## forcing chain

Advanced methods and approaches for solving Sudoku puzzles

### forcing chain

Today's daily "diabolical" puzzle at this link:

http://www.palmsudoku.com/pages/s-o-t-d.php?day=0&level=5

shows how to solve the puzzle step by step (which is a fantastic learning tool) however, unless I am mistaken, the 1st forcing change shown in the solution does not appear to be a forcing chain at all. The only way I can see to proceed is to use the Nishio technique. If anyone gets a chance, would you mind taking a look and letting me know what you think. Thanks much.
ablaho

Posts: 2
Joined: 05 October 2005

### Re: forcing chain

ablaho wrote:Today's daily "diabolical" puzzle at this link:

http://www.palmsudoku.com/pages/s-o-t-d.php?day=0&level=5

shows how to solve the puzzle step by step (which is a fantastic learning tool) however, unless I am mistaken, the 1st forcing change shown in the solution does not appear to be a forcing chain at all. The only way I can see to proceed is to use the Nishio technique. If anyone gets a chance, would you mind taking a look and letting me know what you think. Thanks much.

Nice site, but would be nicer if it showed the chain. Also note that it uses (4,1) to mean column 4, row 1, etc. Here's a picture of one possible chain:
r.e.s.

Posts: 337
Joined: 31 August 2005

### forcing chain

r.e.s.,

I think that I follow your chain, but if you look only at row one, choosing a 9 in cell 4 would then require a 1 in cell 2. Something still seems wrong to me but I'm pretty new at this. Thanks for your help.
ablaho

Posts: 2
Joined: 05 October 2005

### Re: forcing chain

ablaho wrote:r.e.s.,

I think that I follow your chain, but if you look only at row one, choosing a 9 in cell 4 would then require a 1 in cell 2. Something still seems wrong to me but I'm pretty new at this. Thanks for your help.

There are two things going on here:

(1) There is a forcing chain proving r1c2=3; that is, the following are valid implications:
(1a) r1c4=1 => r1c2<>1 => r1c2=3, and
(1b) r1c4<>1 => r1c4=9 => r2c4<>9 => ... => r1c2=3 (tracing the chain clockwise). Therefore r1c2=3.

However, the following also are valid implications:
(2) r1c4<>1 => r1c2=1 => r1c2<>3 (tracing the chain counterclockwise); that is, in conjunction with (1b), r1c4<>1 leads to the contradiction that r1c2<>3 and r1c2=3 (from which it can be concluded that r1c4<>1 is false). This does not affect the validity of the forcing chain.
r.e.s.

Posts: 337
Joined: 31 August 2005

### Re: forcing chain

ablaho wrote:Today's daily "diabolical" puzzle at this link:

http://www.palmsudoku.com/pages/s-o-t-d.php?day=0&level=5

shows how to solve the puzzle step by step (which is a fantastic learning tool) however, unless I am mistaken, the 1st forcing change shown in the solution does not appear to be a forcing chain at all. The only way I can see to proceed is to use the Nishio technique. If anyone gets a chance, would you mind taking a look and letting me know what you think. Thanks much.

I solved it. The only forcing chains I used involved just 7s are were long Turbot fishes (multiple color deductions is another way to view such chains).
Scott H

Posts: 73
Joined: 28 July 2005