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Another good BB

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Tue Sep 30, 2008 12:29 am Post subject: Another good BB

This time, the UR is kind of essential. If not, you need to be more creative!

Code:

Puzzle: BB115543sh
+-------+-------+-------+
| . . . | . 7 . | . . . |
| . . 3 | 4 . 1 | 2 . . |
| . 8 . | 9 . 5 | . 6 . |
+-------+-------+-------+
| . 5 7 | . . . | 1 2 . |
| 9 . . | . . . | . . 3 |
| . 3 1 | . . . | 4 8 . |
+-------+-------+-------+
| . 9 . | 3 . 2 | . 1 . |
| . . 4 | 6 . 9 | 8 . . |
| . . . | . 5 . | . . . |
+-------+-------+-------+

Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Tue Sep 30, 2008 4:34 am Post subject:

Quote:

This time, the UR is kind of essential. If not, you need to be more creative!

Not sure which UR you refer to, perhaps the Type 4 on 69? Here's what I did.

Quote:

I used the hidden UR on 14 and an ER on 6. These two moves removed both the 4 and 6 from r1c1, exposing an XY-Wing on 451 which finished the puzzle.

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Tue Sep 30, 2008 6:02 am Post subject: Re: Another good BB

keith wrote:

This time, the UR is kind of essential. If not, you need to be more creative!

Code:

+--------------------------+--------------------------+--------------------------+
| 1456 146 9 | 2 7 68 | 3 45 1458 |
| 567 67 3 | 4 68 1 | 2 9 58 |
| 14 8 2 | 9 3 5 | 7 6 14 |
+--------------------------+--------------------------+--------------------------+
| 46 5 7 | 8 469 3 | 1 2 69 |
| 9 246 8 | 1 246 46 | 5 7 3 |
| 26 3 1 | 5 269 7 | 4 8 69 |
+--------------------------+--------------------------+--------------------------+
| 78 9 5 | 3 48 2 | 6 1 47 |
| 237 27 4 | 6 1 9 | 8 35 257 |
| 1238 12 6 | 7 5 48 | 9 34 24 |
+--------------------------+--------------------------+--------------------------+

Our friend ( Wink

), the swordfish, is rather helpful.
It can be discovered in columns 2,6,8 (BTW, its mate hides in rows 3,4,7) and takes out 4 from r1c1,r1c9,r5c5 and r9c9.

After cleanup,

Code:

+--------------------------+--------------------------+--------------------------+
| 15-6 46* 9 | 2 7 68* | 3 45 158 |
| 567 67 3 | 4 68 1 | 2 9 58 |
| 14 8 2 | 9 3 5 | 7 6 14 |
+--------------------------+--------------------------+--------------------------+
| 46 5 7 | 8 469 3 | 1 2 69 |
| 9 246# 8 | 1 26 46# | 5 7 3 |
| 26 3 1 | 5 269 7 | 4 8 69 |
+--------------------------+--------------------------+--------------------------+
| 78 9 5 | 3 48 2 | 6 1 47 |
| 237 27 4 | 6 1 9 | 8 35 57 |
| 38 1 6 | 7 5 48 | 9 34 2 |
+--------------------------+--------------------------+--------------------------+

an m-wing (6)r1c2=r1c6 (via row 5) eliminates 6 from r1c1 and opens the overlapping xy-wings 15-45-14, 14-15-45 in boxes 1 and 3.

(edit 1300 GMT+2: now I've looked at Marty's invisible hint - I find it fascinating that my m-wing and his ER use almost exactly the same cells. The ER also makes use of the strong link in col 6, and that same cell r5c5 to form the hinge together with r46c1)

____

Two URs serve the same purpose:
the type 4 (6,9) in r46c59 gets rid of the 6 (r46c5<>6 => r5c2<>6 => r12c1<>6), and
the type 3 (1,4) in r13c19 with strong link on 1 in col 9 removes 4 in r1c1

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Tue Sep 30, 2008 12:17 pm Post subject:

I needed all three the swordfish, ur and xy-wing. good puzzle

cgordon

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

Posted: Tue Sep 30, 2008 1:40 pm Post subject:

It just needs the ER on 6 (C6B4) which removed the 6 from R1C1 leaving an xyz-wing (145) that finished it off. By far the simplest and most elegant solution.

Earl

Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

Posted: Tue Sep 30, 2008 2:43 pm Post subject: Good BB

A four-step xy-chain eliminates the 4 in R9C8, and makes it a one-trick pony. Earl

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Tue Sep 30, 2008 4:05 pm Post subject:

Quote:

an m-wing (6)r1c2=r1c6 (via row 5) eliminates 6 from r1c1

Is this one of those M-Wing types that I don't understand? I don't see one that I can recognize. But in that grid I do see how a Finned X-Wing takes out the 6 from r1c1.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Tue Sep 30, 2008 4:46 pm Post subject:

Marty R. wrote:

Quote:

an m-wing (6)r1c2=r1c6 (via row 5) eliminates 6 from r1c1

Is this one of those M-Wing types that I don't understand? I don't see one that I can recognize. But in that grid I do see how a Finned X-Wing takes out the 6 from r1c1.

Code:

+--------------------------+--------------------------+--------------------------+
| 15-6 46* 9 | 2 7 68# | 3 45 158 |
| 567 67 3 | 4 68 1 | 2 9 58 |
| 14 8 2 | 9 3 5 | 7 6 14 |
+--------------------------+--------------------------+--------------------------+
| 46 5 7 | 8 469 3 | 1 2 69 |
| 9 246* 8 | 1 26 46*# | 5 7 3 |
| 26 3 1 | 5 269 7 | 4 8 69 |
+--------------------------+--------------------------+--------------------------+
| 78 9 5 | 3 48 2 | 6 1 47 |
| 237 27 4 | 6 1 9 | 8 35 57 |
| 38 1 6 | 7 5 48 | 9 34 2 |
+--------------------------+--------------------------+--------------------------+

1) bivalue cells [r1c2]=[r5c6]=46
2) strong links on 4 in [c2],[r5] (*)
3) strong link on 6 in [c6] (#)

As a chain: 6-[r1c2]-4-[r5c2]=4=[r5c6]=6=[r1c6] => [r1c2]<>6

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Tue Sep 30, 2008 4:55 pm Post subject:

Quote:

1) bivalue cells [r1c2]=[r5c6]=46
2) strong links on 4 in [c2],[r5] (*)
3) strong link on 6 in [c6] (#)

Thanks. It's an ordinary M-Wing, I just didn't notice the 4s connection, but I did see a 6s connection.

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Tue Sep 30, 2008 5:22 pm Post subject:

Marty R. wrote:

Is this one of those M-Wing types that I don't understand? I don't see one that I can recognize.

That is quite possible, Marty. The "classic" m-wing has 3 identical bi-value cells that form a small chain, like this:

46-46-46

This pattern ensures that the first and last cell always have the same solution, either both are 4 or both are 6.

When there is a strong link starting in one of the two end-cells, we have an m-wing you'd probably recognize easily, like this pattern, for example:

46-46-46...68

It works like this: if the first cell is NOT 6 (but 4) then the third cell is also not 6 (but 4) and (by virtue of the strong link on 6) the last cell must be 6.

Thus, the first and last cells form a pair of pincers which removes 6 from all cells that see them both.

It is possible to ease the restrictions on some of the cells involved and still preserve the same elimination principle (it makes the pattern a little harder to recognize but the "essence" of the m-wing is still there), like I did here. The pattern is only slightly changed:

46-246-46...68

Again, if the first cell (r1c2) is not 6, then (because there is a strong link on 4 between r5c2 and r5c6) the third cell (r5c6) is also not 6 and, again, r1c6 is 6. The same two pincers, the same elimination.

So, the m-wing still works if the second cell is not identical to the first one, but there HAS TO be a strong link in one of the two candidates (of the starting cell) between second and third cell (NB if both cells are identical, they form a naked pair and there is a strong link in BOTH candidates, naturally. That is nice, of course, it gives two chances instead of one).

Now, to give you the full Monty, it is also possible to make the same elimination even if the third and the last cells have additional candidates (again, this makes finding the pattern even harder).

So,

46-246-4679...12368

would still work, provided:
- the first cell is bi-value (X,Y)
- the second and third cells form a strong link on one of the candidates (X or Y)
- the third and the final cell form a strong link on the other candidate.

Let's say that the first cell is X
It "sees" the second cell, thus second cell cannot be X
There is a strong link on X between the second and third cell, thus third cell is X (and not Y)
There is a strong link on Y between third and last cell, thus last cell is Y

This means, that at least one of the two pincers must be Y and every cell that sees both ends cannot be Y.

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Tue Sep 30, 2008 5:22 pm Post subject:

oops, cross post. I see that my habit of giving the m-wing as a strong link has caused the confusion. The pincers form a strong link on 6. The link that makes it all work is in (4). Sorry

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Tue Sep 30, 2008 10:31 pm Post subject:

After the Type 4 UR on <69>, I get here:

Code:

+----------------+----------------+----------------+
| 145@ 1-46 9 | 2 7 68 | 3 45@ 1458 |
| 57 67 3 | 4 68 1 | 2 9 58 |
| 14@ 8 2 | 9 3 5 | 7 6 14 |
+----------------+----------------+----------------+
| 46 5 7 | 8 49 3 | 1 2 69 |
| 9 24 8 | 1 246 46 | 5 7 3 |
| 26 3 1 | 5 29 7 | 4 8 69 |
+----------------+----------------+----------------+
| 78 9 5 | 3 48 2 | 6 1 47 |
| 237 27 4 | 6 1 9 | 8 35 257 |
| 1238 12 6 | 7 5 48 | 9 34 24 |
+----------------+----------------+----------------+

The swordfish is not needed, nor is an ER. There is an XYZ-wing @ that makes an elimination that solves the puzzle.

(This is not how I originally solved it.)

Keith

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Tue Sep 30, 2008 10:54 pm Post subject:

Without the UR, after the swordfish:

Code:

+-------------+-------------+-------------+
| 156 46 9 | 2 7 68 | 3 45 158 |
| 567 67 3 | 4 68 1 | 2 9 58 |
| 14 8 2 | 9 3 5 | 7 6 14 |
+-------------+-------------+-------------+
| 46 5 7 | 8 469 3 | 1 2 69 |
| 9 246 8 | 1 26 46 | 5 7 3 |
| 26 3 1 | 5 269 7 | 4 8 69 |
+-------------+-------------+-------------+
| 78 9 5 | 3 48 2 | 6 1 47 |
| 237 27 4 | 6 1 9 | 8 35 57 |
| 38 1 6 | 7 5 48 | 9 34 2 |
+-------------+-------------+-------------+

In R12 there are a number of extended XY-wings (4-link chains) that take out: <6> in R2C1; <6> in R1C6; <8> in R1C9; <6> in R2C2.

You only have to look in R12 to find them!

Keith

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