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rare DP

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nataraj

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

Posted: Mon Aug 30, 2010 5:40 am Post subject: rare DP

Today, I have a pretty interesting puzzle for the friends of "very hard"s:

Code:

Nataraj 1756434735 "challenging"

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

After basics (and a w-wing and a UR 36), there is a potential deadly pattern, or so I believe, in this position:

Code:

+--------------------------+--------------------------+--------------------------+
| 3 9 12 | 56 8 4 | 25 16 7 |
| 14 24 8 | 7 9 56 | 25 136 36 |
| 6 7 5 | 12 13 23 | 9 48 48 |
+--------------------------+--------------------------+--------------------------+
| 5 8 7 | 12 134 23 | 6 34 9 |
| 9 1 34 | 56 34 56 | 8 7 2 |
| 2 34 6 | 8 7 9 | 1 5 34 |
+--------------------------+--------------------------+--------------------------+
| 78 5 9 | 3 6 78 | 4 2 1 |
| 78 236 23 | 4 5 1 | 37 9 68 |
| 14 346 134 | 9 2 78 | 37 68 5 |
+--------------------------+--------------------------+--------------------------+

I think that the 12 13 23 in rows 3 and 4 would form a DP and thus r4c5 must be "4". Is this reasoning valid? I feel pretty comfortable with rectangular DPs ("UR" in all its varants), but I am never sure when it comes to larger patterns.

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Mon Aug 30, 2010 12:36 pm Post subject: Re: rare DP

nataraj wrote:

Today, I have a pretty interesting puzzle for the friends of "very hard"s:

After basics (and a w-wing and a UR 36), there is a potential deadly pattern, or so I believe, in this position:

Code:

Nataraj, I believe you have variation of "almost deadly pattern" (ADP) known as a BUG-Lite.

Two options are available to deal with all ADPs. One is the use of the "extra" digits within the ADP cells. In this case the only extra is the 4 in r4c5 as you have already observed.

The second option is the use of the ADP digits in the "external" cells that share a house with the ADP digits. In this case, we do not have any digits 1 or 2 that "see" the corresponding digits in the ADP cells, and only one cell, r5c5 has a 3. Thus r5c5=3 is also a valid solution.

In summary, to prevent the DP, a 4 must go into cell r4c5 and the displaced 3 has only one place to go and that is into r5c5.

Ted

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Tue Aug 31, 2010 1:55 am Post subject:

nataraj

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

Posted: Tue Aug 31, 2010 4:57 am Post subject:

Norm, I like your colorful graphics

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Tue Aug 31, 2010 7:45 pm Post subject:

nataraj wrote:

Norm, I like your colorful graphics Smile

thanx, but I think the footprints i am walking in have nataraj signs labeled nice and clearly.

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