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Marty R. · Posted: Wed Jul 22, 2009 4:42 pm Post subject: Hit the brick wall

This is Vanhegan Fiendish, 5-1510879, rated 2.4.2.2. I'm here, stuck, after a couple of ERs, X-Wing, Kite and XYZ-Wing.

nataraj · Posted: Wed Jul 22, 2009 6:48 pm Post subject:

x-wing (1) cols 3 and 6

coloring:
3:-r1c3=r1c2-r7c2=r7c9-r5c9=r4c7- ; r4c3<>3
9:-r3c8=r1c7-r1c4=r8c4-r8c9=r5c9- ; r5c8<>9

hope this helps Smile

nataraj

edit 2115 GMT+2 (CEDT): needed a short xy-chain later.

{5,7} in r6c9 and {2,7} in r7c8 connected via box 9

keith · Posted: Wed Jul 22, 2009 8:25 pm Post subject:

There is an X-wing on <1> that advances it to here:

Marty R. · Posted: Thu Jul 23, 2009 12:31 am Post subject:

Thank you both. How I miss such things is beyond me. Embarassed

daj95376 · Joined: 23 Aug 2008 Posts: 3854

I'm unable to recreate the short XY-Chain.

nataraj · Posted: Thu Jul 23, 2009 6:28 am Post subject:

There is an m-wing

(9) r3c6=r1c4 (via the strong link on 5 in col 4)

At first glance, it eliminates the 9 from r2c6 and r1c5.
But, since both pincers of the m-wing end up in the same house, there is also a weak link between the pincers (9) r3c6-c1c4

This turns the discontinuous AIC of the m-wing into a continuous loop and all links in the loop become strong links. This applies to cell r8c4, too.

Therefore, r8c4 cannot be 1, then r8c7=1 and the xy-chain appears.

Sorry, must hurry ... I'll be able to give a better explanation in the evening.

nataraj · Posted: Thu Jul 23, 2009 10:35 am Post subject:

Seems I forgot one more step:
there is another m-wing (3) r7c9=r8c5 via the strong link on 7 in row 9.
This gets rid of the "3" in r8c9.

nataraj · Posted: Thu Jul 23, 2009 11:27 am Post subject:

After the x-wing (1), coloring (3 and 9), and some basics, I arrive here:

The green m-wing removes 3 from r8c79
The red m-wing removes 9 from r2c6, r1c5

Since both ends of the m-wing are in the same house, there is also a weak link (blue).
The loop is closed.

To show that there is now a strong link where before there was a weak link, look at cell r8c4:

if r8c4 is not 9, then (following the strong link up) r1c4 is 9.
NOW, we can use the convenient (blue) weak link: then r3c6 is not 9.

And, continuing along the loop, then r3c6 is 5, r2c4 is not 5, r8c4 is 5.

Which means that r8c4 is either 9 or 5, but not "1"

Marty R. · Posted: Thu Jul 23, 2009 4:43 pm Post subject:

nataraj · Posted: Thu Jul 23, 2009 5:40 pm Post subject:

Marty, I am truly sorry.

I think I will not be able to explain. Sad

In sudopedia, "coloring" is used as a generic term for a variety of closely related methods: http://www.sudopedia.org/wiki/Coloring

In this case, I have used what would be the "x-chain" variant. Maybe Andrew Stuart's explanation helps, he calls it x-cycles. Be sure to read part 2.

I agree that those sources may not be easy to understand, but I certainly cannot do any better.

nataraj · Posted: Thu Jul 23, 2009 5:54 pm Post subject: