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

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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*