22 Jan, 2006 Nightmare

[David Bryant]

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]

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]

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]

You are starting from:

Code: Select all

.-----------------------.-----------------------.-----------------------.
|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