dailysudoku.com

[storm_norm]

ran into another tough one so I posted it for those that want a challenge. ok, that is an understatement, its a big challenge.

[ravel]

[storm_norm]

[Asellus]

Some steps/details omitted from the solutions posted above:

(1) Kite or ER or basic coloring removed <1> from r7c6.

(2) The <1> coloring that removes <1> from r8c6 is multi-coloring (weak link in r7). This might not be apparent to some.

After ravel's <1> elimination in r7c3, there are two steps not shown that get to the next grid:

(1) <8> Skyscraper in c38.

(2) Kite, ER or <6> coloring removes the <6> in r7c5, making the next W-Wing step possible.

[ravel]

Thanks Asellus, for completing the solution path.

[nataraj]

[ravel]

In the (very) old sense forcing chains started from a bivalue cell A(xy) and only used bivalue cells. They had the form
A=x => .. => C=z
A=y => .. => C=z

or (E could have more candidates)
A=x => .. => E<>z
A=y => .. => E<>z

The next step were triple forcing chains (from three value cells) and those starting with conjugate pairs or all 3 occurences of a number in a unit.

Then some people also included conjugate links, others also subsets on the way.
Others call every chain elimination a forcing chain. So its the same chaos here.

Forcing chains can always be expressed as contradiction chains. E.g the first one, for the first line use (A=>B) <=> (not B => not A):
C<>z => A<>x => A=y => C=z, contradiction

But i cant see in the moment, how to write my contradiction chain as forcing chain, though probably there will be some way.

It could be expressed as AIC with the link (1)r79c2=(1)r7c3- ... -(48=1)r2c3, but it turned out, that i am too lazy to learn to write that correctly

[nataraj]

thanks, ravel, for the explanation. "...same chaos" - that about seems so sum it up.

I find myself using the same type of inference logic all the time while scanning the grid for useable attacks once the "regular" techniques don't yield easy results any more (bout the time I start looking for xy-chains).
Nothing really formal, just take a cell, look at linked cells, see where it leads, look at another cell, and so on.

Often when I find something it turns out to be a regular xy-wing. Many times it takes the form of pincers that are connected. Those chains, even if they involve some sort of branching or grouped links seem to be well accepted. Sometimes what I find is just a logical inference, mostly a contradiction. That's when I get that guilty feeling and I am loath to use the solution, and instead keep looking for a more "acceptable" one that does not involve the bad forcing / T&E way. Of course, if nothing turns up, I am happy to use what I found and solve the puzzle. I did, after all, find it.
"Go with what works". Maybe it's just that I find it hard to communicate such a solution.

[Asellus]

When I posted before, I was going to complement ravel on the nice use of ALS (Almost Locked Set) chaining. So, I will now. ALSs can often be exploited in chains such as this and it's really not so difficult to do. Like ravel, when I get to a point in tough puzzles where the usual tools no longer help, I start examining the ALSs to see if they look like they can help. ravel's chain uses 3 ALSs in sequence, plus that pair of strongly-linked <5>s. Seeing that those <5>s can be used is probably the tricky bit for many.

This chain is certainly an AIC (Alternate Implication Chain) and can be notated thusly:

(1-5)r7c3=(5)r9c1-(5={36})r16c1-(6)r23c1=({248})r23c1|r3c3-({48}=1)r2c3-(1)r7c3; r7c3<>1

Out of interest, I solved this puzzle, ignoring those URs, by using only Medusa multicoloring ("MMC"). It makes a good puzzle for practicing that technique. MMC does not reveal ALS-based AICs because of the grouped links. Interestingly, the <1> in r7c3 is also eliminated by MMC, but via a completely different AIC.