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CathyW
Master

Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

Posted: Wed May 02, 2007 10:59 am    Post subject: Daily Nightmare 2-5-07

Don't look if you haven't done today's puzzle yet!!

I found a cool uniqueness move, an x-wing and finally a forcing chain to solve this puzzle

My walkthrough:

1. NP {28} in N5 -> r4c4=6 -> NP {39} in c6/N5 -> r1c6 = 1/6/7
2. NT {147} in c6/N8 -> r1c6 = 6, r9c4 = 2/5/8
3. NP {57} in c4/N2 -> r1c4 = 1, r23c5 = {39}, r9c4 = 2/8
4. HS r6c6 = 3, r4c6 = 9

5. Grid now:
 Code: *-----------------------------------------------------------------------------*  | 2       379     3579    | 1       4       6       | 35      79      8       |  | 457     3479    1       | 57      39      8       | 2       4679    4569    |  | 4578    6       345789  | 57      39      2       | 345     1       459     |  |-------------------------+-------------------------+-------------------------|  | 48      234     348     | 6       1       9       | 7       5       249     |  | 9       127     78      | 4       28      5       | 168     268     3       |  | 148     5       6       | 28      7       3       | 148     2489    1249    |  |-------------------------+-------------------------+-------------------------|  | 14567   8       457     | 9       25      147     | 1456    3       12456   |  | 14567   147     2       | 3       58      147     | 9       468     1456    |  | 3       149     459     | 28      6       14      | 1458    248     7       |  *-----------------------------------------------------------------------------*

r23c4 = {57} -> r23c1 cannot both be {57}
Either r2c1 = 4 or r3c1 = 4 or 8.
Since r4c1 = 4/8, 4 and 8 cannot go elsewhere in c1 -> r6c1 = 1 -> r78c1 = {567}
6. NT {278} in r5c235 -> r5c8 = 6, r5c7 = 1
7. 8 locked to r6 in N6 -> r6c4 = 2 -> several naked and hidden singles to here:

 Code: *--------------------------------------------------------------------*  | 2      379    359    | 1      4      6      | 35     79     8      |  | 457    3479   1      | 57     39     8      | 2      479    6      |  | 4578   6      34589  | 57     39     2      | 345    1      459    |  |----------------------+----------------------+----------------------|  | 48     34     348    | 6      1      9      | 7      5      2      |  | 9      2      7      | 4      8      5      | 1      6      3      |  | 1      5      6      | 2      7      3      | 8      49     49     |  |----------------------+----------------------+----------------------|  | 57     8      45     | 9      2      147    | 6      3      145    |  | 6      147    2      | 3      5      147    | 9      8      14     |  | 3      149    459    | 8      6      14     | 45     2      7      |  *--------------------------------------------------------------------*

8. x-wing on 5 in r1c37, r9c37 -> r3c3, r3c7, r7c3 <> 5 -> r7c3 = 4
9. Forcing chain:
If r7c6 = 1 -> r9c6 = 4, r9c7 = 5, r9c3 = 9, r9c2 = 1, r8c2 = 7
If r7c6 = 7 -> r7c1 = 5, r9c3 = 9, r9c2 = 1, r8c2 = 7
The rest is singles.
Para
Yokozuna

Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

 Posted: Wed May 02, 2007 12:07 pm    Post subject: Re: Daily Nightmare 2-5-07 Hi I missed that UR and went through an alternative solution path. Tend to miss unique subset moves. But for your walkthrough, that forcing chain can be replaced by: xy-wing: On R7C19 + R8C2: R8C9 <> 1 greetings Para
CathyW
Master

Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

 Posted: Wed May 02, 2007 12:56 pm    Post subject: So it can! Thanks - should have spotted that. I was pleased with the UR move - I can't remember using UR in combination with a bivalue cell before to make eliminations. I know some people don't hold with using uniqueness moves but I find them valuable and I'm 100% certain that Ruud would not supply a puzzle with more than one solution.
rep'nA
Hooked

Joined: 19 Jan 2007
Posts: 49
Location: Union City, California

Posted: Wed May 02, 2007 11:58 pm    Post subject: Re: Daily Nightmare 2-5-07

Or at this point...

 Code: *--------------------------------------------------------------------*  | 2      379    359    | 1      4      6      | 35     79     8      |  | 457    3479   1      | 57     39     8      | 2      479    6      |  | 4578   6      34589  | 57     39     2      | 345    1      459    |  |----------------------+----------------------+----------------------|  | 48     34     348    | 6      1      9      | 7      5      2      |  | 9      2      7      | 4      8      5      | 1      6      3      |  | 1      5      6      | 2      7      3      | 8      49     49     |  |----------------------+----------------------+----------------------|  | 57     8      45     | 9      2      147    | 6      3      145    |  | 6      147    2      | 3      5      147    | 9      8      14     |  | 3      149    459    | 8      6      14     | 45     2      7      |  *--------------------------------------------------------------------*

you could skip both the x-wing and the forcing chain (or Para's alternative) with Subset Counting on r7c136 and r9c67 (or equivalently the ALS xz-rule). The candidates 1,4,5,7 appear with max multiplicities {1,2,2,1}. As there are 5 cells, any placement eliminating all of the 4's or all of the 5's must be false. Hence, r7c9, r9c3 <> 5, and the puzzle is reduced to singles.
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