## Solution to Ocean's #5/gold

Advanced methods and approaches for solving Sudoku puzzles

### Solution to Ocean's #5/gold

Solution to Ocean's #5/gold, using SS.
Code: Select all
` *-----------* |..1|..2|...| |.3.|.4.|.5.| |6..|7..|8..| |---+---+---| |..6|...|..7| |.1.|...|.3.| |9..|...|6..| |---+---+---| |..7|..1|..8| |.4.|.3.|.2.| |...|5..|9..| *-----------*    gsfr=99960 ER=N/A`

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) ?7a7... (?3d4...??)-3d4... (?3d6...??)-3d6... (?3f6...??)-3f6... (?1h7...??)-1h7... (?4k9...??)-4k9...?? -7a7 (remove 7 at a7).

(3) ?-79a8... (?3f6...??)-3f6,(?3f4...??)-3f4... (?1k9...??)-1k9... (?5h7...??)-5h7... (?4g7...??)-4g7... (?4a1...??)-4a1... (?8k3...??)-8k3, 2k3...?? (7a8 OR 9a8), -46a8...

(4) ?7b7...?? -7b7...

(5) ?3k9... (?4g7...??)-4g7... (?1c8...??)-1c8...?? -3k9...

(6) ?3d6...?? -3d6.

(7) ?3f6...?? -3f6...

(8) ?3f3...?? -3f3...

(9) ?1c8...?? -1c8... End.

- No sub-sub-nets this time, maybe because of the rather foxy double elimination in step (3) (GMET).
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Last edited by gurth on Fri Nov 17, 2006 5:17 am, edited 1 time in total.
gurth

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

### Re: Solution to Ocean's #5/gold

gurth wrote:Solution to Ocean's #5/gold, using SS.
Solution:

(1)...

(2) ?7a7... (?3d4...??)-3d4... (?3d6...??)-3d6... (?3f6...??)-3f6... (?1h7...??)-1h7... (?4k9...??)-4k9...?? -7a7 (remove 7 at a7).

how did you know to guess 7a7 first?
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

gsf, thanks for taking an interest! My answer might well be of greater interest to less eminent minds than yours.

Why I chose 7a7 as my first "move":

Speaking within the context of the "net" starting move (a move which is chosen to be in drastic conflict with the known reality) we get the following FALSE results:

The move 7a7 immediately places 7s in all the boxes. It's not hard to see that that will be so: it's like looking a few moves ahead in chess.

7a7 creates a single 7 in box 1, whereas 7b7 would not do so; it also creates the RIGHT single 7 in box 9, one that will in turn create a single 7 in box 8, and one visualises quite easily that the 7s will be placed in all the boxes.

Starting with 7k5 would have worked just as well, and maybe I should have tried that as an alternative start, and then chosen the shorter one! But as I always say, I am not looking for the best solution, but the quickest. What works well enough, I stick with.

In general, one looks for moves that have as many consequences (eliminations and placings) as possible, because then we are more likely to get a contradiction before getting stuck.

So 7a7 I judged to be an adequate starting point, without even considering say the 3s which might have proved a viable alternative. The other candidates do not look so promising at the start.
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gurth

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

Very interesting, it reminds me on what Maria said here:
a) The longer a forcing net will run, the more probable it is to run into a contradiction. So don't look for short chains!

When the move places all 7's, you have good chances for a long run.
ravel

Posts: 998
Joined: 21 February 2006

Other solution :

C#z means "zC leads to contradiction using singles".

Code: Select all
`   abc def ghi  *-----------*1 |..1|..2|...|2 |.3.|.4.|.5.|3 |6..|7..|8..|  |---+---+---|4 |..6|...|..7|5 |.1.|...|.3.|6 |9..|...|6..|  |---+---+---|7 |..7|..1|..8|8 |.4.|.3.|.2.|9 |...|5..|9..|  *-----------* `

1) if 3i3 then a1#4, c3#8, a1#7, f8#7, g2#1, and contradiction using singles
so -3i3.

2) after that, if 7f8 then i9#4, d8#8, h7#6, d2#6, h4#9, b1#9, and contradiction using singles
so -7f8

3) after that, if 3g1 then g2#1, a1#4, b1#9, and contradiction using singles
so -3g1

4) after that, a9#3, i3#2, and finish using singles.
leon1789

Posts: 37
Joined: 15 November 2006

### Solution to Ocean's #5/gold

Thank you for your solutions to this puzzle - both gurth and leon1789! Hope it was a bit challenging. Interesting to see what kind of resistance the puzzle gives to various solving strategies.
Ocean

Posts: 442
Joined: 29 August 2005