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storm_norm · Joined: 18 Oct 2007 Posts: 1741

this is from book 100 puzzle number 1 on his toughest list.

x x 2 6 x x 9 x x

x 6 8 9 1 x x x 2

x 5 x x x x x x x

5 1 x 8 x x x x x

x x 9 x 2 x 1 x x

x x x x x 1 x 4 3

x x x x x x x 1 x

1 x x x 6 7 3 9 x

x x 6 x x 9 5 x x

enjoy,

Norm

nataraj · Posted: Thu Oct 18, 2007 9:05 pm Post subject:

after an XYZ wing (2,3,4) removes 4 from r7c56, this is where it ends - for now:

nataraj · Posted: Fri Oct 19, 2007 6:25 am Post subject:

update on progress:

started coloring a bit.
managed to eliminate 3 from r4c5 using a group instead of a single cell to create a strong link between r4c3 and r9c5:
if r4c3 not 3 then r7c3=3, then none of r7c456 can be 3 then r9c5=3.

A similar argument removes 8 from r3c6, and also 3 can be removed from that cell. (I cannot re-create the chains without some effort, I used the
GEM (graded equivalence marks, http://www.sudopedia.org/wiki/Graded_Equivalence_Marks) method because it is rather easy to do on paper)

But then - nothing more (might be some ALS/APE but I cannot find those so I don't try - yet)

That's it. I give up.

storm_norm · Joined: 18 Oct 2007 Posts: 1741

sorry for the post out of nowhere, I am new to the forum but not new to the site. I love the insight in this particular forum because it seems everyone is moving along with the difficulty of the puzzles. hence my learning curve has skyrocketed over the last couple months. since the puzzles have included xy wings, x wings, simple coloring as of late, my feelings about sudoku have deepened and I am in the same camp of those who can't get enough.

anyways, enough blabber, the reason for posting this puzzle is because I was told that these puzzles are great for looking for chains and I need help on chains in the worst way.

Norm

nataraj · Posted: Fri Oct 19, 2007 1:32 pm Post subject:

no reason to be sorry. On the contrary, I was looking for a challenge anyway, and judging from some of the posts here I am not the only one. I do hope someone comes up with a solution path (death blossom, anyone?). As for chains I rather doubt they will get us over the barrier here. Except of course the (bad, bad! Evil or Very Mad

) forcing chains (e.g. cell r8c4: setting it to "2" leads to a contradiction, "4" solves the puzzle easily)

storm_norm · Joined: 18 Oct 2007 Posts: 1741

ok, took it to work, had about 5 people stare at it for a while. we all agree that there is some kind of overlapping als in r6c1,2... r5,c1,2
and over at r4,c5 and r5c4, and possibly in r4,c6 and r5,c6...

so we see the commons as the 6's in the first two columns, the 3's in the 5th row and but the 4's in column 6 don't match up.

Asellus · Posted: Sat Oct 20, 2007 12:14 am Post subject:

I solved it using a branched AIC that led to a contradiction. But, since many would object that is too close to forcing, I looked for another way of describing the underlying constraint. I suspect that there is some Sue de Coq way of describing this, but I couldn't come up with it. (Perhaps someone more proficient in Sue de Coq methods can find such an explanation.) Some of those ALSs are the key, in any case. I have used a coloring approach.

But first...
nataraj: Your <3> elimination in R4C5 can also be described as an ER elimination; the ER is in Box 8.

I start coloring with the {34} pair in C3: