- Code: Select all
dml #6 - ER 10.7 - gsfr 99955
*-----------*
|9..|..4|...|
|.8.|.2.|.3.|
|..5|7..|...|
|---+---+---|
|..1|...|..4|
|.6.|.8.|.7.|
|3..|...|5..|
|---+---+---|
|...|..5|..1|
|.7.|.3.|.9.|
|...|6..|2..|
*-----------*
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:
(0) ...
(1) ?1f6... (?5h1...??)-5h1...?? -1f6.
(2) ?1f4... (?5h1...??)-5h1...?? -1f4.
(3) ?3e6... (?5h1...??)-5h1...?? -3e6.
(4) ?1a5... (?6b1...??)-6b1, (?6b3...??)-6b3...?? -1a5.
(The idea behind 1a5: to force the 5-chain the OTHER way, the RIGHT way. See comments below.)
(5) ?6c5... (?4g2...??)-4g2...?? -6c5.
(6) ?8h1...?? -8h1.
(7) ?2h1... (?3c2...??)-3c2...?? -2h1.
(8) ?4h1... (?4g4...??)-4g4... (?1c8...??)-1c8...?? -4h1.
(9) ?6h1... (?7a3...??)-7a3...?? -6h1.
(10) ?8k8...?? -8k8.
(11) ?2d2...?? -2d2.
(12) ?2e4...?? -2e4.
(13) ?3e4...?? -3e4.
(14) ?4e4...?? -4e4.
(15) ?9e4...?? -9e4.
(16) ?6b9...?? -6b9.
(17) ?7b9...?? -7b9.
(18) ?9g2... (?9h6...??)-9h6...?? -9g2.
(19) ?9k2...?? -9k2.
(20) ?7g7... (?5k2...??)-5k2... (?8f9...??)-8f9...?? -7g7...
(21) ?7f3...?? -7f3...
(22) ?3a4...?? -3a4...
(23) ?9f9...?? -9f9...
(24) ?9f5...?? -9f5.
(25) ?8c7...?? -8c7.
(26) ?8c8...?? -8c8 and 50 singles to End.
Comments:
The most striking feature, after preliminary moves, was the candidate 5s. All in one chain, so eliminating any 5 would place them all. It soon seemed that this would not be easy, so I had a new idea. And that was to leave the solving of the 5s to the end!
This tactic could be exploited as follows: Each "wrong" 5 in each box was in a cell with several other candidates. so by assuming each of those candidates in turn, I would in any case be placing all the 5s correctly as the net proceeded. So I could test each of those candidates (except the true one) and eliminate them by placing all the 5s and other resultant placements.
So this led me to a setup where all the wrong 5s were united in bivalue cells to the true candidate for that cell, whereas the true 5s still had all their original companion candidates.
It followed that none of this work could help me to test the fives, because by assuming any 5, I would turn all those bivalues into 5s, so that the candidates I had eliminated would serve no purpose! So what was my idea?
Simply to avoid testing the 5s ever, except in subnets, where I could always give them their TRUE set of values. If ever one of the false 5s DID get eliminated outside a net, then I would cash in on the whole series of eliminated candidates, because all the bivalues they had formed would now instantly be singles.
So I expected the puzzle to collapse dramatically and suddenly. When this happened no candidate had been solved completely, but the remaining 50 cells all fell as singles.
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