dailysudoku.com

Marty R. · Posted: Fri Aug 17, 2007 3:53 pm Post subject: Please bail me out

This is the puzzle that would have been Mepham July 20.

Mogulmeister · Joined: 03 May 2007 Posts: 1151

An elimination can be made at r1c3 if you pay attention to pincers at r2c3 and r1c7.

klimke · Joined: 17 Aug 2007 Posts: 5

New to the site. Do not see how you conclude the pincers you reference are of opposite polarity. I do see a "play ahead" that determines r2c4 but I don't like that method. Help is welcomed.

keith · Posted: Fri Aug 17, 2007 9:03 pm Post subject:

How about this:

Look at the <49> UR in R34C89. Either R3C9 is <3> and/or R4C9 is <6>. Either way, R5C7 is <3>.

Takes you to here:

Marty R. · Posted: Fri Aug 17, 2007 9:24 pm Post subject:

Thanks MM, but I don't see it. I can't get a W-Wing or XY-Chain out of that, so you might as well tell me directly.

Klimke, welcome to the forum. I don't know what your disliked method is to solve r2c4, but if it's a forcing chain or other trial-and-error, I've already solved it easily with one chain that leads to a contradiction.

Keith, I looked at that rectangle and realized that one had to be 3 or the other one 6, but I didn't go forward with it. I haven't settled on an opinion as to whether that's rectangle theory or a forcing chain. Actually, it's using rectangle theory to steer one towards a forcing chain. How do you view it re: its degree of trial-and-error?

Update, 15 minutes later. MM, I see it now but don't know what to call it, as it doesn't strictly meet the definition of an XY-Chain.

Mogulmeister · Joined: 03 May 2007 Posts: 1151

They are the pincers of an xy chain.

klimke · Joined: 17 Aug 2007 Posts: 5

Thanks for all the info.

Keith, I did get the 3's using the UR. Thanks for explaining.

I'm still stuck on the pincer argument. I see the convergence of the two pincer cells at r1c3 but do not understand how a conclusion that they are opposites is arrived at.

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

There is an 7-cell xy-chain which eliminates <2> in R2C4
Starting with <8> in R7C4.
[28][84][49][98][85][59][92]

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

klimke,

Welcome to the forum.

keith · Posted: Fri Aug 17, 2007 10:37 pm Post subject:

klimke · Joined: 17 Aug 2007 Posts: 5

Thanks for the info on the xy-chains, however, I am still confused.

In the Johan post, I don't see how E-F is a conjugate pair in 5's.

In the TKiel post, I don't see how C-D is a conjugate pair in 9's.

In both cases, it appears there are more than 2 candidates per row or column. Any clarification would be welcome.

Also, going back to the original Mogulmeister reply, it was implied that 2 simple pincers (r2c3 & r1c7) could cause an exclusion at r1c3. While elegant, I can not justify that move logically. Clarification there would be appreciated also.

Klimke

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

klimke,

An XY-chain involves only bi-value cells. They do not have to be conjugates, but the values within the cells are strongly linked (i.e. if X, then not Y; if not X, then Y.

In my post above, I said the conclusion was that if r1c3 were <5> then the chain would lead back to a contradiction in that there would be two <9>'s in row 4. It is not true that the contradiction would have to be in row 4 (it could be elsewhere in the chain) but let's look at how that would happen.

If r1c3 were <5>, then r1c9 would not be <5>, would have to be <9>.
If r1c9 were <9>, then r3c8 would not be <9>, would have to be <4>.
If r3c8 were <4>, then r4c8 would not be <4>, would have to be <9>.

If r1c3 were <5>, then r2c3 would not be <5>, would have to be <9>.
If r2c3 were <9>, then r2c2 would not be <9>, would have to be <2>.
If r2c2 were <2>, then r4c2 would not be <2>, would have to be <9>.

So even though the cells in the chain are not conjugates, the values within the cells are strongly linked, because an XY-chain uses only bi-value cells.

Marty R. · Posted: Sat Aug 18, 2007 12:56 am Post subject:

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Hello Klimke,

Sometimes a picture is worth a thousand words. The pincers are in green and the steps between them shown in pink. The eliminated 5 in yellow.

A quick look at x-y chains in sudopedia should help but as Tracy and others have shown, the 5 in r1c3 can not endure because there will always be a situation where one of the pincers will always contain 5.

[Edited to replace original image which was lost when Tinypic folded]

klimke · Joined: 17 Aug 2007 Posts: 5

The picture was worth it, I see it now.

Thanks for all the assistance from the group. Very helpful.

Mogulmeister · Joined: 03 May 2007 Posts: 1151

The philosophy of sudoku is very interesting and I find myself seeing that a cut and dried position is not so easy for me personally. Why ?

Simply that when I tackle extreme puzzles I will use anything in my armoury because they are so darned hard to begin with.

Under normal circumstances and in attempting puzzles that are sub-diabolical I will eschew forcing chains and unique rectangles. As Keith mentioned it's a personal choice but the first one feels like nishio (trial and error/bifurcation) and UR's feel like a backdoor cheat (to me anyway).

Needless to say when I'm up against it I use both methods! Smile

Marty R. · Posted: Sun Aug 19, 2007 4:00 pm Post subject:

keith · Posted: Sun Aug 19, 2007 4:15 pm Post subject:

After my UR elimination above, there are four 5-link chains that make the following eliminations:

R2C2 is not <9>.
R2C3 is not <5>.
R3C3 is not <7>.
R3C4 is not <5>.

You only need the first one to solve the puzzle. Easy to see, once you know it's there!

keith · Posted: Sun Aug 19, 2007 9:15 pm Post subject:

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Your mother-in-law sounds like a real purist Keith - I can assure you I'm not one of those ! Smile

No, my reason for not going to a UR as an immediate technique is personal philosophical sentiment and not based on some lofty logical standpoint.

Whilst acknowledging (and sometimes using) URs, I feel they are like an external agent - a get out of jail card. I'm not as extreme as Glassman but don't really care if a puzzle has one solution - albeit that these days the best ones do seem to.

It's more to do with a feeling that the UR is like a gamer's trapdoor - that it is not really an intrinsic part of the game - more like penalties after extra time in football* (or rushing the goal-tender 1-on-1 after regulation in an ice-hockey game). The after extra time penalties are really nothing to do with football. The UR to my mind takes advantage of uniqueness, a global given, rather than logical interplay between the candidates.

Incidentally, I'd be interested to see if anyone has been able to create a puzzle that could only be solved if a UR was used.

It's a powerful technique but it sometimes feels as if someone has brought a pump action shotgun grouse shooting.

*The game known as "soccer" in the US.