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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 9:28 am Post subject: Freep Dec 21, 2007 |
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Still chipping away at this one:
| Code: | Puzzle: FP122107
+-------+-------+-------+
| 5 . . | . 6 3 | . . 2 |
| 1 . 2 | . 8 . | 9 . 6 |
| . . . | 4 . . | . . . |
+-------+-------+-------+
| . . . | . 3 2 | . . . |
| . . 9 | . 1 . | 6 . . |
| . . . | 8 7 . | . . . |
+-------+-------+-------+
| . . . | . . 8 | . . . |
| 8 . 6 | . 9 . | 2 . 3 |
| 9 . . | 3 5 . | . . 7 |
+-------+-------+-------+ |
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Dec 21, 2007 10:21 pm Post subject: |
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I made a half-dozen moves and got stuck. I had printed out your post on Medusa (your second post in this thread: http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2171&highlight=crayola)
So I stumbled and bumbled my way though the process and used it to solve the puzzle, or else I got lucky.
I have questions. Maybe I'll pester you via PMs if I can't find the answers on my own. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Dec 21, 2007 10:30 pm Post subject: |
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After basics there are a fairly obvious X-Wing and XY Wing, after which one arrives here:
| Code: | +-----------------+-------+---------------+
| 5 78 478 | 9 6 3 | 1478 178 2 |
| 1 34 2 | 7 8 5 | 9 34 6 |
| 6 9 378 | 4 2 1 | 378 378 5 |
+-----------------+-------+---------------+
| 47 18 158 | 6 3 2 | 57 9 14 |
| 237 37 9 | 5 1 4 | 6 237 8 |
| 234 6 15 | 8 7 9 | 35 235 14 |
+-----------------+-------+---------------+
| 37 1357 137 | 2 4 8 | 15 6 9 |
| 8 45 6 | 1 9 7 | 2 45 3 |
| 9 2 14 | 3 5 6 | 148 18 7 |
+-----------------+-------+---------------+ |
At this point, it is possible to solve it using a sequence of XY Chains. However, I found a single AIC that does the trick by determining that r9c3 must be <4>:
(4)r9c3=(4)r1c3-(4=3)r2c2-(3=7)r5c2-(7=4)r4c1-(4=1)r4c9-({18}=5)r4c23-(5=1)r6c3-(1=4)r9c3; r9c3=4
You can see how this works by considering r5c2. If it is <3>, then (via Box 1) r9c3 must be <4>. However, if r5c2 is <7>, then r4 resolves with r4c3=5, again making r9c3 <4>. |
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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 11:34 pm Post subject: |
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This is a good puzzle! Here's how I solved it:
First, there is a naked quad in B4. I am convinced I found it easily because I am slow to put in pencil marks. You are here:
| Code: | +----------------+----------------+----------------+
| 5 478 478 | 9 6 3 | 1478 1478 2 |
| 1 34 2 | 7 8 5 | 9 34 6 |
| 6 9 378 | 4 2 1 | 378 378 5 |
+----------------+----------------+----------------+
| 47 158 158 | 6 3 2 | 57 9 14 |
| 237 37 9 | 5 1 4 | 6 237 8 |
| 234 6 15 | 8 7 9 | 35 235 14 |
+----------------+----------------+----------------+
| 37 1357 1357 | 2 4 8 | 15 6 9 |
| 8 45 6 | 1 9 7 | 2 45 3 |
| 9 2 14 | 3 5 6 | 148 148 7 |
+----------------+----------------+----------------+ |
An X-wing on <4> in R28 leads to an XY-wing on <5> with pivot in R9C3.
We are here:
| Code: | +----------------+----------------+----------------+
| 5 78 478 | 9 6 3 | 1478 178 2 |
| 1 34 2 | 7 8 5 | 9 34 6 |
| 6 9 378 | 4 2 1 | 378 378 5 |
+----------------+----------------+----------------+
| 47 18 158# | 6 3 2 | 57# 9 14 |
| 237 37 9 | 5 1 4 | 6 237 8 |
| 234 6 15@ | 8 7 9 | 35 235 14 |
+----------------+----------------+----------------+
| 37 1357 -137 | 2 4 8 | 15@ 6 9 |
| 8 45 6 | 1 9 7 | 2 45 3 |
| 9 2 14 | 3 5 6 | 148 18 7 |
+----------------+----------------+----------------+ |
The cells @ are a W-wing with strong link # on <5>. This takes out <1> in R7C3. Which makes a pair <37> in R7.
An XYZ-wing takes out <7> in R1C3. After cleaning up, we are at:
| Code: | +-------------+-------------+-------------+
| 5 78B 48 | 9 6 3 |14-7 17 2 |
| 1 34 2 | 7 8 5 | 9 34 6 |
| 6 9 37b | 4 2 1 | 378 378 5 |
+-------------+-------------+-------------+
| 47a 18 158 | 6 3 2 | 57A 9 14 |
| 237 37 9 | 5 1 4 | 6 237 8 |
| 234 6 15 | 8 7 9 | 35 235 14 |
+-------------+-------------+-------------+
| 37b 15 37B | 2 4 8 | 15 6 9 |
| 8 45 6 | 1 9 7 | 2 45 3 |
| 9 2 14 | 3 5 6 | 148 18 7 |
+-------------+-------------+-------------+
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Starting coloring in R47C1, at least one of a or b is false, so either A and / or B is true <7>. Takes out <7> in R1C7.
Then, you have a choice: There is an XY-wing and an XYZ-wing, either finishes it off.
Nice puzzle!
Keith |
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