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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Wed Dec 19, 2007 9:54 pm Post subject: Enjoyable |
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On the hard side, but I liked it a lot.
| Code: | Puzzle: M5617944sh(21)
+-------+-------+-------+
| 9 7 . | . . 8 | . . . |
| 2 . . | . 5 9 | . . 6 |
| 4 5 . | 7 . . | 9 . . |
+-------+-------+-------+
| 5 2 . | . . . | 6 . . |
| . 8 . | . . . | . 9 . |
| . . 4 | . . . | . 5 7 |
+-------+-------+-------+
| . . 7 | . . 5 | . 4 8 |
| 3 . . | 8 7 . | . . 9 |
| . . . | 6 . . | . 1 5 |
+-------+-------+-------+ |
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 20, 2007 2:02 am Post subject: |
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I'm throwing in the towel, thinking that I should have been able to finish this. Just yesterday I did one with a (36) rating which took just four ordinary techniques. Here I've made nine moves involving six techniques, and thinking there's another XY-Chain, but unable to find it.
| Code: |
+-----------+-------------+------------+
| 9 7 36 | 234 126 8 | 5 23 134 |
| 2 13 138 | 34 5 9 | 48 7 6 |
| 4 5 368 | 7 236 136 | 9 238 13 |
+-----------+-------------+------------+
| 5 2 9 | 1 48 7 | 6 38 34 |
| 7 8 13 | 5 346 346 | 14 9 2 |
| 16 36 4 | 39 389 2 | 18 5 7 |
+-----------+-------------+------------+
| 16 69 7 | 29 129 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-----------+-------------+------------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 20, 2007 2:37 am Post subject: |
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| Code: | Puzzle: M5617944sh(21)
+-------+-------+-------+
| 9 7 . | . . 8 | . . . |
| 2 . . | . 5 9 | . . 6 |
| 4 5 . | 7 . . | 9 . . |
+-------+-------+-------+
| 5 2 . | . . . | 6 . . |
| . 8 . | . . . | . 9 . |
| . . 4 | . . . | . 5 7 |
+-------+-------+-------+
| . . 7 | . . 5 | . 4 8 |
| 3 . . | 8 7 . | . . 9 |
| . . . | 6 . . | . 1 5 |
+-------+-------+-------+ |
Basic methods get you to here:
| Code: | +-------------------+-------------------+-------------------+
| 9 7 136 | 1234 12346 8 | 5 23 134 |
| 2 13 138 | 134 5 9 | 148 7 6 |
| 4 5 1368 | 7 1236 1236 | 9 238 13 |
+-------------------+-------------------+-------------------+
| 5 2 9 | 14 148 7 | 6 38 134 |
| 7 8 13 | 5 1346 1346 | 14 9 2 |
| 16 136 4 | 1239 12389 123 | 18 5 7 |
+-------------------+-------------------+-------------------+
| 16 169 7 | 129 129 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-------------------+-------------------+-------------------+ |
There is a Type 4 UR on <16> that takes out <1> in R67c2.
Then, coloring (turbot fish, kite) on <4> in R2 and C9 solves R4C4 as <1>.
After some cleaning up:
| Code: | +----------------+----------------+----------------+
| 9 7 36 | 234 1236 8 | 5 23 134r |
| 2 1r3g 138 | 3g4r 5 9 | 4g8 7 6 |
| 4 5 368 | 7 1236 1236 | 9 238 13 |
+----------------+----------------+----------------+
| 5 2 9 | 1 48 7 | 6 38 34g |
| 7 8 1r3 | 5 346 346 | 1g4r 9 2 |
| 1g6 36 4 | 239 2389 23 | 18 5 7 |
+----------------+----------------+----------------+
| 1r6 69 7 | 29 129 5 | 3 4 8 |
| 3 1g 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+----------------+----------------+----------------+ |
Medusa coloring colors the same candidate across strong links, and different candidates in cells that have only two candidates.
Coloring on <1> starts with r(ed) in R2C2, ending with g(reen) in R5C7. Then, xx to <4>, r(ed) in R5C7, and continue coloring on <4> to R2C4.
Look at R2. If we now color <3>, there are two candidates that are g(reen). Red must be true, and the puzzle is solved.
This is a lot easier than it seems at first glance. Medusa gives you a net of possibilities for the whole grid: Above I have noted the chain that happened to solve it for me.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 20, 2007 4:59 am Post subject: |
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| Needless to say, Medusa was not one of the techniques I used. I think I have a reasonable grasp of what I'd call the more "mechanical" techniques, such as Wings, URs, ERs, simple coloring and the easier forms of multi-coloring, and maybe some others that don't come to mind at the moment. Should Medusa be the next one that I try to learn? Would that provide the most bang for the buck? |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Dec 20, 2007 11:15 am Post subject: |
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Marty, you missed the xy-wing with pivot in r6c2 in your grid. But it does not solve the puzzle, though an xyz-wing follows.
| Code: | +-------------+-------------+------------+
| 9 7 36 | 234 126 8 | 5 23 134 |
| 2 1-3 138 |#34 5 9 |#48 7 6 |
| 4 5 368 | 7 236 136 | 9 238 13 |
+-------------+-------------+------------+
| 5 2 9 | 1 48 7 | 6 38 34 |
| 7 8 13 | 5 346 346 | 14 9 2 |
|#16 #36 4 |-39 389 2 |#18 5 7 |
+-------------+-------------+------------+
| 16 69 7 | 29 129 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-------------+-------------+------------+
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An xy-chain solves it. If r2c4<>3, then
r2c4=4 => r2c7=8 => r6c7=1 => r6c1=6 => r6c2=3 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 20, 2007 4:44 pm Post subject: |
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| Quote: | | Marty, you missed the xy-wing with pivot in r6c2 in your grid. But it does not solve the puzzle, though an xyz-wing follows. |
Ravel, I'm not seeing where that XY-Wing does anything at all. My notes show that I did use that Wing with pincer coloring to eliminate one or more 1s. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Dec 20, 2007 5:32 pm Post subject: |
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| Code: | +-----------+-------------+------------+
| 9 7 36 | 234 126 8 | 5 23 134 |
| 2 13 138 | 34 5 9 | 48 7 6 |
| 4 5 368 | 7 236 136 | 9 238 13 |
+-----------+-------------+------------+
| 5 2 9 | 1 48 7 | 6 38 34 |
| 7 8 13 | 5 346 346 | 14 9 2 |
| 16#36 4 |#39 389 2 | 18 5 7 |
+-----------+-------------+------------+
| 16#69 7 |2-9 129 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-----------+-------------+------------+ |
I meant this one taken out the 9 in r7c4 and leading to an xyz-wing in row 1/box3. So you get 4 numbers, but they dont really help. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 20, 2007 6:07 pm Post subject: |
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| ravel wrote: | | Code: | +-----------+-------------+------------+
| 9 7 36 | 234 126 8 | 5 23 134 |
| 2 13 138 | 34 5 9 | 48 7 6 |
| 4 5 368 | 7 236 136 | 9 238 13 |
+-----------+-------------+------------+
| 5 2 9 | 1 48 7 | 6 38 34 |
| 7 8 13 | 5 346 346 | 14 9 2 |
| 16#36 4 |#39 389 2 | 18 5 7 |
+-----------+-------------+------------+
| 16#69 7 |2-9 129 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-----------+-------------+------------+ |
I meant this one taken out the 9 in r7c4 and leading to an xyz-wing in row 1/box3. So you get 4 numbers, but they dont really help. |
I missed that one and still wondering how I can miss XY-Wings while searching for them systematically.
But after the eliminations from that 36-39-69 XY-Wing, I'm left here:
| Code: | +-----------+-------------+------------+
| 9 7 36 | 34 126 8 | 5 23 134 |
| 2 13 138 | 34 5 9 | 48 7 6 |
| 4 5 368 | 7 26 16 | 9 238 13 |
+-----------+-------------+------------+
| 5 2 9 | 1 48 7 | 6 38 34 |
| 7 8 13 | 5 346 346 | 14 9 2 |
| 16#36 4 | 9 38 2 | 18 5 7 |
+-----------+-------------+------------+
| 16#69 7 | 2 19 5 | 3 4 8 |
| 3 14 5 | 8 7 14 | 2 6 9 |
| 8 49 2 | 6 349 34 | 7 1 5 |
+-----------+-------------+------------+ |
I hope I have this right, but for the first time ever, I used an Aligned Pair Exclusion in box 3. R1c89 can't be 13 or 34, so that forces r1c8 = 2. However, the bad news is that it doesn't seem to help very much.
Update: following the APE, two more XY-Wings, both requiring pincer coloring, did the trick. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Dec 21, 2007 12:05 am Post subject: |
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Marty,
Here is what Sudopedia says:
| Quote: | 3D Medusa or Advanced Coloring is a coloring technique which considers multiple digits.
When the technique is limited to a single cluster, you can also replicate its effects by placing Equivalence Marks in the pencilmark grid, making it a good advanced technique for pencil and paper solvers. |
http://www.sudopedia.org/wiki/3D_Medusa
I have found it useful to solve some difficult puzzles, and also to gain insights into how multicoloring works.
Medusa probably works best when you have many 2-candidate cells, i.e., a BUG+n situation.
Try it! The mechanics of Medusa are pretty easy. But, I am still learning how to interpret the implications.
Keith
Keith |
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