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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Jul 12, 2008 5:59 pm Post subject: A day for easy puzzles? |
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Today's Brain Bashers Super Hard. See if you can do it with one (advanced) step. | Code: | Puzzle: BB071208sh
+-------+-------+-------+
| . 1 5 | . . . | 6 8 . |
| 2 . . | 5 . 4 | . . 3 |
| 3 . . | . . . | . . 5 |
+-------+-------+-------+
| . 6 . | . 8 . | . 2 . |
| . . . | 2 . 6 | . . . |
| . 5 . | . 4 . | . 7 . |
+-------+-------+-------+
| 5 . . | . . . | . . 7 |
| 6 . . | 3 . 8 | . . 4 |
| . 9 4 | . . . | 1 3 . |
+-------+-------+-------+ |
Keith |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sat Jul 12, 2008 6:17 pm Post subject: easy |
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A w-wing,
Earl |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jul 12, 2008 7:23 pm Post subject: |
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After basics,
| Code: |
+--------------------------+--------------------------+--------------------------+
| 4 1 5 | 79 2379 2379 | 6 8 29 |
| 2 8 69 | 5 69 4 | 7 1 3 |
| 3 7 69 | 8 1269 129 | 29 4 5 |
+--------------------------+--------------------------+--------------------------+
| 179 6 3 | 179 8 5 | 4 2 19 |
| 1789 4 78 | 2 379 6 | 3589 59 189 |
| 189 5 2 | 19 4 39 | 389 7 6 |
+--------------------------+--------------------------+--------------------------+
| 5 3 18 | 4 129 129 | 28 6 7 |
| 6 2 17 | 3 17 8 | 59 59 4 |
| 78 9 4 | 6 5 27 | 1 3 28 |
+--------------------------+--------------------------+--------------------------+
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Neither the 69 UR r23c35 nor the 59 UR r58c78 solve the puzzle.
But ...
coloring on "8" solves r5c3=7 and the puzzle
or
w-wing 78 strong link on 8 col 9. Again, don't know if it solves the puzzle, but it should because the w-wing also gives r5c3=7
The diagram for "8":
w-wing clearly visible (both 7s see the ends of the strong link in col 9), as is the skyscraper (rows 6,9) and the kite (col 9, row7)
| Code: |
+·····+·····+·····+
· · · ·
· · · ·
· · · ·
· · · ·
· · · ·
+·····+·····+·····+
· · · ·
· · · ·
·o 7· ·o *·
· |· · |·
·*-----------* |·
+····|+·····+····|+
· 1-------2 |·
· / · · \ |·
· / · · \ |·
· / · · \|·
·7---------------2·
+·····+·····+·····+
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 12, 2008 7:41 pm Post subject: |
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Earl,
I used the same pair as the basis of an M-wing!
| Code: | +----------------+----------------+----------------+
| 4 1 5 | 79 2379 2379 | 6 8 29 |
| 2 8 69 | 5 69 4 | 7 1 3 |
| 3 7 69 | 8 1269 129 | 29 4 5 |
+----------------+----------------+----------------+
| 179 6 3 | 179 8 5 | 4 2 19 |
| 1789 4 78 | 2 379 6 | 3589 59 189 |
| 189 5 2 | 19 4 39 | 389 7 6 |
+----------------+----------------+----------------+
| 5 3 18 | 4 129 129 | 28 6 7 |
| 6 2 17 | 3 17 8 | 59 59 4 |
| 78 9 4 | 6 5 27 | 1 3 28 |
+----------------+----------------+----------------+ |
I think Earl means the pair <78> which, with the strong link on <8> in C9, takes out <7> in R8C3.
I got only to here, not having solved all the singles, and only having marked some of the bivalue cells:
| Code: | +---------+---------+----------+
| 4 1 5 | . . . | 6 8 29 |
| 2 8 69 | 5 . 4 | 7 1 3 |
| 3 7 69 | 8 . . | 29 4 5 |
+---------+---------+----------+
| . 6 3 | . 8 5 | 4 2 19 |
| . 4 78 | 2 . 6 | . 59 . |
| . 5 2 | 19 4 . | . 7 6 |
+---------+---------+----------+
| 5 3 18 | 4 . . | . 6 7 |
| 6 2 17 | 3 . 8 | . 59 4 |
| 78 9 4 | 6 . 27 | 1 3 . |
+---------+---------+----------+ |
Note that the <78>'s in B47 are a complementary pair. In the solution, they have the same value. Also, there is a strong link on <8> in R9C19, so we have an M-wing: R5C9 cannot be <8>. The only place for <8> in C9 is now R9C9, and the puzzle is solved.
(I saw it by noting that the cells <18> and <17> in B7 together act like
<78>. Looking at it again, the pattern can also be seen as a regular M-wing, as a kite, or as coloring on <8>.)
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Jul 12, 2008 9:00 pm Post subject: |
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| {7,8} w-wing removes 7 in r56c1 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 12, 2008 9:18 pm Post subject: |
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Did you notice?
These <78>'s are both a complementary pair and a W-wing. Forget about pincers: We can solve them both as <7>. Blowing the puzzle apart!
The logic:
W-wing: At least one of them is <7>.
Complementary Pair: Both are the same value.
QED.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Sat Jul 12, 2008 9:40 pm Post subject: |
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| Quote: | | See if you can do it with one (advanced) step. |
Whoops - missed that - so I guess I won't report my 2 UR's, 2 ER's and one skyscraper. At least that recent "Impossible" encouraged me to check out colouring traps and wraps instead of abusing the users.
So give me another minute (or two). |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 12, 2008 9:40 pm Post subject: |
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Cool! A Medusa loop:
If the strong link ab is 8x=8y
where x and y are anything, and = is a strong link.
And, the complementary pair cde is 78=7z=78
where z is anything.
Then we have a loop bcdea (and back to b):
8y-78=7z=78-8x
where - is a weak link.
One end must be <8>, which forces <7> in each of the <78> cells.
Keith |
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