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Daily Telegraph 31/12/10
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peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Fri Dec 31, 2010 3:48 pm Post subject: Daily Telegraph 31/12/10

Code:

*-----------*
|..5|...|7..|
|..9|...|.1.|
|2.6|...|..3|
|---+---+---|
|6.7|.2.|.8.|
|4..|7.8|...|
|.1.|...|2.9|
|---+---+---|
|7..|...|6.8|
|.6.|...|1..|
|..2|.3.|4..|
*-----------*

This is my daily newspaper so I do them "ink pen" in situ - this was quite hard! Now to go back to see what I missed!

Happy New Year to everyone!

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Fri Dec 31, 2010 5:50 pm Post subject:

I'm almost scared to post, I've been burned so much lately, but I will anyways.

Quote:

A key was the 245678 sextet (some would say hidden pair) in box 2. An XY-Wing (254) didn't do anything. However, there was a potential DP 39-34-49 in boxes 258. Killers were either 6 in r6c4 or 6 or a pseudo cell 25 in r7c46. Said pseudo cell led to r7c5=4 which led to an invalidity; r7c5<>4

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Fri Dec 31, 2010 6:46 pm Post subject:

Marty, nice spot on the DP - I am sure you are right on the contradiction. Can I persuade to try to post some of the logic on your DP moves? -sometimes I struggle to follow the consequences through.

I found the same xy-wing and assorted xy-chain/loop, but this m-ring move cracked it for me...

Code:

*----------------------------------------------------------------------*
| 1 (48) 5 | 39 46(8) 39 | 7 24 26 |
| 3 (47) 9 | 2456 456(7) 2456-7 | 8 1 56 |
| 2 78-4 6 | 458 1 457 | 9 45 3 |
|----------------------+------------------------+----------------------|
| 6 9 7 | 15 2 15 | 3 8 4 |
| 4 2 3 | 7 9 8 | 5 6 1 |
| 5 1 8 | 346 46 346 | 2 7 9 |
|----------------------+------------------------+----------------------|
| 7 3 1 | 2459 45 2459 | 6 25 8 |
| 9 6 4 | 258 (7)(8)-5 257 | 1 3 25 |
| 8 5 2 | 16 3 16 | 4 9 7 |
*----------------------------------------------------------------------*
#1 m-ring-like(78) ; (7=4)r2c2-(4=8)r1c2 - r1c5=(8-7)r8c5=r2c5 -loop ; r3c2<>4, r8c5<>5, r2c6<>7
#2 skyscraper(5) c5, c8 ; r2c9<>5, r3c4<>5

Last edited by peterj on Sat Jan 01, 2011 9:43 am; edited 1 time in total

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Fri Dec 31, 2010 9:05 pm Post subject:

Quote:

Can I persuade to try to post some of the logic on your DP moves? -sometimes I struggle to follow the consequences through.

I don't know that I have a lot to say. There was the 39 pair in box 2 and I noticed that the 3 was an X-Wing, so the 34 or 36 pair was in box 5. Then I looked to see what was in box 8 and there was a 49 pair, so the box 5 would have to be a 34.

It was convenient that both cells in box 5 had the same killer of 6 and that box 9 had the 25 pseudo cell, so only two things had to be tested.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 01, 2011 12:05 am Post subject:

Marty R. wrote:

Quote:

Can I persuade to try to post some of the logic on your DP moves? -sometimes I struggle to follow the consequences through.

I see all of that, but r7c5<>4 is not a common outcome for each of the four extra candidates. However ...

(4=5)r7c5 - BUG-Lite(349)r167c46:[(qnp25)r7c468 = (6)r6c46] - (6=4)r6c5 - loop ==> r12c5<>4

... although it doesn't help much.

'qnp' stands for 'quantum naked pair', the combination of a bivalue in a quantum cell of the uniqueness pattern (your pseudo-cell) and a bivalue external to the uniqueness pattern.

[edit: Indicate continuous loop in AIC expression]

Last edited by ronk on Sat Jan 01, 2011 8:32 am; edited 1 time in total

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 2:02 am Post subject:

Quote:

I see all of that, but r7c5<>4 is not a common outcome for each of the four extra candidates. However ...

OK, I'll accept that, but what are you trying to say? When testing possibilities for killing a DP, is finding out that one leads to an invalidity less acceptable than finding a common outcome for each possibility?

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 01, 2011 3:02 am Post subject:

Marty R. wrote:

Quote:

I see all of that, but r7c5<>4 is not a common outcome for each of the four extra candidates. However ...

Perhaps but, with such imprecision, it's hard to know. What "one" leads to what "invalidity?"

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 4:50 am Post subject:

Quote:

Perhaps but, with such imprecision, it's hard to know. What "one" leads to what "invalidity?"

I hope I'm interpreting the question correctly. The pseudo cell of 25 in r7c46 forces r7c5=4 which leads to an invalidity, i.e., duplicates in a house.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 01, 2011 8:27 am Post subject:

Marty R. wrote:

Quote:

Perhaps but, with such imprecision, it's hard to know. What "one" leads to what "invalidity?"

I hope I'm interpreting the question correctly. The pseudo cell of 25 in r7c46 forces r7c5=4 which leads to an invalidity, i.e., duplicates in a house.

Which duplicates in which house?

Last edited by ronk on Sat Jan 01, 2011 11:39 am; edited 1 time in total

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Sat Jan 01, 2011 10:18 am Post subject:

Marty R. wrote:

Quote:

Can I persuade to try to post some of the logic on your DP moves? -sometimes I struggle to follow the consequences through.

Marty, thanks for the insight. I am OK on how you found the DP, I was wondering how involved was your logic to find the contradiction. I could not see anything simple - sure if I plug the numbers in then I end up with too many or too few of something somewhere. But there comes a point where I might as well have just plugged a number into a promising bivalue to see if it worked!

Fur fun here is a chain with memory (with help from an SE Dynamic Contradiction Forcing Chain!) that does "show" (with obvious contradictions!) that both outcomes of the DP lead to r7c5<>4 Laughing

Code:

BUG-Lite(349)r167c46
(6)r6c48 - (6=4)r6c5 ; r7c5<>4
||
QNP(25)r7c468 - (5=4)r7c5* - (4=6)r6c5* - r1c5=r1c9 - (6=5)r2c9 - *(465=7)r2c5 - r2c2=(7-8)r3c2=r3c4 - *(48=6)r1c5 - (6=4)r6c5 ; r7c5<>4

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Sat Jan 01, 2011 4:44 pm Post subject:

My first pass was a three stepper............ xy-wing 2-45 vertex (25)r7c8; r1c5<>4 ANP(45=7)r3c68-r8c6=(7-8)r8c5=r1c5-(8=4)r1c2-r1c8=(4)r3c8; r3c4<>4 xy-wing -568 vertex (68)r1c5 and pseudocell (56)r67c5; r2c5,r78c4<>5 Ted Now I intend to go read all the interesting activity already posted.

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 5:49 pm Post subject:

Quote:

Which duplicates in which house?

Here's one scenario. Note the two 5s in r2.

Code:

+-------+--------------+---------+
| 1 4 5 | 39 8 39 | 7 2 6 |
| 3 7 9 | 2456 5 2456 | 8 1 5 |
| 2 8 6 | 45 1 457 | 9 45 3 |
+-------+--------------+---------+
| 6 9 7 | 15 2 15 | 3 8 4 |
| 4 2 3 | 7 9 8 | 5 6 1 |
| 5 1 8 | 34 6 34 | 2 7 9 |
+-------+--------------+---------+
| 7 3 1 | 259 4 259 | 6 5 8 |
| 9 6 4 | 258 57 257 | 1 3 25 |
| 8 5 2 | 16 3 16 | 4 9 7 |
+-------+--------------+---------+

Play this puzzle online at the Daily Sudoku site

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Sat Jan 01, 2011 6:10 pm Post subject:

Marty, After basics, r7c5=45. If you assume r7c5=4, then you get the contradiction result you posted above; thus r7c5 must equal a 5 which completes the puzzle in one step. The entire process does not involve any aspect of a potential DP, other than the suggestion that it was interesting to evaluate r7c5=4 Ted.

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 6:17 pm Post subject:

tlanglet wrote:

Marty,

After basics, r7c5=45. If you assume r7c5=4, then you get the contradiction result you posted above; thus r7c5 must equal a 5 which completes the puzzle in one step. The entire process does not involve any aspect of a potential DP, other than the suggestion that it was interesting to evaluate r7c5=4

Ted.

Ted, I got there from the potential 39-34-49 DP. How else could I have known to test that?

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Jan 01, 2011 6:49 pm Post subject:

Code:

after basics
+-----------------------------------------------------------------------+
| 1 48 5 | 39 468 39 | 7 24 26 |
| 3 47 9 | 2456 4567 24567 | 8 1 56 |
| 2 478 6 | 458 1 457 | 9 45 3 |
|-----------------------+-----------------------+-----------------------|
| 6 9 7 | 15 2 15 | 3 8 4 |
| 4 2 3 | 7 9 8 | 5 6 1 |
| 5 1 8 | 346 46 346 | 2 7 9 |
|-----------------------+-----------------------+-----------------------|
| 7 3 1 | 2459 45 2459 | 6 25 8 |
| 9 6 4 | 258 578 257 | 1 3 25 |
| 8 5 2 | 16 3 16 | 4 9 7 |
+-----------------------------------------------------------------------+
# 50 eliminations remain

Starting with:

Code:

DP[(6)r6c46] - (6=4)r6c5 - (4)r7c5

-OR-

DP[(6)r6c46 = (25)r7c46+8] - (5=4)r7c5

Leaves us with two possibilities: r7c5<>4 or r7c5=4. Testing r7c5=4 results in forcing network assignments (*) and contradiction (#):

Code:

*--------------------------------------------------------------------*
| 1 *4 5 | 39 *8 39 | 7 *2 *6 |
| 3 #7 9 | 2456 #57 24567 | 8 1 #5 |
| 2 78 6 | 45 1 457 | 9 45 3 |
|----------------------+----------------------+----------------------|
| 6 9 7 | 15 2 15 | 3 8 4 |
| 4 2 3 | 7 9 8 | 5 6 1 |
| 5 1 8 | 34 *6 34 | 2 7 9 |
|----------------------+----------------------+----------------------|
| 7 3 1 | 259 *4 259 | 6 5 8 |
| 9 6 4 | 258 57 257 | 1 3 25 |
| 8 5 2 | 16 3 16 | 4 9 7 |
*--------------------------------------------------------------------*

Since the forcing network contradiction was derived from investigating the internal DP possibilities, this is different than Ted's approach of Kraken cell r7c5={4|5}.

Unfortunately, without specifics from Marty, it left the rest of us to fill in a lot of the solution.

===== ===== ===== ===== alternative solution eluded to by Peter

Code:

<25+4> XY-Wing r7c8/r1c8+r7c5 <> 4 r1c5

c59\r28 finned X-Wing <> 5 r8c46

+-----------------------------------------------------------------------+
| 1 48 5 | 39 68 39 | 7 24 26 |
| 3 47 9 | 2456 4567 24567 | 8 1 56 |
| 2 478 6 | 458 1 457 | 9 45 3 |
|-----------------------+-----------------------+-----------------------|
| 6 9 7 | 15 2 15 | 3 8 4 |
| 4 2 3 | 7 9 8 | 5 6 1 |
| 5 1 8 | 346 46 346 | 2 7 9 |
|-----------------------+-----------------------+-----------------------|
| 7 3 1 | 2459 45 2459 | 6 25 8 |
| 9 6 4 | 28 578 27 | 1 3 25 |
| 8 5 2 | 16 3 16 | 4 9 7 |
+-----------------------------------------------------------------------+
# 47 eliminations remain

(4=8)r1c2 (=645)r167c5 (=24)r71c8 - loop => r2c5<>46; r7c46<>5

The final step is my latest attempt at shorthand for an XY-Chain/Loop.

Marty: the XY-Wing was important after all.

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 7:40 pm Post subject:

Quote:

Unfortunately, without specifics from Marty, it left the rest of us to fill in a lot of the solution.

What specific information are you looking for, not that I can guarantee I'd be able to supply it. And what have we concluded from this discussion?

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 01, 2011 7:52 pm Post subject:

Marty R. wrote:

tlanglet wrote:

Ted, I got there from the potential 39-34-49 DP. How else could I have known to test that?

Marty, one uses a DP by showing that all internal extra candidates individually lead to the same outcome. Alternatively, one can show that all potential external DP busters lead to a common outcome. Doing either would be using logical deduction, as opposed to induction.

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Sat Jan 01, 2011 8:00 pm Post subject:

Marty R. wrote:

And what have we concluded from this discussion?

For me two conclusions ...
- Words are always imprecise and some sort of notation is necessary if the goal is to quickly convey a solution
- There is a spectrum of solution types from "pure" pattern plays, to AICs, to Kraken moves, to straight T&A. Many of the patterns we see - especially DPs and BrokenWings etc are just starting points for essentially forcing chains, sometimes contradictory chains as in this case, sometimes more "appealing" AICs using strong links from the pattern.

My other conclusion would be it's astonishing this simple little puzzle can engender quite so much variety in the approaches that people take to solve it! Long may it continue.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Jan 01, 2011 9:52 pm Post subject:

Marty R. wrote:

And what have we concluded from this discussion?

1) That it's hard to argue with a chain:

Code:

(4=6)r6c5 - DP[(6)r6c46 = (25)r7c46+8] - (5=4)r7c5 => r2c5<>4

2) Not all solutions can be reconstructed ... and it's the wise person who knows when not to try. Very Happy

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 01, 2011 10:52 pm Post subject:

Quote:

Are you saying that your difference between deduction and induction can depend on the result, not just the process?

Consider:

Code:

+-----------+-------+-------+
| . . . | . . . | . . . |
| 45 . 45 | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-------+-------+
| . . . | . . . | . . . |
| 456 . 458 | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Obviously, a 6 or 8 can kill this DP, so I test each one. (I still view this as a Forcing Chain except I found a place to start one rather than choosing one arbitrarily). So if a 6 and 8 produce a common outcome, that is logical deduction? If one leads to an invalidity, that's induction, presumably a finding with less cachet than the common outcome?

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