Solution to Tarek's Gyroscope #1

Advanced methods and approaches for solving Sudoku puzzles

Solution to Tarek's Gyroscope #1

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Solution to tarek's Gyroscope #1
Code: Select all
`  . 6 . 9 . . . . 3  5 . . . . 4 . 2 .  . . . . 8 . 4 . .  8 . . . . . . 5 .  . . 3 . . . 7 . .  . 9 . . . . . . 1  . . 1 . 5 . . . .  . 7 . 3 . . . . 9  9 . . . . 2 . 4 .      SE=N/A, gsfr=99960, Suexr=830`

NOTE: "..." denotes steps using Simple Sudoku program.
Sub-nets are enclosed thus: (?xay...??) and sub-sub-nets thus: ((?xay...??)).

Solution:

(1) 9g6, -5e6(MC)...

(2) ?5k2... (?9c3..., -1c24e2k4 (X-Wing 1bd24)...??)-9c3... (?3g2..., -7g4(colours)..., -1cd2e16(colours)...??)-3g2... (?3c2...??)-3c2..., -7g4(colours)..., -7c3(MC)..., -6de9(XY-Wing 678ae8b9)...?? -5k2..., -4d5(MC).

(3) ?5c6..., -4d3e15g1(Swordfish 4afh135)... (?3g2...??)-3g2, (?3c2...??)-3c2..., -8g8(MC), (?9b3..., -7af35(X-Wing 7af17)..., -1a5e4h57(Swordfish 1aeh168)...??) -9b3..., -1e4(MC), (?8b3...??)-8b3... (?7c4...??)-7c4, (?1c2...??)-1c2...?? -5c6.

(4) ?5k7..., -4d3e15g1(Swordfish 4afh135)... (?9b3..., -7g4(colours)..., -1e6(colours)...??) -9b3..., -1e4(MC), (?1c2...??)-1c2...?? -5k7.

(5) ?5a7..., -3d7(MC)... (?9c3..., -1ek4(X-Wing 1bd24)... ((?8b2...??))-8b2...??) -9c3... (?3g2...??)-3g2, (?3g8...??)-3g8..., -8h7(MC)... (?3g7...??)-3g7...?? -5a7..., -4d3e15g1(Swordfish 4afh135), -2d5(MC).

(6) ?3g2...?? -3g2.

(7) ?3g1...?? -3g1...

(8) ?1b2...?? -1b2..., -1d4(MC)..., -7c3(MC), -7a5(MC).

(9) ?7b3...?? -7b3... End.
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Notes:
Only one sub-sub-net used, in step (5).
I discarded as unsuitable the following tries:
In step 2, ?-3c1 soon got into a sub-sub-sub-net...
In step 3, ?5k7 got messy and was discarded. Later, after the good ?5c6 start, a sub-net (?9c2 was discarded in favour of (?9b3 which worked better.
______________________________

Tarek, congratulations on joining the ranks of the beyond-SE composers! For my money, this is the hardest of the 4 beyond-SE puzzles published to date. The only one where I had to think twice about any nets.
_______________________________[/b]
gurth

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

Other solution :

Code: Select all
`   a b c d e f g h i +------------------1| . 6 . 9 . . . . 32| 5 . . . . 4 . 2 .3| . . . . 8 . 4 . .4| 8 . . . . . . 5 .5| . . 3 . . . 7 . .6| . 9 . . . . . . 17| . . 1 . 5 . . . .8| . 7 . 3 . . . . 99| 9 . . . . 2 . 4 . `

(1) if 5g1 then h7#3, b4#4, a8#6, d3#2, c9#8, b3#2, and contradiction using singles
so -5g1.

(2) after that, if 3g9 then g1#8, a3#3, d7#4, b5#5, and contradiction using singles
so -3g9.

(3) after that, a1#1, b3#2, e4#9 (after the remark of ravel), and finish with singles.
Last edited by leon1789 on Sun Nov 19, 2006 3:37 pm, edited 1 time in total.
leon1789

Posts: 37
Joined: 15 November 2006

Hi Leon,

welcome on this forum.
This is a very nice solution, using only 15 singles chains on bivalue/bilocation numbers in contradiction nets/subnets. (I suppose the last step should say d4#9).
It shows, how mighty subnets are, even when restricted to the most primitive technique and bivalue/bilocation.

I wonder, if the other top hardest puzzles also can be solved this way.
[PS: think, the chances are good, i needed less than an hour with SS to find a first number in Ocean's nr 5/gold: r1c4=3 => r1c1<>4, r2c1<>8, r1c1<>5, r3c5<>5, r5c6<>7, r4c6<>3, r7c4<>2 => singles contradiction. SE was stuck before finding a number, rating with 3 in r3c6 is 9.9]
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:Hi Leon,
welcome on this forum.

thanks

ravel wrote:This is a very nice solution, using only 15 singles chains on bivalue/bilocation numbers in contradiction nets/subnets. (I suppose the last step should say d4#9).

it 's e4#9 ! I have overwritten.

ravel wrote:It shows, how mighty subnets are, even when restricted to the most primitive technique and bivalue/bilocation.

I wonder, if the other top hardest puzzles also can be solved this way.
[PS: think, the chances are good, i needed less than an hour with SS to find a first number in Ocean's nr 5/gold: r1c4=3 => r1c1<>4, r2c1<>8, r1c1<>5, r3c5<>5, r5c6<>7, r4c6<>3, r7c4<>2 => singles contradiction. SE was stuck before finding a number, rating with 3 in r3c6 is 9.9]

sometimes, locked sets have to be added to primitive techniques... but I think all puzzles can be solved this way. Let's go to Ocean's #5/gold http://forum.enjoysudoku.com/viewtopic.php?p=38050#p38050
leon1789

Posts: 37
Joined: 15 November 2006