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David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

 Posted: Mon Jan 23, 2006 1:28 am    Post subject: 22 Jan, 2006 Nightmare Hi, all! I thought this puzzle was difficult, but maybe not as much fun as some of the other nightmares I've worked through. After finding a two-step XY-Wing in boxes 4 & 7 (the first one revealed the second one) and doing quite a bit of coloring I spotted a pattern (136 / 36 / 36 / 36) in r1c4, r1c6, r6c4, & r6c6. By assuming that the puzzle had a unique solution I then placed a "1" at r1c4 and the rest of the puzzle went pretty quickly. Generally I don't like to rely on this assumption to solve a puzzle, but I was getting tired of working on this one, and I'm sure Ruud isn't going to stick me with an invalid puzzle. I'm curious if someone else found another, cleaner way through this thicket. dcb
lac
Hooked

Joined: 02 Jan 2006
Posts: 43
Location: Göteborg, Sweden

 Posted: Mon Jan 23, 2006 12:14 pm    Post subject: I solved it without resorting to uniqueness. (fixed typos) I first proved that c7r5 could not be 8. (either c3r5 or c7r9 is) This means that c9 r6 must be the 8. (fixed typo, I had c2r5, wrong) You then get some more hidden pairs/triples, and an X wing on 1s c2r2 c2r6 c5r2 c5r6. Then I proved that 9 could not be in c7r9 or c9r9 (either c3r9 or c6r9 is) This lead to proving that in c9r1 the 1 and the 9 had the same state. So they cannot exist. So the other state exists. c9r7 is 9 (among others). The whole thing falls out. More longwinded explanation of how I proved these available if you want ... apologies for the typos when I first posted this. Laura
David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

 Posted: Mon Jan 23, 2006 10:24 pm    Post subject: Thank, Laura! Thanks for the quick response, Laura. I'll have to think about what you said for a little bit. Maybe I'll have to read your "novel" again. Give me a day or two to puzzle it out ... I probably won't need the long-winded explanation, but you never know. Have a great day! dcb
lac
Hooked

Joined: 02 Jan 2006
Posts: 43
Location: Göteborg, Sweden

Posted: Tue Jan 24, 2006 12:22 am    Post subject: Just to make sure ...

You are starting from:

 Code: .-----------------------.-----------------------.-----------------------. |7      34      129     |136    8       369     |1249   5       1249    | |6      19      5       |2      19      4       |3      8       7       | |8      34      129     |137    5       379     |1249   24      6       | :-----------------------+-----------------------+-----------------------: |5      6       3       |18     124     28      |7      9       124     | |4      128     18      |9      7       5       |128    6       3       | |9      12      7       |36     124     36      |5      24      1248    | :-----------------------+-----------------------+-----------------------: |1      5       4       |78     29      2789    |6      3       289     | |2      89      6       |4      3       1       |89     7       5       | |3      7       89      |5      6       289     |2489   1       2489    | '-----------------------'-----------------------'-----------------------'

There is only one interesting coloured chain here. It starts on c2r8 (the doubleton 89 ).

Nothing would be more annoying than not understanding me because
we aren't starting at the same point.

Laura
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