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

An easy UR (256). Found it harder to locate the hidden <12> in Box 5.

nataraj · Posted: Sat Jul 19, 2008 3:45 pm Post subject:

I tried to avoid the UR (25 type 1), and found:

- multi-coloring (3)
- kite (6)
- even a w-wing (38, r3c2, r5c1)

but in the end had to use the UR to finish the puzzle.
It would be interesting to see which non-UR solutions I missed...

Here's my "final" grid before the UR:

keith · Posted: Sat Jul 19, 2008 4:50 pm Post subject:

nataraj,

In your grid, Sudoku Susser has two short chains.

The first, in B78, takes out <5> in R9C5.

The second, in R78, takes out <5> in R8C2.

I can't explain these as anything other than guessing. They do not solve the puzzle without still using the UR.

Keith

storm_norm · Joined: 18 Oct 2007 Posts: 1741

is this puzzle an example how a UR doesn't impede the solution?? I remember a discussion earlier in the forum about how a UR might disrupt flow occasionally.

keith · Posted: Sat Jul 19, 2008 8:51 pm Post subject:

Norm,

I think this is a rather rare example of how a UR is "essential" to the solution. In other words, if you use the UR, you are done. If not, the puzzle is REALLY DIFFICULT.

A couple of years ago, someone posted an example of how an additional value in the initial grid made a puzzle much more difficult. The idea was something like this:

Suppose you arrive at a UR:

storm_norm · Joined: 18 Oct 2007 Posts: 1741

Asellus · Posted: Sat Jul 19, 2008 11:36 pm Post subject:

I am about 99% certain that you can still use DP logic to place the <6> in the lower left corner of all three of those examples. If the 4 cells are confined to 2 boxes (as required for the UR in the first place), then the lower left cell cannot be <4> no matter what eliminations have been made amongst the other 3 {24} cells. If the lower left cell is <4>, you have a DP: the <2>s and <4>s can be interchanged. So, it must be <6>.

The problem is merely recognizing that the DP is present once you've made the eliminations. But, the DP isn't destroyed until that <6> is placed.
[Edit to add...]
I mis-read Keith's post as the upper left <2> in the 2nd and 3rd examples having been solved as <2>. However, I now see that he states it as initially given as <2>. In that case, there is no DP and the <6> cannot be placed.

Asellus · Posted: Sun Jul 20, 2008 12:16 am Post subject:

Without trying to find those SudokuSusser chains and without using any coloring, there is an interesting chain that I didn't find too hard to spot (though I've been practicing a lot!). What makes it interesting is that it utilizes an "almost wing" to form the chain.

Note that there is an "almost 58 W-Wing" in r7c4|r8c2. Only the <2> in r8c2 prevents it from being so. However, any chain in which that <2> is false induces the strong link of the W-Wing pincers and allows the resulting eliminations to be considered. The grouped strong link (or ER) on <8> in b8 could then be exploited.

Happily, the <2> in r8c6 is strongly linked with the <2> in r5c6. Then, there is a 2-cell XY Chain to the <8> in r2c5, which provides a useful pincer end for the chain. For at least some experienced folks out there, this shouldn't be too hard to see.

So the chain in ordinary language: Either r2c5 is 8 or it is 1. If it is 1, r5c5 is 2, r5c6 is not 2, r8c6 is 2, r8c2 is not 2, the 58 Wing is true, the 8s in r8c456 are false, so r7c4 is 8. In either case, r4c2 cannot be 8.

In Eureka, we might write:
(8=1)r2c5 - (1=2)r5c5 - (2)r5c6=(2)r8c6 - (2)r8c2=[58 W Wing in r78] - (8)r8c456=(8)r7c4; r4c2<>8

The idea of using an entire wing as a "node" in a chain is probably unfamiliar to many folks. By, I've looked for examples ever since Myth Jellies mentioned the technique in a post long ago.

keith · Posted: Sun Jul 20, 2008 12:18 am Post subject:

Asellus,

If the UR will solve it, why go to heroic efforts to find a different Unique argument?

Keith

Asellus · Posted: Sun Jul 20, 2008 12:30 am Post subject:

keith · Posted: Sun Jul 20, 2008 7:18 am Post subject:

Asellus,

I tried Medusa, and got nowhere Crying or Very sad

I agree with you. As I have learned to recognize patterns that identify chains, I have come to regard them more as a systematic technique.

Now, I need to figure out how to identify Medusa candidates!

Keith

keith · Posted: Sun Jul 20, 2008 7:54 am Post subject:

keith · Posted: Sun Jul 20, 2008 8:00 am Post subject:

wapati · Posted: Sun Jul 20, 2008 12:45 pm Post subject:

ravel · Joined: 21 Apr 2006 Posts: 536

keith · Posted: Sun Jul 20, 2008 8:26 pm Post subject:

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

... And lets not forget who first reported the UR eh.

wapati · Posted: Sun Jul 20, 2008 10:52 pm Post subject:

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

In so far as I am not in the mafia - I seriously suggest that the UR classification be re-examined. You don't have top be a sudoku expert to recognise anomalies.