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Johan · Joined: 25 Jun 2007 Posts: 206 Location: Bornem Belgium

This VH has a one step move that succumbs the puzzle completely.

Marty R. · Posted: Mon Aug 20, 2007 5:08 am Post subject: Re: Aug 20 VH

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

I found an xy wing 48, 38, 34(pivot) that got rid of 8s in R9, Box 8 and opened the way. (Also some subsequent x wings on 4s - but I'm not sure whether x wings fall in the VH category).

Actually I've spent a few months trying to learn about URs, ERs and W-wings but can never spot them - certainly can't see any here. I am even wondering if they are of academic interest only - particularly since I have yet to find a VH that I couldn't solve without xy or xyz wings.

Is that controversial??

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

I also used the same XY-wing as cgordon but there seemed to be almost as many basic moves after it as before it, before everything turned to singles.

nataraj · Posted: Mon Aug 20, 2007 3:40 pm Post subject:

Same xy-wing as cgordon,
then xy-wing 89-39-38 (pivot r9c8) making r8c6=4.
x-wing on 4s r3,7 clears c2,3
only singles from there

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

It appears most reached the 'same' point, but with much different looking grids.

nataraj · Posted: Mon Aug 20, 2007 5:59 pm Post subject:

Tracy you are right - the "key move" is the same, the other moves probably depend on the preferred order of methods one applies.

When trying to recreate the "same" point, I arrived at this position:

Johan · Joined: 25 Jun 2007 Posts: 206 Location: Bornem Belgium

The xy-wing with pivot in R8C3 is the key-move, after that it's just basic eliminations.

Johan,

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Marty R. · Posted: Mon Aug 20, 2007 9:57 pm Post subject:

bette · Posted: Tue Aug 21, 2007 12:28 am Post subject:

Usually I can solve these VH or at least understand how you more experienced folks solved them but I've been staring at this one for quite some time and I just can't see how the 1 and 3 were eliminated from R5C3. Can someone help, please?

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

Marty R. · Posted: Tue Aug 21, 2007 3:53 am Post subject:

Craig, see my above post responding to Tracy. If you're unfamiliar with UR theory, you can read Keith's primer at:

http://www.sudoku.com/forums/viewtopic.php?p=29105#29105

Bette, I don't know about the 3, but as for the 1, look at box 6. The only possibilities for a 1 in that box are in row 5, so a 1 can't exist anywhere else in row 5.

nataraj · Posted: Tue Aug 21, 2007 7:04 am Post subject:

Bette, in my previous post I mentioned an AIC that gets rid of the '1' in r5c3. It works as follows:

notice the chain of cells containing '1': 62=12-18=58.
The notation A=B means: if A is 1 then B isn't, if A isn't 1, then B is (strong link).
Strong links are relatively easy to spot. They have exactly two cells with '1' in a row, column or box.

A-B means: if A is 1 then B is not. (weak link)

a chain like this 62=12-18=58 means:
if r6c2 is not 1 then r1c2 is (strong). Then r1c8 is not (weak). Then r5c8 is 1.

As a whole, any such chain with strong links at both ends and alternating weak and strong links in between (called an alternating inference chain, or AIC for short) means that one of the ends must contain '1'

So any cell that "sees" both ends cannot contain '1'.

A similar argument holds for '3'. This time the chain is 58=98-89=83

bette · Posted: Tue Aug 21, 2007 12:29 pm Post subject:

Marty, thanks for the response. I guess I was assuming the "1" was eliminated from R5C3 first. Perhaps the "1" was eliminated from R6C7 first, in which case your explanation is logical. Now I've got a whole new problem.

Obviously there are some new techniques being applied here other than the ususal X wings, XY wings and XYZ wings which up to now have solved these puzzles for me.

I'm going to have to study a bit more on nataraj's theory as its still fuzzy in my brain yet.

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

bette,

Another way to look at what nataraj mentioned above.

This is the grid a few steps before the one shown in nataraj's post. Only cells that could contain <1> are shown.

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

bette · Posted: Tue Aug 21, 2007 5:50 pm Post subject:

Thanks, Tracy....your explanation helped me see the logic. I don't know if I could spot another one on my own but this certainly brought a whole new meaning to the "VH" puzzles. I'll be looking for them in the future.

nataraj · Posted: Tue Aug 21, 2007 6:02 pm Post subject:

Men at work .... (just for fun)

if you are so inclined (and don't mind looking at muscles, sweat and blood) this is a photo of the (de-)construction site Wink

now that I lookat it, I realize I missed many strong links ( in 8, 2 in 4, in 9 ) - oh my, how do I ever solve any of these?

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

Marty: You are right - there was an Type 2 UR on 236. I printed out that UR website before but there were no diagrams for Type 2s. I gotta have pictures!!

I didn't need the UR to solve - but this does challenge my earlier statement that they are never around.