dailysudoku.com :: View topic - oct 3 competition

dailysudoku.com
Discussion of Daily Sudoku puzzles

FAQ

Memberlist

Usergroups

Profile

oct 3 competition

dailysudoku.com Forum Index -> Other puzzles

View previous topic :: View next topic

Author

Message

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Fri Oct 03, 2008 5:33 am Post subject: oct 3 competition

Code:

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

the difficulty of this one is a refreshing jolt to the system after several weeks of dissatisfaction from the competition puzzles.

nataraj

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

Posted: Fri Oct 03, 2008 7:10 am Post subject:

refreshing, yes.
So far, I have:
- overlapping xy-wings box 1 and 3, 25-58-28-25, sets r1c1=2, r3c1=5.
- a UR (12) combined with x-wing (1): r7c6<>2
- a UR (78) /w SL (8): r9c9<>7
- one m-wing (9) r8c6=r5c5 via SL (5) in col 5: r5c6<>9
- an xy-chain / extended xy-wing 28-[58-59]-29: r3c5<>2

Code:

+--------------------------+--------------------------+--------------------------+
| 2 7 1 | 389 59# 359 | 6 4 58# |
| 3 8 4 | 12 6 125 | 9 257 57 |
| 5 9 6 | 278 -247 24 | 28* 3 1 |
+--------------------------+--------------------------+--------------------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 29* 26 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+--------------------------+--------------------------+--------------------------+
| 9 4 78 | 1267 257 156 | 3 257 5678 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 78 | 2367 247 2346 | 28 9 68 |
+--------------------------+--------------------------+--------------------------+

the possible DP 78-67-68 in boxes 7,8,9 might be useful, I just do not see, how, at the moment. Maybe other xy-chains? Hm.

We'll see

Asellus

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

Posted: Fri Oct 03, 2008 10:27 am Post subject:

This one is certainly tougher than it looks. I got to the same place as nataraj though by a somewhat different route.

Code:

+------------+------------------+----------------+
|#2-5 7 1 | 2389 259 2359 | 6 4 a58 |
| 3 8 4 | 12 6 125 | 9 257 57 |
|a25 9 6 | 278 2457 245 |a28 3 1 |
+------------+------------------+----------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 29 269 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+------------+------------------+----------------+
| 9 4 78 | 1267 257 1256 | 3 b257 5678 |
| 6 2 3 | 79 8 59 | 1 b57 4 |
| 1 5 b78 | 2367 247 2346 |b28 9 @6-78 |
+------------+------------------+----------------+

After basics there is a 258 XY Wing (marked "a") to remove <5> from r1c1. Then, there is a ALS elimination ("b") that removes <7> from r9c9: The {278} in r9 and {257} in c8 have shared exclusive <2> and shared common <7>. [Note: This can also be viewed as a "Finned XY Wing" with fin <5> in r7c8.]

Code:

+----------+------------------+---------------+
| 2 7 1 | 389 a59 359 | 6 4 58 |
| 3 8 4 |a12 6 a125 | 9 257 57 |
| 5 9 6 | 278 @-247 24 | 28 3 1 |
+----------+------------------+---------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 a29 #26-9 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+----------+------------------+---------------+
| 9 4 78 | 1267 257 1256 | 3 257 5678 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 78 | 2367 247 2346 | 28 9 68 |
+----------+------------------+---------------+

Now there is another ALS elimination ("a") of <2> in r3c5: {125} in r2 and {259} in c5 have shared exclusive <5> and shared common <2>. (This, too, can be viewed as a "Finned XY Wing".)

I noticed the same M-Wing as nataraj, which removes <9> from r5c6 (#). This is the point nataraj reached.

Code:

+----------+--------------------+---------------+
| 2 7 1 | 389 d59 359 | 6 4 e58 |
| 3 8 4 | 12 6 125 | 9 257 57 |
| 5 9 6 | 278 j47 i24 |h28 3 1 |
+----------+--------------------+---------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 |b269 c29 26 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+----------+--------------------+---------------+
| 9 4 78 | 1267 #25-7 1256 | 3 257 f5678 |
| 6 2 3 |a79 8 59 | 1 57 4 |
| 1 5 H78 |#236-7 #24-7 @234-6 |g28 9 f68 |
+----------+--------------------+---------------+

Ignore all the annotations in the grid for a moment and notice the 5-cell XY Chain from r5c6 via c5-r1-c9 to r9c9 that removes <6> from r9c6 (@).

Now for the annotations: A branched AIC removes the <7>s marked #. The chain branches after "g" to continue with "H" and "h":

(7=9)r8c4 - (9)r5c4=(9)r5c5 - (9=5)r1c5 - (5=8)r1c9 - (8)r79c9=(8)r9c7 -> Branches

Branch H: - (8=7)r9c3; removes <7> at r9c45
Branch h: - (8=2)r3c7 - (2=4)r3c6 - (4=7)r3c5; removes <7> at r79c5

This chain is entirely XY Chain except for the strong <9> pair in r5 and the grouped strong link on <8> in b9.

After this there is a 257 XYZ Wing in r78 that removes <5> from r7c9. But that still doesn't solve it!

Code:

+-------+------------------+--------------+
| 2 7 1 | 389 b59 b359 | 6 4 58 |
| 3 8 4 |c12 6 c125 | 9 27 57 |
| 5 9 6 |d28 7 4 |e28 3 1 |
+-------+------------------+--------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 29 26 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+-------+------------------+--------------+
| 9 4 8 | 1267 25 1256 | 3 257 67 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 7 | 236 4 a23 |#-28 9 68 |
+-------+------------------+--------------+

I used one more AIC, an ALS Chain, which is the same as XY Chain except not limited to single-cell ALS (i.e. bivalues):

(2=3)r9c6 - ALS[(3)r1c6=(5)r1c56] - ALS[(5)r2c6=(2)r2c46] - (2=8)r3c4 - (8=2)r3c7; r9c7<>2

That finishes it!

nataraj

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

Posted: Fri Oct 03, 2008 2:19 pm Post subject:

There is a post by Asellus now, which I think I'll read after posting my path. No peeking, I promise!

- After that xy-chain/extended xy-wing, all I could find was one more xy-chain. Sad

It connects r5c6 via col 5 and row 1 to r9c9 and kills 6 in r9c6.

... which gets us to here:

Code:

+--------------------------+--------------------------+--------------------------+
| 2 7 1 | 389 59# 359 | 6 4 58# |
| 3 8 4 | 12 6 125 | 9 257t 57 |
| 5 9 6 | 278 47 24 | 28* 3 1 |
+--------------------------+--------------------------+--------------------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 29* 26 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+--------------------------+--------------------------+--------------------------+
| 9 4 78 | 1267 -257 156 | 3 257T 5678 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 78 | 2367 247 234 | 28 9 68 |
+--------------------------+--------------------------+--------------------------+

there is a useless xy-chain / extended xy wing between r3c7 and r5c5:
28-(58-59)-29.
No elimination can be performed directly, but one of the pincers can be transported (through col. 8 ) and 2 in r7c5 is toast

(2)r7c5-r7c8=r2c8-r3c7=[xy-chain]=r5c5-r7c5; r7c5<>2

Some cleanup, then coloring on (2) (SLs in box 3, row 7): r3c4<>2
One more xy-wing (59-57-79 in col.5/box 8 ): r1c4<>9
brings us here:

Code:

+--------------------------+--------------------------+--------------------------+
| 2 7 1 | 38 59 359 | 6 4 58 |
| 3 8 4 | 12 6 125 | 9 257 57 |
| 5 9 6 | 78 -47 24* | 28# 3 1 |
+--------------------------+--------------------------+--------------------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 29 26 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+--------------------------+--------------------------+--------------------------+
| 9 4 8 | 126 57 16 | 3 257 567 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 7 | 236 24* 23-4 | 28# 9 68 |
+--------------------------+--------------------------+--------------------------+

A rather conspicuous w-wing (4)r9c5=r3c6 via col. 7 removes 4 from r3c5 and r9c6

Singles from there.

(now I'll go look at Asellus' post Smile

)

Edit 1838 GMT+2: I did. Amazing! After the initial xy-chain, totally different approach. I think I should learn to see those ALSs in their possible relationships. So far, too much effort for no return at all. Best I can do is re-trace someone else's steps.

Asellus

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

Posted: Fri Oct 03, 2008 9:40 pm Post subject:

nataraj wrote:

I think I should learn to see those ALSs in their possible relationships. So far, too much effort for no return at all. Best I can do is re-trace someone else's steps.

Tracing someone else's steps is a good way to learn. But, let's see if I might be able to shed any additional light.

Regarding those two ALS eliminations (XZ Wings, I believe some call them), I already mentioned that they can be seen as finned XY Wings since that, in fact, is how I first spotted them. (If an XY(Z) Wing hunt is not being productive, I start looking for fins.)

But, there is yet another way to view them that uses the binary "pseudo-cell" notion that has been bandied about here recently. Any ALS can be seen as one or more binary pseudo-cells. In the case of the smallest ALS, it is just an actual binary (no "pseudo"). With multi-cell ALS, we get a variety of "pseudo" binaries.

Take that 2578 ALS elimination of <7> from r9c9 in the first grid of my post. Let's consider the {257} ALS in r78c8. We can see this as any one of three pseudo-binaries: {25}; {27}; {57}. (Take my word for it for a moment in case it isn't obvious.) But in r9, we have the binaries {78} and {28}. All we need to complete an XY Wing on the {28} end is a {27} binary peer of the {28} at r9c7. The {27} ALS pseudo-binary in r78c8 satisfies this need. Thus, we have an XY Wing using that {27} "pseudo-cell" to eliminate the <7> in r9c9.

The ALS elimination in the second grid can be viewed the same way. The {29} and {59} in c5 combine with the {25} pseudo-binary in r2c46 to provide the XY Wing that eliminates <2> in r3c5.

The only difference between this "XY Wing" way of seeing it and the XZ Wing ALS way of seeing it is that in the ALS view the two actual binaries are viewed as a 2-cell, 3-digit ALS that forms its own pseudo-cell. So, in the first case, we have a {27} pseudo-binary in r9 and a {27} pseudo binary in c8 that are weakly linked by the <2>s in box 9 (the "shared exclusives"). Thus, the <7>s (the "shared commons") have a strong inference and work as pincers. In the second case, we have a {25} pseudo-binary in c5 and another in r2 with the <5>s weakly linked in box 2.

(All XY and XYZ Wings can be viewed in this same "XZ Wing" ALS way. That's because XY and XYZ Wings are just the simplest examples of the more general 2-ALS or "XZ Wing" technique. It can be helpful to "re-learn" them in this way.)

The two digits of a binary cell have a strong inference (they can't both be false). (They also have a weak inference since they are conjugate; but that isn't of interest at the moment.) So we can write (7=8)r9c3 and (8=2)r9c7. We can write the pseudo-binaries of any ALS similarly. The difference is that we have to take care to group any digit that occurs more than once. So, in the r78c8 {257} ALS considered as a {27} pseudo-binary, we must group the <7>s thusly: (7)r78c8. We can now write our {27} pseudo-binary strong link: ALS[(2)r7c8=(7)r78c8]. That is just a way of writing the pseudo-binary in Eureka notation.

So, our XY-Wing with the {27} pseudo-cell in Eureka is:
(7=8)r9c3 - (8=2)r9c7 - ALS[(2)r7c8=(7)r78c8]

Because of the grouped <7>s in the pseudo-cell, we have 3 pincer <7>s rather than 2. The victim must be a peer of all three (i.e., must be weakly linked to both ends of this "wing"). To help make certain, we can include the victim(s) in the full discontinuous loop notation:
(7)r9c9 - (7=8)r9c3 - (8=2)r9c7 - ALS[(2)r7c8=(7)r78c8] - (7)r9c9; r9c9<>7

Seen as an XZ Wing ALS elimination, the Eureka notation should now be evident:
(7)r9c9 - ALS[(7)r9c3=(2)r9c7] - ALS[(2)r7c8=(7)r78c8] - (7)r9c9; r9c9<>7

We see the two ALS pseudo binaries easily in the notation, with their weakly linked <2>s joining them.

These ALS pseudo binaries work the same way in ALS Chains, which are really otherwise identical to XY Chains. That final chain in my post above should make this clear.

All that remains is to explain how an ALS can be such a pseudo-binary, in case it isn't obvious. All instances of any one digit in an ALS can be false, leaving a locked set. However, if all instances of any two digits in an ALS were false, there wouldn't be enough digits remaining to satisfy the cells. Thus, it is impossible for all instances of any two digits of an ALS both to be false. This means that they are strongly linked. That is our pseudo-binary.

(Various weak inference links can also be formed within ALS. However, this is a bit more complex and not so often useful.)

I hope this helps at least a couple of light bulbs to start glowing for those interested in learning to use the power of Almost Locked Sets in sudoku solving.

PS: I imagine that the puzzle above would be a good one for applying Medusa multi-coloring. In fact, that is probably the easiest way to solve it.

Asellus

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

Posted: Fri Oct 03, 2008 10:44 pm Post subject:

Medusa multi-coloring is MUCH easier.

Code:

+-----------+-------------------+------------------+
| 2 7 1 | 38a9 5c9C 359 | 6 4 5a8A |
| 3 8 4 | 12 6 125 | 9 2a57 57 |
| 5 9 6 | 278A -24B7 2B4b | 2A8a 3 1 |
+-----------+-------------------+------------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 269 2C9c 269 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+-----------+-------------------+------------------+
| 9 4 78 | 1267 -25C7 1256 | 3 2A-57 5678 |
| 6 2 3 | 79 8 59 | 1 57 4 |
| 1 5 7-8 | 2367 -24b7 234B6 | 2a8A 9 678 |
+-----------+-------------------+------------------+

I started with an Aa cluster in the <8>s. The Bb cluster has a weak AB link to Aa in r3, and the Cc cluster a weak ac link to Aa in r1. Thus, we have the strong pairs: ab, AC and, by induction, bC.

There is an AC trap of the <2>s in r37c5. The <2> in r3c5 sees 2A and 2C. The <2> in r7c5 sees 2A and 5C. The <5> in r7c8 is trapped in the same way.

There is a bC trap of <2> in r9c5 (it sees 2C and 4b).

Next, with <5> gone from r7c8, there is a 278 XY Wing in r79 that removes <8> from r9c3.

All of these eliminations lead here:

Code:

+-------+-------------+------------------+
| 2 7 1 | 38a 9 35 | 6 4 5a8A |
| 3 8 4 | 12 6 125 | 9 2a7 57 |
| 5 9 6 | 28A 7 4 | 2A8a 3 1 |
+-------+-------------+------------------+
| 7 3 2 | 4 1 8 | 5 6 9 |
| 4 1 5 | 9 2 6 | 7 8 3 |
| 8 6 9 | 5 3 7 | 4 1 2 |
+-------+-------------+------------------+
| 9 4 8 | 126 5 12 | 3 2A7a 67 |
| 6 2 3 | 7 8 9 | 1 5 4 |
| 1 5 7 | 236 4 23 | 2a8A 9 68 |
+-------+-------------+------------------+

Continued coloring of the Aa cluster will solve it. But, we can also use that Type 6 12 UR, which leads to a BUG+1.

Display posts from previous:

	dailysudoku.com Forum Index -> Other puzzles	All times are GMT
Page 1 of 1

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum