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another random from sudokupuzz

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Mar 05, 2008 3:01 am    Post subject: another random from sudokupuzz Reply with quote

ran into another tough one so I posted it for those that want a challenge. ok, that is an understatement, its a big challenge.

Code:
+-------+-------+-------+
| . . 7 | 8 . . | 2 . . |
| . 5 . | . 7 . | 3 9 . |
| . 9 . | . . . | . . 1 |
+-------+-------+-------+
| 1 . . | . . 3 | . 6 . |
| . . . | . 8 . | . . . |
| . 8 . | 4 . . | . . 7 |
+-------+-------+-------+
| 9 . . | . . . | . 2 . |
| . 4 2 | . 3 . | . 5 . |
| . . 6 | . . 9 | 4 . . |
+-------+-------+-------+



random puzzle from...
http://www.sudokupuzz.com/?js_sudoku_t=fiendish


Code:
36     136    7      | 8      9      16     | 2      4      5
2468   5      148    | 126    7      1246   | 3      9      68
2468   9      48     | 3      246    5      | 76     78     1
------------------------------------------------------------------
1      27     49     | 79     5      3      | 8      6      24
34567  2367   3459   | 1679   8      167    | 59     13     24
356    8      359    | 4      126    126    | 59     13     7
------------------------------------------------------------------
9      137    1358   | 1567   146    4678   | 167    2      368
78     4      2      | 167    3      678    | 167    5      9
3578   137    6      | 1257   12     9      | 4      78     38


this grid is after coloring on 1 which is where I am going to have to start medusa

enjoy,
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Mar 05, 2008 12:27 pm    Post subject: Reply with quote

Code:
 *-------------------------------------------------------*
 |&36    &136   7     | 8     9    16    | 2    4   5    |
 | 2468   5     148   | 126   7    1246  | 3    9   68   |
 | 2468   9     48    | 3     246  5     | 67   78  1    |
 |--------------------+------------------+---------------|
 | 1      27    49    | 79    5    3     | 8    6   24   |
 |&34567 &2367 *3459  | 1679  8    167   |*59   13  24   |
 | 356    8    *359   | 4     126  126   |*59   13  7    |
 |--------------------+------------------+---------------|
 | 9      137   1358  | 1567  146  4678  | 167  2   368  |
 | 78     4     2     | 167   3    1678  | 167  5   9    |
 | 3578   137   6     | 1257  12   9     | 4    78  38   |
 *-------------------------------------------------------*

coloring (3 SL) 1 => r8c6<>1, UR 36 => r5c1<>3, UR 59 => r5c3<>5
Code:
 *-------------------------------------------------------*
 | 36     136   7     | 8     9    16    | 2    4   5    |
 | 2468   5     148   | 126   7    1246  | 3    9   68   |
 | 2468   9     48    | 3     246  5     | 67   78  1    |
 |--------------------+------------------+---------------|
 | 1      27    49    | 79    5    3     | 8    6   24   |
 | 4567   2367  349   | 1679  8    167   | 59   13  24   |
 | 356    8     359   | 4     126  126   | 59   13  7    |
 |--------------------+------------------+---------------|
 | 9      137   1358  | 1567  146  4678  | 167  2   368  |
 | 78     4     2     | 167   3    678   | 167  5   9    |
 | 3578   137   6     | 1257  12   9     | 4    78  38   |
 *-------------------------------------------------------*

r7c3=1 => r9c1=5 => r16c1=36 => r23c1,r3c3=248 => r2c3=1
Code:
 *-----------------------------------------------------*
 | 36    36    7     | 8     9    1     | 2    4   5   |
 | 248   5     1     | 26    7    246   | 3    9   68  |
 | 248   9     48    | 3    @246  5     |#67  *78  1   |
 |-------------------+------------------+--------------|
 | 1    *27    49    |*79    5    3     | 8    6   24  |
 | 4567  2367  349   | 1679  8   #67    | 59   13  24  |
 | 356   8     359   | 4    @126  26    | 59   13  7   |
 |-------------------+------------------+--------------|
 | 9     137   358   | 1567  14   4678  | 167  2   36  |
 | 78    4     2     | 167   3    678   | 167  5   9   |
 | 357   137   6     | 1257  12   9     | 4   *78  38  |
 *-----------------------------------------------------*

w-wing 67, 7 transported to r4c2 and r9c8 => r9c2<>7
Code:
 *-----------------------------------------------------*
 | 36    36    7     | 8     9    1     | 2    4   5   |
 | 2-48  5     1     | 26    7   #246   | 3    9   68  |
 | 248   9    #48    | 3     2-46 5     | 67   78  1   |
 |-------------------+------------------+--------------|
 | 1     27    49    | 79    5    3     | 8    6   24  |
 | 4567  2367  349   | 1679  8    67    | 59   13  24  |
 | 356   8     359   | 4     126  26    | 59   13  7   |
 |-------------------+------------------+--------------|
 | 9     137  #358   | 1567  14  #4678  | 167  2   36  |
 | 78    4     2     | 167   3    678   | 167  5   9   |
 | 357   13    6     | 1257  12   9     | 4    78  38  |
 *-----------------------------------------------------*

r3c3=8 => r7c6=8 => r2c6=4
=> r2c1<>4, r3c5<>4
Code:
 *---------------------------------------------------*
 |#36   -36    7     | 8     9   1    | 2    4   5   |
 | 28    5     1     | 26    7   4    | 3    9   68  |
 | 248   9     48    | 3    #26  5    | 67   78  1   |
 |-------------------+----------------+--------------|
 | 1     27    49    | 79    5   3    | 8    6   24  |
 | 4567  2367  349   | 1679  8   67   | 59   13  24  |
 |#356   8     359   | 4    #16  2    | 59   13  7   |
 |-------------------+----------------+--------------|
 | 9     137   358   | 1567  4   678  | 167  2   36  |
 | 78    4     2     | 167   3   678  | 167  5   9   |
 |-357  #13    6     | 1257 #12  9    | 4    78  38  |
 *---------------------------------------------------*

r1c1=6 => r6c5=6 => r3c5=2 => r9c5=1 => r9c2=3
r1c2<>3, r9c1<>3
Code:
 *-------------------------------------------------*
 | 3     6    7    | 8     9   1    | 2    4   5   |
 | 28    5    1    | 26    7   4    | 3    9   68  |
 | 248   9    48   | 3    #26  5    | 67   78  1   |
 |-----------------+----------------+--------------|
 | 1     27   49   | 79    5   3    | 8    6   24  |
 | 4567  237  349  | 1679  8   67   | 59   13  24  |
 |#56    8    359  | 4     1-6 2    | 59   13  7   |
 |-----------------+----------------+--------------|
 | 9     137  358  | 1567  4   678  | 167  2   36  |
 | 78    4    2    | 167   3   678  | 167  5   9   |
 |#57   #13   6    | 1257 #12  9    | 4   #78 #38  |
 *-------------------------------------------------*

xy-chain: r3c5=2 => ... => r6c1=6
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Mar 05, 2008 7:00 pm    Post subject: Reply with quote

Quote:
r2c1=1 => r7c3=1 => r9c1=5 => r16c1=36 => r23c1|r3c3=248 => r2c3=1


Ravel,

very nice, just to clarify some things... would the first cell in your quote be r2c3?? and not r2c1??

also...

Quote:
UR 59 => r5c3<>5


I can't find any examples that point to an exact type of UR that falls under.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Mar 05, 2008 10:56 pm    Post subject: Reply with quote

Some steps/details omitted from the solutions posted above:

(1) Kite or ER or basic coloring removed <1> from r7c6.

(2) The <1> coloring that removes <1> from r8c6 is multi-coloring (weak link in r7). This might not be apparent to some.

After ravel's <1> elimination in r7c3, there are two steps not shown that get to the next grid:

(1) <8> Skyscraper in c38.

(2) Kite, ER or <6> coloring removes the <6> in r7c5, making the next W-Wing step possible.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Mar 06, 2008 11:18 am    Post subject: Reply with quote

Thanks Asellus, for completing the solution path.

storm_norm wrote:
Quote:
r2c1=1 => r7c3=1 => r9c1=5 => r16c1=36 => r23c1|r3c3=248 => r2c3=1


Ravel,

very nice, just to clarify some things... would the first cell in your quote be r2c3?? and not r2c1??

Its a contradiction chain, that shows, that r2c1 cannot be 1. I have spotted it this way, later i saw that the first link is not needed (r2c1=1 => r7c3=1) and deleted it. Now it says that r7c3 cannot be 1, with the same effect, namely r2c3 must be 1.
To explain it in words:
If r7c3=1, then (because of the strong link for 5 in box 7), r9c1=5, which leads to the pair 36 in r16c1 (r6c1<>5). Thus the 6 is locked to these cells in column 1 and cannot be in r23c1. This gives a triple 248 in box 1 in the cells r23c1 and r3c3, which locks 48 to these cells. Thus only the 1 remains in r2c3. This is a contradiction to the starting point r7c3=1 (two 1's in the same column), which cannot be true therefore.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Mar 06, 2008 12:37 pm    Post subject: Reply with quote

ravel wrote:

Its a contradiction chain, ...


Would that be the same as a forcing chain, then?
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Mar 06, 2008 4:01 pm    Post subject: Reply with quote

In the (very) old sense forcing chains started from a bivalue cell A(xy) and only used bivalue cells. They had the form
A=x => .. => C=z
A=y => .. => C=z

or (E could have more candidates)
A=x => .. => E<>z
A=y => .. => E<>z

The next step were triple forcing chains (from three value cells) and those starting with conjugate pairs or all 3 occurences of a number in a unit.

Then some people also included conjugate links, others also subsets on the way.
Others call every chain elimination a forcing chain. So its the same chaos here.

Forcing chains can always be expressed as contradiction chains. E.g the first one, for the first line use (A=>B) <=> (not B => not A):
C<>z => A<>x => A=y => C=z, contradiction

But i cant see in the moment, how to write my contradiction chain as forcing chain, though probably there will be some way.

It could be expressed as AIC with the link (1)r79c2=(1)r7c3- ... -(48=1)r2c3, but it turned out, that i am too lazy to learn to write that correctly Embarassed
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Mar 06, 2008 4:52 pm    Post subject: Reply with quote

thanks, ravel, for the explanation. "...same chaos" - that about seems so sum it up.

I find myself using the same type of inference logic all the time while scanning the grid for useable attacks once the "regular" techniques don't yield easy results any more (bout the time I start looking for xy-chains).
Nothing really formal, just take a cell, look at linked cells, see where it leads, look at another cell, and so on.

Often when I find something it turns out to be a regular xy-wing. Many times it takes the form of pincers that are connected. Those chains, even if they involve some sort of branching or grouped links seem to be well accepted. Sometimes what I find is just a logical inference, mostly a contradiction. That's when I get that guilty feeling and I am loath to use the solution, and instead keep looking for a more "acceptable" one that does not involve the bad forcing / T&E way. Of course, if nothing turns up, I am happy to use what I found and solve the puzzle. I did, after all, find it.
"Go with what works". Maybe it's just that I find it hard to communicate such a solution.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Mar 06, 2008 9:29 pm    Post subject: Reply with quote

When I posted before, I was going to complement ravel on the nice use of ALS (Almost Locked Set) chaining. So, I will now. ALSs can often be exploited in chains such as this and it's really not so difficult to do. Like ravel, when I get to a point in tough puzzles where the usual tools no longer help, I start examining the ALSs to see if they look like they can help. ravel's chain uses 3 ALSs in sequence, plus that pair of strongly-linked <5>s. Seeing that those <5>s can be used is probably the tricky bit for many.

This chain is certainly an AIC (Alternate Implication Chain) and can be notated thusly:

(1-5)r7c3=(5)r9c1-(5={36})r16c1-(6)r23c1=({248})r23c1|r3c3-({48}=1)r2c3-(1)r7c3; r7c3<>1

Out of interest, I solved this puzzle, ignoring those URs, by using only Medusa multicoloring ("MMC"). It makes a good puzzle for practicing that technique. MMC does not reveal ALS-based AICs because of the grouped links. Interestingly, the <1> in r7c3 is also eliminated by MMC, but via a completely different AIC.
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