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DB Saturday Puzzle - May 27, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Sat May 27, 2006 9:13 am    Post subject: DB Saturday Puzzle - May 27, 2006 Reply with quote

Here it is:
Code:

Puzzle: DB052706  ******
+-------+-------+-------+
| . 2 . | . . . | 8 . 4 |
| . . 3 | . . . | . 9 1 |
| . . . | 2 4 . | . 3 . |
+-------+-------+-------+
| 5 . . | . 1 . | 9 . 3 |
| . 3 . | . . . | . 6 . |
| 8 . 6 | . 3 . | . . 5 |
+-------+-------+-------+
| . 8 . | . 5 9 | . . . |
| 3 7 . | . . . | 6 . . |
| 9 . 2 | . . . | . 1 . |
+-------+-------+-------+

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sat May 27, 2006 4:58 pm    Post subject: Reply with quote

My take: the puzzle started off generously, allowing five cells to be solved during the initial scan of bands and stacks. After filling in cells with their candidates and doing the usual scan of rows, columns and blocks, a nice Type 1 rectangle of 78 was exposed. This eliminated some candidates, solved some cells and exposed a 17 Type 1 rectangle.

Whoops! That 78 rectangle was in FOUR boxes! A very easy trap to fall into if one's brain is not focused on ALL details at ALL times. I tried to re-create the grid as it was before that false rectangle, thinking that the puzzle would end up with duplicates as a result of my error. But, I found out, I was fortunate enough to have re-created the grid correctly.

Further scanning exposed two more Type 1 rectangles of 37 and 36 and that was enough to finish it off.

Type 1 rectangles are right up my alley, as they are very compatible with my reasoning powers. Laughing
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Sat May 27, 2006 10:37 pm    Post subject: A lesson? Reply with quote

Marty,

Your message just reinforces my opinion that Unique Rectangles are easy for humans. Use them when you find them.

If you use the "official" hierarchy of solution methods with this puzzle, you get to here:
Code:

+-------------------+-------------------+-------------------+
| 167   2     15    | 136   9     136   | 8     57    4     |
| 4     56    3     | 5678  678   5678  | 2     9     1     |
| 17    9     8     | 2     4     15    | 57    3     6     |
+-------------------+-------------------+-------------------+
| 5     4     7     | 68    1     268   | 9     28    3     |
| 2     3     9     | 45    78    45    | 1     6     78    |
| 8     1     6     | 9     3     27    | 47    247   5     |
+-------------------+-------------------+-------------------+
| 16    8     14    | 13467 5     9     | 347   47    2     |
| 3     7     145   | 148   2     148   | 6     458   9     |
| 9     56    2     | 34678 678   34678 | 3457  1     78    |
+-------------------+-------------------+-------------------+

The way forward is an X-wing on <6> in C25. But, wait! Look at the diagonal UR on <47> in R67C78. There is a strong link in R6: The only possibilities for <4> in R6 are on corners of the rectangle.

This means R7C7 cannot be <4>! If it is <4>, it forces <7> on the other diagonal of the UR, and the strong link completes the deadly pattern with <4> in R6C8.

Wonderful stuff! Too bad, it does not help to solve this puzzle!

But, I will bet you a FedEx can of Mountain Dew: There is no commercial or public solver that finds the above elimination with the same UR / Strong Link reasoning.

Keith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun May 28, 2006 12:26 am    Post subject: XY-Wing cracks it wide open Reply with quote

Code:
+-------------------+-------------------+-------------------+
| 167   2     15    | 136   9     136   | 8     57    4     |
| 4     56    3     | 5678  678   5678  | 2     9     1     |
| 17    9     8     | 2     4     15    | 57    3     6     |
+-------------------+-------------------+-------------------+
| 5     4     7     | 68    1     268   | 9     28    3     |
| 2     3     9     | 45    78    45    | 1     6     78    |
| 8     1     6     | 9     3     27    | 47    247   5     |
+-------------------+-------------------+-------------------+
| 16    8     14    | 13467 5     9     | 347   47    2     |
| 3     7     145   | 148   2     148   | 6     458   9     |
| 9     56    2     | 34678 678   34678 | 3457  1     78    |
+-------------------+-------------------+-------------------+

At this point in the puzzle the XY-Wing from r1c3 blows it wide open. Not quite coincidentally, it forces r7c7 <> 4 also. dcb
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon May 29, 2006 9:31 am    Post subject: Re: A lesson? Reply with quote

keith wrote:

This means R7C7 cannot be <4>! If it is <4>, it forces <7> on the other diagonal of the UR ...

Please explain, why, i did not see that.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Mon May 29, 2006 12:19 pm    Post subject: Reply with quote

Ravel,

If R7C7 is <4>, it forces both R6C7 and R7C8 to be <7>. Then, the strong link in R6 forces R6C8 to be <4>, and you have the deadly solution.

Keith
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon May 29, 2006 1:46 pm    Post subject: Reply with quote

Thanks Keith,

i had looked at the wrong cell, i mixed R7C7 and R7C8 Smile
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