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BB for Jan 31

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Feb 01, 2009 7:28 pm    Post subject: BB for Jan 31 Reply with quote
Code:
Puzzle: BB013109sh
+-------+-------+-------+
| 1 . . | . . . | . . 8 |
| . 4 . | 3 . 2 | . 1 . |
| . . . | 8 1 9 | . . . |
+-------+-------+-------+
| . 3 6 | . 2 . | 7 5 . |
| . . 2 | 9 . 5 | 6 . . |
| . 1 5 | . 6 . | 8 3 . |
+-------+-------+-------+
| . . . | 2 9 3 | . . . |
| . 9 . | 5 . 7 | . 8 . |
| 2 . . | . . . | . . 5 |
+-------+-------+-------+

Quote:
See if you can find the XY-cycle that make 4 eliminations in 3 different candidates.

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Sun Feb 01, 2009 10:29 pm    Post subject: Re: BB for Jan 31 Reply with quote
[quote="keith"]
Quote:
See if you can find the XY-cycle that make 4 eliminations in 3 different candidates.


I solved the puzzle easily, but I can NOT find the "Fun" solution. I am especially interested in "how" you found the solution.

Ted
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Feb 01, 2009 11:27 pm    Post subject: Reply with quote
After basics:
Code:
+-------------+-------------+-------------+
| 1   25c 39  | 4   57  6   | 39  27b 8   |
| 568 4   789 | 3   57  2   | 59  1   67  |
|356 2-56 37  | 8   1   9   |345 26-7 34  |
+-------------+-------------+-------------+
| 4   3   6   | 1   2   8   | 7   5   9   |
| 7   8   2   | 9   3   5   | 6   4   1   |
| 9   1   5   | 7   6   4   | 8   3   2   |
+-------------+-------------+-------------+
|5-68 56d 48  | 2   9   3   | 1   67a 4-67|
| 36  9   1   | 5   4   7   | 2   8   36  |
| 2   7   34  | 6   8   1   | 34  9   5   |
+-------------+-------------+-------------+

abcda is the loop. Choose a is <7>, then <6>. Tabulate the solutions. They are
5 2
6 7
and
2 7
5 6
You will see that each side of the rectangle eliminates a candidate in its line.

How did I find it? I do not have a system.

I solve using pencil and paper, and I initially fill in only pencil marks for cells that have two candidates. I look for XY-wings and extended XY-wings (4-cell chains) each time I find another bivalue cell.

In this case, I found the cycle long before I was done with basics, so there were another couple of eliminations!

Credits: Sudoku Susser finds these, but does not explain them so you believe you might find them yourself. A few weeks ago, re'born pointed out that if the pincers of a chain are in the same house, you have a cycle. Eureka!

I don't think it solves the puzzle, but these are really cool to find!

Keith Very Happy
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Mon Feb 02, 2009 1:02 am    Post subject: Reply with quote
I did it twice and didn't find it, and don't know if I had the same grid as you. But it's solvable with a few of the moves that are commonly discussed here.

My next XY-Loop will be my first.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Mon Feb 02, 2009 3:25 am    Post subject: Reply with quote
Marty R. wrote:
I did it twice and didn't find it, and don't know if I had the same grid as you. But it's solvable with a few of the moves that are commonly discussed here.

My next XY-Loop will be my first.

Marty,

I have only ever found a few. However, you will only find them if you are looking for at least four-cell chains. XY-wings are only three cells.

Also, they do not seem to be puzzle busters like W-wings are.

These cycles are incredibly cool to find. However, they can be regarded as an assembly of a number of 4-cell chains that make eliminations in one candidate only.

Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Feb 02, 2009 6:16 pm    Post subject: Reply with quote
Keith,
ever notice how the perfect square xy-loops resemble x-wings?
in the easier VH puzzles, there have been xy-loops contained in x-wing cells.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Mon Feb 02, 2009 9:39 pm    Post subject: Reply with quote
storm_norm wrote:
Keith,
ever notice how the perfect square xy-loops resemble x-wings?
in the easier VH puzzles, there have been xy-loops contained in x-wing cells.

Norm,

Yes, but I hesitate to go there. (By "perfect square" I presume you mean "4-cell rectangular".) X-wings require you to find two strong links (in the same candidate) that line up.

I don't see how to explain an XY-loop as a variant of an X-wing, or vice-versa.

Keith
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