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Hard, or not so?

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wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Sun Jun 29, 2008 9:14 pm Post subject: Hard, or not so?

I (try to ) post a puzzle a day that is difficult, yet needs not chains.
That is because I solve puzzles on paper and I don't know chains and I don't know coloring, I just haven't learned those methods.

Here is a puzzle that just does not fit.

Code:

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

I know many ways to solve this, it takes some work.
Two of the three solvers I use want chains.

What do you see?

Thanks.

keith

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

Posted: Sun Jun 29, 2008 9:42 pm Post subject:

It can be solved in one step:

Code:

+-------------------+-------------------+-------------------+
| 1789 2 3 |-17-9 4 78-9 | 19b 6 5 |
| 4 69 189 | 5 19a 2689 | 7 28 3 |
| 16789 5 1789 | 12679 3 26789 | 4 28 19 |
+-------------------+-------------------+-------------------+
| 567 67 457 | 3 2 1 | 8 9 47 |
| 3 8 2 | 79 79 4 | 5 1 6 |
| 79 1 479 | 8 6 5 | 2 3 47 |
+-------------------+-------------------+-------------------+
| 1789 3 1789 | 1279 5 279 | 6 4 129 |
| 2 79 6 | 4 179c 3 | 19d 5 8 |
| 159 4 159 | 1269 8 269 | 3 7 129 |
+-------------------+-------------------+-------------------+

The cells a and b are a remote pair, taking out <19> in R1B2. (acdb is a chain of strong links on <1>.)

You may consider this to be coloring. (I do.)

Otherwise, there is an XY-wing, and an XYZ-wing, and a Unique Rectangle. They do not solve it.

If you see this only as a skyscraper that eliminates <1> in R1C4, it is a hard slog to the end, including an extended XY-wing.

Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Jun 29, 2008 10:05 pm Post subject:

Code:

.---------------------.---------------------.---------------------.
| 1789 2 3 | 179 4 789 | 19 6 5 |
| 4 69 189 | 5 19 2689 | 7 28 3 |
| 16789 5 1789 | 12679 3 26789 | 4 28 19 |
:---------------------+---------------------+---------------------:
| 567 67 457 | 3 2 1 | 8 9 47 |
| 3 8 2 | 79 79 4 | 5 1 6 |
| 79 1 479 | 8 6 5 | 2 3 47 |
:---------------------+---------------------+---------------------:
| 1789 3 1789 | 1279 5 279 | 6 4 129 |
| 2 79 6 | 4 179 3 | 19 5 8 |
| 159 4 159 | 1269 8 269 | 3 7 129 |
'---------------------'---------------------'---------------------'

sorry, can't give you an ALS solution or a mega fish that solves this

its a pitty you don't like chains, since coloring is a form of creating chains, you can do some massive coloring on 1 and eliminate three 1's.

there is an xy-wing present in the grid and a UR {4,7} which still leaves with either an ALS finish or a xy-chain...

but there is an xy-chain that solves the whole thing
(1=9)r2c5-(9=6)r2c2-(6=7)r4c2-(7=9)r8c2-(9=1)r8c7; r8c5<>1 and its solved.

ah keith, I was posting when you were

wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Sun Jun 29, 2008 10:35 pm Post subject:

storm_norm wrote:

but there is an xy-chain that solves the whole thing

Just wondering, you see that when paper solving?

wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Sun Jun 29, 2008 10:55 pm Post subject:

keith wrote:

It can be solved in one step:

Code:

The cells a and b are a remote pair, taking out <19> in R1B2.

Keith

I know of remote pairs. I don't see them here.

Steve R

Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

Posted: Mon Jun 30, 2008 12:02 am Post subject:

A W-Wing is an alternative.

This is the sticking point:

Code:

+-------------------------------------------------+
| 1789 2 3 | 179 4 789 | 19 6 5 |
| 4 †69 189 | 5 *19 2689 | 7 28 3 |
| 16789 5 1789 | 12679 3 26789 | 4 28 19 |
---------------------------------------------------
| 567 67 457 | 3 2 1 | 8 9 47 |
| 3 8 2 | 79 79 4 | 5 1 6 |
| 79 1 479 | 8 6 5 | 2 3 47 |
---------------------------------------------------
| 1789 3 1789 | 1279 5 279 | 6 4 129 |
| 2 †79 6 | 4 179 3 | *19 5 8 |
| 159 4 159 | 1269 8 269 | 3 7 129 |
+-------------------------------------------------+

The (19)s in r2c5 and r8c7 are linked by the conjugates for 9 in column 2. So 1 can be eliminated from r8c5 and the puzzle is solved.

Steve

Marty R.

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

Posted: Mon Jun 30, 2008 12:39 am Post subject:

wapati wrote:

storm_norm wrote:

but there is an xy-chain that solves the whole thing

Just wondering, you see that when paper solving?

XY-Chains and many other techniques can be used when using pencil and paper. Sometimes it's necessary to test things, so keeping some blank grids handy for testing greatly facilitates things.

keith

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

Posted: Mon Jun 30, 2008 2:14 am Post subject:

wapati wrote:

I know of remote pairs. I don't see them here.

wapati,

Take at look at: http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143

A remote pair needs a chain in only one of the candidates. Most explanations use a chain of both candidates.

And, by the way, these are easily found with pencil and paper. If you have two cells with the same two candidates that are not a pair, look for a remote pair, a W-wing, or an M-wing.

Keith

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