## Solution to dml #11

Advanced methods and approaches for solving Sudoku puzzles

### Solution to dml #11

Solution to dml #11

Code: Select all
` *-----------* |1..|.5.|...| |..6|..9|...| |.8.|2..|..4| |---+---+---| |.4.|.3.|..8| |..7|...|.6.| |9..|...|1..| |---+---+---| |.3.|8..|..2| |...|..4|.5.| |...|.1.|7..| *-----------*   SE 10.7`

Note: This solution is designed to be followed using the Simple Sudoku program.
"..." means proceed as far as SS allows, following the hints given by SS in the order given.
This will facilitate rapid checking of this solution.

"?" introduces a move that will be disproved by contradiction. (These moves are only introduced when SS grinds to a halt, saying "no hint available".) In order to "play" this move, you will have to turn off the "block invalid moves" feature of the program. Then insert the move and follow all hints given until you see a contradiction. Once you find the contradiction, you must retrace (withdraw in reverse order) all moves made since the disproved move, by clicking the "undo" arrow repeatedly. Then "correct" the disproved move. EG if this move was "?3f6", then REMOVE the 3 at f6, because you have proved the 3 at f6 false.

SOLUTION:

(1) ...

(2) ?1h3... (4e4...??)-4e4, (?3e7...??)-3e7, (?4f4...??)-4f4... (?4g1...??)-4g1, (?4g3...??)-4g3... (?7b4...??)-7b4... (?6a4...??)-6a4...?? -1h3...

(3) ?1d4... (?4e4...??)-4e4, (?3e7...??)-3e7, (?3c7...??)-3c7, (?3b7...??)-3b7... (?3b9...??)-3b9... (?3a4...??)-3a4... (?3f9...??)-3f9... (?3b1...??)-3b1...?? -1d4...

NOTE: At this stage the 1's consist of 2 conjugate sets: set A (1b4, 1c8, 1d6, 1e2, 1g3 and 1h9 all equivalent to each other) and set B (1b9, 1c6, 1d3, 1e4, 1g8 and 1h2 all equivalent to each other). SS shows that placing set B leads to -5de7, -7bc1, -7f5. Therefore 5d7, 5e7, 7b1, 7c1 and 7f5 each necessarily implies that set A is true. This fact will be used in step (7).

(4) ?6c6... (?4e4...??)-4e4, (?5d1...??)-5d1, (?3c7...??)-3c7... (?9g7...??)-9g7... (?8f3...??)-8f3... (?5e9...??)-5e9, (?9e9...??)-9e9... (?4f5...??)-4f5, (?4f4...??)-4f4...?? -6c6.

(5) ?2h2...?? -2h2.

(6) ?7b1...?? -7b1.

(7) ?7f5... place 1's of set A (see note above) ...?? -7f5.

(8) ?5e7...?? -5e7.

(9) ?5d7... (?9d4...??)-9d4... (?7c5...??)-7c5...?? -5d7...

(10) ?4g8... (?7c5...??)-7c5, (?2d1...??)-2d1, (?3c7...??)-3c7... (?3c3...??)-3c3... (?4f4... ((?9g5...??))-9g5...??)-4f4...?? -4g8.

(11) ?7c6... (?7a8...??)-7a8, (?7b8...??)-7b8... (?8a8...??)-8a8...?? -7c6.

(12) ?3b9...?? -3b9.

(13) ?2d3...?? -2d3.

(14) ?4e4...?? -4e4.

(15) ?5e4...?? -5e4.

(16) ?6h2...?? -6h2.

(17) ?9h2...?? -9h2.

(18) ?9d4... (?4f4...??)-4f4... (?8f6...??)-8f6...?? -9d4...

(19) ?9e5... ?? -9e5 and all singles to End.
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gurth

Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

### isomorph

An isomorph? Good, that means it was just as hard, and see how my sub-sub-nets came down from 12 to 1!
gurth

Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa