The New Sudoku Players' Forum

[Xuba]

I got stuck at this point:

|*32|*97|65*|
|69*|3*5|72*|
|57*|*2*|391|

|*49|2**|835|
|386|459|172|
|25*|*38|946|

|92*|***|5*3|
|*63|5*2|4*9|
|*15|9*3|267|

The original grid was checked and the puzzle was considered valid but Very Hard (unfair).
Can anyone help me? I even found a X-Wing but it took me no further.

[udosuk]

Look out for the 1s. On r2 it must be in r2c35, on r6 it must be in r6c34. Therefore at least one of r2c5 and r6c4 must be 1, or else we'd be forced to have two 1s on c3 (r26c3). Therefore r1c4 cannot possibly be 1, and must be 8. The rest will follow easily...

I think they have a special name for this move (finned fish or something) but I never really learned it...

[CathyW]

Colouring conjugate 1s also solves the puzzle.

[Xuba]

Thank you very much! After your help I kept looking for similar procedures and saw that r6c4 can not hold a 1 (consider the chain r6c4-r6c3-r4c1-r1c1-r1c4).
Would this be a Forced Chain or is it what CathyW meant by Colouring conjugate 1s?

[Xuba]

Never mind. I understand, now: it is not a Forcing Chain; it is Colouring.

[Carcul]

Hi Xuba.

it is not a Forcing Chain; it is Colouring

Colouring is in fact a special type of forcing chain.

Colouring conjugate 1s also solves the puzzle.

Here is another solution, similar to that colouring of "1s":

Let's consider that r7c4 is not "1": in that case, we would have a Deadly Turbot Fish in cells r6c4/r1c4/r1c1/r4c1/r6c3, where according to the TIL Argument we could write simultaneously 1) [r6c4]-1-[r6c3]=1=[r4c1]-1-[r1c1]=1=[r1c4]-1-[r6c4], => r6c4<>1, and 2) [r6c4]=1=[r6c3]-1-[r4c1]=1=[r1c1]-1-[r1c4]=1=[r6c4], => r6c4=1. This is a contradiction situation, and so we must have r7c4=1 which solve the puzzle.

Carcul