The New Sudoku Players' Forum

[Wolfgang]

(Thought i posted this yesterday - if it was removed, please tell me why)
As a compensation for the bad sample last time i want to show, how a pretty hard sudoko can be solved. Its nr 149 from the outlaws in the sudoko gallery.
Of course i know that there are many ways to solve it (rubylip's says, a 3 in r2c5 would lead to a contradiction), but i think, the steps might be interesting for others.

Code: Select all

. . 1 | . 5 . | . . 2
6 . . | 4 . . | . . .
. 9 . | . . . | 3 . .
----------------------
. . 8 | . . 7 | . . 1
. . 5 | 6 . . | 4 . .
2 . . | . . . | 9 . .
----------------------
. . 7 | . . . | . 8 .
. . . | . . 3 | . . 5
4 . . | . 2 . | 6 . .


The first time i got stuck here:

Code: Select all

378   3478   1      3789   5       689     78   4679  2         
6     23578  23     4      13789   1289    1578 1579  79         
578   9      24     1278   1678    1268    3    14567 467       

39    346    8      2359   349     7       25   2356  1         
1379  137    5      6      1389    1289    4    237   378       
2     13467  346    1358   1348    1458    9    3567  3678       

135   12356  7      159    1469    14569   12   8     349       
18    1268   269    1789   146789  3       127  12479 5         
4     1358   39     15789  2       1589    6    1379  379     


(The swordfish in 4 doesnt really help)

Elminate 3 from r9c3:
r9c3=3,r7c9=3
. r8c3=9,r6c3=6,r3c3=4,r1c8=4,r7c9=4
=> r9c3=9

Eliminate 2 from r4c7:
r4c7=2,r7c7=1,r8c7=7,r9c8={39},r9c9={39}
not possible, because r9c3={39}
=> (2 numbers for 3 cells) r4c7=5

Eliminate 2 from r8c3:
r2c3=3->r1c1<>3
r3c3=4,(r1c2<>3),r1c2={78},(r1c7={78}),r1c1<>{78}
=> (no number left for r1c1) r8c3=6

Eliminate 2 from r4c8:
r4c8=2,r5c6=2,r4c4=2,r3c3=4
. r4c2=6,r4c5=4,r6c3=4,r3c3<>4
Eliminate 3 from r4c1:
r4c1=3,r6c3=4
. r4c8=6,r4c2=4.r6c3<>4
=>r4c1=9, r4c5<>9

Elminate 3 from r6c3:
r6c3=3,r4c2=4,(r4c5<>9),r4c5=3,r1c4=3
r2c3=2, r3c3=4 (r1c2<>4), triple {378} in row 1 (c127)->r1c4=9
=>r6c3=4

With this i got here:

Code: Select all

7   4   1     3   5    69     8  69  2         
6   58  3     4   89   2      1  59  7         
58  9   2     18  7    168    3  56  4         

9   6   8     2   4    7      5  3   1         
13  7   5     6   139  19     4  2   8         
2   13  4     158 138  158    9  7   6         

135 13  7     15  6    4      2  8   9         
18  2   6     9   18   3      7  4   5         
4   58  9     7   2    58     6  1   3         


Matter of taste, eg
weak chain in 8: r2c2-r9c2~r9c6-r8c5~r2c5-r2c2 -> r2c2=8
or double forcing chain:
r8c1=8,r3c1=5,r2c2=8
r8c5=8,r2c5=9,r2c2=8

[Jeff]

Wolf

Is this grid really hard? I solved this one using Angus' program with nothing more than conjugate colours or a turbot fish. Have I missed out something? If what I have done was correct, then you have applied some very advanced techniques to a not too difficult puzzle.

By the way, you reasonings are very logical, though the first line should read 'Elminate 3 from r9c3'.

[Wolfgang]

I solved this one using Angus' program with nothing more than conjugate colours or a turbot fish.

Maybe i have overlooked something (not the first time ). Please could you reproduce it?

By the way, you reasonings are very logical, though the first line should read 'Elminate 3 from r9c3'.

Yes, thanks.

[Wolfgang]

BTW, a simple (noname?) pattern solves outlaw 8 (the rest is turbot fish and pairs)

Code: Select all

Boxes 8 and 9:
23479 234 2479    178 5   12         
237   8   27      17  9   6         
56    1   56      478 247 3 


A=x->...->B=y, C={xy}, A~C~B
=> eliminate x from A (r7c456)

[tso]

A=x->...->B=y, C={xy}, A~C~B
=> eliminate x from A (r7c456)

I'm cannot figure out what any of this means. Could you define

your shorthand? Are you using '->' to mean something different

from '=>'? In what sense are you using '~'? What are A, B and C?

Also, from the first post in the thread:

Elminate 3 from r9c3:
r9c3=3,r7c9=3
. r8c3=9,r6c3=6,r3c3=4,r1c8=4,r7c9=4
=> r9c3=9

-- What is the period at the beginning of the line?
-- What reasoning was there for choosing to suggest that r9c3=3?
-- Are these eliminations listed in a some sort of order?
-- I can't keep up -- it seems like your short hand is a little to short and variable.

[Wolfgang]

Are you using '->' to mean something different
from '=>'?

no, both means "follows"

In what sense are you using '~'? What are A, B and C?

A, B, and C are cells, A~B means, A and B share a unit (are weakly linked)

9c3=3,r7c9=3
. r8c3=9,r6c3=6,r3c3=4,r1c8=4,r7c9=4
=> r9c3=9
-- What is the period at the beginning of the line?
-- What reasoning was there for choosing to suggest that r9c3=3?
-- Are these eliminations listed in a some sort of order?

The period: i wanted to put some blanks there to indicate thet the second line also starts with 9c3=3, but they were gone in the post, so i tried a period and some blanks
Why r9c3=3: because i wanted to eliminate the 3.
The order: You can do it in this order to solve the puzzle.

[stuartn]

Grief - I thought this was getting sorted - but it's getting more confusing as people insist on using their own logic signs.

Can we PLEASE agree a common method?... it does nobody (not least the regulars) any favours to bring in more and more confusing nomenclature.

Rant over. Who will take responsibility for overseeing this?

stuartn

[Wolfgang]

Grief - I thought this was getting sorted - but it's getting more confusing as people insist on using their own logic signs.

im sorry for that. It was not the first time i used it, for me it is just the shortest way to describe it, eg a xy chain would look similar:
A={x,y}, A=x->...->B=y, A~C~B
=> eliminate y from C.