ------32 81=7*
  • -------34 65=2 SBN 38={58} => 8 => contrad.
  • -------34 65=8*
  • --------35 75=2 contrad.
  • --------35 75=7* contrad.
  • ---7 71=7*contrad. (check this!) incorrect savepoint 7, should have been
  • 7 71=5* [resolved]
  • -36 77=3
  • --37 72=2
  • ---38 89=2 contrad.
  • ---38 89=7* SBN 62={68} => 8 => [full solution]

uniqueness proof:

  • --37 72=4*
  • ---39 76=2
  • ----40 89=2 contrad.
  • ----40 89=7* contrad.
  • ---39 76=9*