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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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 Posted: Wed May 28, 2008 6:01 am Post subject: colorful "very hard" |
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A little something to practice the basics and go beyond.
| Code: |
+-----------+-----------+-----------+
| 5 . 2 | . . 9 | . . . |
| . . . | . . 4 | 8 . . |
| . 9 1 | 3 . . | . . . |
+-----------+-----------+-----------+
| . . . | 8 . . | . . 6 |
| 1 . 3 | . . . | 7 . 2 |
| 7 . . | . . 1 | . . . |
+-----------+-----------+-----------+
| . . . | . . 8 | 2 4 . |
| . . 6 | 1 . . | . . . |
| . . . | 4 . . | 9 . 5 |
+-----------+-----------+-----------+
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play online
I used multi coloring (on 5, be sure to make all the eliminations)
and an xy-wing (the xy-wing 25-26-56 in boxes 2 and 5 opens after the 5 in r3c6 is removed by coloring)
enjoy! |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed May 28, 2008 6:26 am Post subject: |
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| Code: | .------------------.------------------.------------------.
| 5 4 2 | 7 8 9 | 6 1 3 |
| 6 3 7 | 25 1 4 | 8 25 9 |
| 8 9 1 | 3 256 256 | 45 257 47 |
:------------------+------------------+------------------:
| 29 25 4 | 8 357 37 | 1 359 6 |
| 1 68 3 | 569 4 56 | 7 589 2 |
| 7 68 59 | 2569 2356 1 | 45 3589 48 |
:------------------+------------------+------------------:
| 39 7 59 | 56 356 8 | 2 4 1 |
| 4 25 6 | 1 9 25 | 3 78 78 |
| 23 1 8 | 4 237 37 | 9 6 5 |
'------------------'------------------'------------------' |
{3,7} UR r49c56 means that r49c5 <>3, right off the blocks...
then one coloring elimination takes out 5 in r6c4. just for coloring sake.
xy-wing {2,5,7} (5=2)r8c6-(2=7)r9c5-(7=5)r4c5; means that r7c5 and r5c6 <>5, as marked below.
| Code: | .------------------.------------------.------------------.
| 5 4 2 | 7 8 9 | 6 1 3 |
| 6 3 7 | 25 1 4 | 8 25 9 |
| 8 9 1 | 3 256 256 | 45 257 47 |
:------------------+------------------+------------------:
| 29 25 4 | 8 *57 37 | 1 359 6 |
| 1 68 3 | 569 4 56 | 7 589 2 |
| 7 68 59 | 269 2356 1 | 45 3589 48 |
:------------------+------------------+------------------:
| 39 7 59 | 56 356 8 | 2 4 1 |
| 4 25 6 | 1 9 *25 | 3 78 78 |
| 23 1 8 | 4 *27 37 | 9 6 5 |
'------------------'------------------'------------------' |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed May 28, 2008 2:48 pm Post subject: |
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| storm_norm wrote: |
{3,7} UR r49c56 means that r49c5 <>3, right off the blocks...
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And indeed after the xy-wing no more coloring is even necessary.
But then, again, the newspaper I took this sudoku from never said their puzzles would have a unique solution ...  so in this particular case I tend to stay clear from the uniqueness arguments (so far I've not come across one with duplicates and I'm sure they syndicate from a decent source, but who knows ?) |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed May 28, 2008 10:25 pm Post subject: |
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I am still looking at this one, but let me note the following: After basics,
| Code: | +----------------+----------------+----------------+
| 5 4 2 | 7 8 9 | 6 1 3 |
| 6 3 7 | 25a 1 4 | 8 25b 9 |
| 8 9 1 | 3 256 256 | 45c 257 47 |
+----------------+----------------+----------------+
| 29 25 4 | 8 357 37 | 1 359 6 |
| 1 68 3 | 569 4 56 | 7 589 2 |
| 7 68 59e |2-569 2356 1 | 45d 3589 48 |
+----------------+----------------+----------------+
| 39 7 59f |-56 356 8 | 2 4 1 |
| 4 25 6 | 1 9 25 | 3 78 78 |
| 23 1 8 | 4 237 37 | 9 6 5 |
+----------------+----------------+----------------+ |
I would not mention it, except I saw it in another puzzle yesterday.
ab are a pair, cd are a pair. b and c are in the same house. If you think about it, any cell that sees both a and d cannot be <5>.
Coupled pairs? It goes further, to the pair e and f. Any cell that sees both a and f cannot be <5>.
Now, we are here:
| Code: | +----------------+----------------+----------------+
| 5 4 2 | 7 8 9 | 6 1 3 |
| 6 3 7 | 25a 1 4 | 8 25b 9 |
| 8 9 1 | 3 256 256 | 45c 257 47 |
+----------------+----------------+----------------+
| 29 25 4 | 8 357 37 | 1 359 6 |
| 1 68 3 | 59@ 4 56 | 7 589 2 |
| 7 68 59@ | 2-9 2356 1 | 45d 3589 48 |
+----------------+----------------+----------------+
| 39 7 59 | 6 35 8 | 2 4 1 |
| 4 25 6 | 1 9 25 | 3 78 78 |
| 23 1 8 | 4 237 37 | 9 6 5 |
+----------------+----------------+----------------+ |
The two cells @ are sort of a W-wing excited by the chain abcd: R6C4 cannot be <9>.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed May 28, 2008 10:31 pm Post subject: |
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And, an XYZ-wing finishes it off.
I suppose my coupled pairs are actually a skyscraper / kite. And, the extension is multi-coloring.
The W-wing excited by a skyscraper? I don't know, but I believe it is not necessary to solve this puzzle.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu May 29, 2008 5:35 pm Post subject: |
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| Quote: | {3,7} UR r49c56 means that r49c5 <>3, right off the blocks...
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Can you run that by me again - I'm not sure what you mean by <>3. I can't see a UR here - even a Type 3.
Cheers |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu May 29, 2008 8:08 pm Post subject: |
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| cgordon wrote: | | Quote: | {3,7} UR r49c56 means that r49c5 <>3, right off the blocks...
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Can you run that by me again - I'm not sure what you mean by <>3. I can't see a UR here - even a Type 3.
Cheers |
cgordon,
"<>" is how I write "not equal".
if you look at my grid, in col 6 you will notice the {3,7} pair in row 4 and row 9.
then in col 5 you will notice the same pair in those same two rows.
in col 5, the 7's are conjugate ( they are the only two 7's in col 5) this tells us that a 7 must go in either r49c5.
the deadly pattern arises when {3,7} is left in all of the four cells which would give us more than one solution.
so we can safely remove the 3's from r49c5 in order to break up the deadly pattern.
I believe this is a type 4 UR.
----
nataraj,
good puzzle for different approaches in solution paths.  |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu May 29, 2008 8:47 pm Post subject: |
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| Quote: | | so we can safely remove the 3's from r49c5 in order to break up the deadly pattern. |
Norm: There's the rub. I've had severe difficulties with these type 4s recently. Some chaps tried explaining them to me - and I established a rote procedure. I now see my procedure applies just fine in this case. I guess I just need practice.
Cheers. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri May 30, 2008 2:33 pm Post subject: |
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| keith wrote: | And, an XYZ-wing finishes it off.
I suppose my coupled pairs are actually a skyscraper / kite. And, the extension is multi-coloring.
The W-wing excited by a skyscraper? I don't know, but I believe it is not necessary to solve this puzzle.
Keith |
Keith,
Is this a "finned kite" with the fin being r3c8? It functions it that manner. Otherwise, multi-coloring eliminates the <5> in r6c4.
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri May 30, 2008 11:57 pm Post subject: |
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| Quote: | I would not mention it, except I saw it in another puzzle yesterday.
ab are a pair, cd are a pair. b and c are in the same house. If you think about it, any cell that sees both a and d cannot be <5>. |
keith,
as a matter of fact, you are stringing together xy-chains. hate to spoil the fun, but all of the cells have exactly two candidates which defines the cells you need to use to form a xy-chain.
notice the links between candidates below. the if/then nature of the chain makes the end 5's pincers.
this is your next chain, a little longer...
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 31, 2008 2:15 pm Post subject: |
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| Quote: | | hate to spoil the fun |
You're not spoiling anything. I find these things by looking for patterns. These linked pairs struck me as a little unusual.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 31, 2008 10:20 pm Post subject: |
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| tlanglet wrote: | | keith wrote: | And, an XYZ-wing finishes it off.
I suppose my coupled pairs are actually a skyscraper / kite. And, the extension is multi-coloring.
The W-wing excited by a skyscraper? I don't know, but I believe it is not necessary to solve this puzzle.
Keith |
Keith,
Is this a "finned kite" with the fin being r3c8? It functions it that manner. Otherwise, multi-coloring eliminates the <5> in r6c4.
Ted |
Ted,
I am not sure what a "Finned Kite" is. R3C8 does not figure in my argument here.
Keith |
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