EMERGING STRATEGIES

Often one finds a more or less complete conjugate chain of 5-candidates. (Replace 5 by x if you want to be more general.) Two 5-candidates per unit. Half of them are true, and half false.

Using the method of contradiction (as opposed to what is called guesswork) we may not DIRECTLY test the true candidates: only the false. The reason is obvious: testing the true 5s cannot lead to a contradiction.

Here is the rub: experience bears out that in more than 90% of cases, testing the true 5s directly (which can't lead to a contradiction, and so may not be done) DOES usually lead to many more results (eliminations and placings) than testing the false 5s.

The obvious and most direct approach would be to take a false 5 and show it leads to a contradiction. This would then immediately place all the true 5s. Unfortunately, testing a false 5 usually leads to almost nothing, and very little success.

THERE IS A WAY AROUND THIS DIFFICULTY. A way to exploit the fact that placing TRUE 5s leads to many results:

Test some false candidate that forces all the true 5s to be placed! Such a candidate is any false candidate in the same cell as a false 5! Call it Candy. Assuming Candy, all the true 5s are immediately placed, with many results, leading easily (in comparison to other tactics) to a contradiction. Thus all candidates Candy are sitting ducks, eady and ripe for speedy elimination.

So, once you have fashioned that nice conjugate chain of 5s (or x's), or even before, start eliminating Candies, and don't stop until you have done them all.

This is exactly the technique I used almost exclusively on dml #4, and mostly on dml #3 before that.

- Code: Select all
`dml #4 : SR 10.6, gsfr 99961`

*-----------*

|8..|..3|...|

|.7.|.6.|.9.|

|..4|5..|...|

|---+---+---|

|..2|...|..4|

|.3.|..1|.7.|

|5..|...|8..|

|---+---+---|

|...|..9|..1|

|.6.|.7.|.3.|

|...|2..|5..|

*-----------*

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) ... (Right now my strategy is already clearcut: I will create one conjugate chain of all the 5s, and create bivalues in all the "wrong" 5-cells in that chain: starting with g2.)

(2) ?4g2... (?2h0...??)-2h9, (?2h7...??)-2h7... (?7g7...??)-7g7... (?2a8...??)-2a8...?? -4g2.

(3) ?2g2... (?4f4...??)-4f4, (?4f5...??)-4f5, (?4f6... ((?6k8...))-6k8...??)-4f6... (?6k8...??)-6k8...?? -2g2...

(4) ?5a9... (?8d4...??)-8d4, (?8d6...??)-8d6, (?8d5...??)-8d5...?? -5a9.

(5) ?1a8...?? -1a8.

(6) ?2a8...?? -2a8.

(7) ?6a8...?? -6a8.

(8) ?5a3...?? -5a3.

(9) ?3b3...?? -3b3...

(10) ?6e9...?? -6e9. (a short step).

(11) ?9e9...?? -9e9. (a short step).

(12) ?3d5...?? -3d5. (singles only in this step).

(13) ?9d5...?? -9d5. (singles only in this step).

At this point I have reached my first aims stated above. The next thing is two steps to force one of those not-5 bivalues (here 45a8) to become true, by eliminating the other two 4s in the column). There shouldn't be much left to do after that.

(14) ?4k8... (?7c7...??)-7c7... (?7d4...??)-7d4, (?7d6...??)-7d6...?? -4k8.

(15) ?4g8 (I'm hoping this might be the last step! as everything is set up for a kill) ...(?7c7... ((?7d1...??))-7d1...??)-7c7, (?7d4...??)-7d4, (?7d6... ((?3b1...??))-3b1...??)-7d6... (?7g3...??)-7g3... (?7f4...??)-7f4...?? -4g8...59 singles to End.

Notice that all my net steps, 2 to 14, did not solve a single cell. All cells were solved consecutively as singles at the very end.

PS My solution to dml#2 is now also complete, and posted on a new thread. It is very much a follow on from this, as the two puzzles are very similar.

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