## Help with "moderate" puzzle

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### Help with "moderate" puzzle

Hi

Help with the following would be much appreciated. I just can't see what the next logical step is

4** *13 **8
*58 7** 1*4
1** **4 9**
89* 2*7 4*1
*41 *** 27*
7*2 451 *89
*17 3** 846
**4 178 592
28* 64* *1*

Thanks,

June
Prunie

Posts: 5
Joined: 30 July 2005

### try hypothesis in the square with less gaps

Squares:

(0,0) (1,0) (2,0)
(0,1) (1,1) (2,1)
(0,2) (1,2) (2,2)

The square with less gaps is : (2,2).

Only there are two different hypotheses:

846
592
317

and

846
592
713

Try the first hypothesis and the rest of sudoku is trivial
supertorpe

Posts: 2
Joined: 30 July 2005

### Trial and error

Tso

Sorry that I have posted an incomplete reply due to lack of time.

Your solution using forcing chains is just as 'trail and error' as Supertorpe's solution.

Supertorpe's 'trial and error' is a direct and obvious one, but yours is subtle and happened behind the scene. I agree that the forcing chains you used to deduce the number is logical and it just look so simple after the final chains are listed. However, I will find it hard to believe that you are able to pinpoint exactly the chains that would lead to a solution the first time every time, as we know that these chains do not follow a set patten. You would have to try a few or quite a few chains and follow them through to see which ones would give you a solution. If not, you would have to try again, and again.......... It is this chain finding process that is 'trial and error'.

With this grid, you don't have to use forcing chains. After removing the 3 in r4c8, there is a xy-wing in r4c5,c8 & r5c5,c9 which would give you 3 in a few places. Subsequently apply colours to 6s and the complete puzzle is solved.
Jeff

Posts: 708
Joined: 01 August 2005

This one was actually pretty hard.

Puzzle as given:

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

The candidates are:
Code: Select all
`{4}    {267}  {69}   {59}   {1}    {3}    {67}   {256}  {8}    {369}  {5}    {8}    {7}    {269}  {269}  {1}    {236}  {4}    {1}    {2367} {36}   {58}   {268}  {4}    {9}    {2356} {357}  {8}    {9}    {356}  {2}    {36}   {7}    {4}    {356}  {1}    {356}  {4}    {1}    {89}   {3689} {69}   {2}    {7}    {35}   {7}    {36}   {2}    {4}    {5}    {1}    {36}   {8}    {9}    {59}   {1}    {7}    {3}    {29}   {259}  {8}    {4}    {6}    {36}   {36}   {4}    {1}    {7}    {8}    {5}    {9}    {2}    {2}    {8}    {359}  {6}    {4}    {59}   {37}   {1}    {37}   `

1) The pair of 36s in column 2 allows removal of other 3's and 6's in column.
2) The pair of 37s in row 9 allows removal of other 3's and 7's in row.

This leaves:
Code: Select all
`{4}    {27}   {69}   {59}   {1}    {3}    {67}   {256}  {8}    {369}  {5}    {8}    {7}    {269}  {269}  {1}    {236}  {4}    {1}    {27}   {36}   {58}   {268}  {4}    {9}    {2356} {357}  {8}    {9}    {356}  {2}    {36}   {7}    {4}    {356}  {1}    {356}  {4}    {1}    {89}   {3689} {69}   {2}    {7}    {35}   {7}    {36}   {2}    {4}    {5}    {1}    {36}   {8}    {9}    {59}   {1}    {7}    {3}    {29}   {259}  {8}    {4}    {6}    {36}   {36}   {4}    {1}    {7}    {8}    {5}    {9}    {2}    {2}    {8}    {59}   {6}    {4}    {59}   {37}   {1}    {37} `

Look at the remaining cells that can hold 3s:
Code: Select all
` . . . | . . . | . . .+3 . . | . . . | .-3 . . .-3 | . . . | . 3 3-------+-------+------  . .+3 | . 3 . | .[3]. 3 . . | . 3 . | . . 3 . 3 . | . . . | 3 . . -------+-------+------  . . . | . . . | . . . 3 3 . | . . . | . . . . . . | . . . | 3 . 3`

The 3s marked with + and - signs exclude the [3] in brackets. This demonstrates exclusion by "colors".
If r4c3=3, then r3c3<>3, then r2c1=3, then r2c8<>3.
If r4c3<>3, then r3c3=3, then r2c1<>3, then r2c8=3.
Therefore, either r4c3=3 or r2c8=3.
In either case, r4c8<>3.

This leaves:
Code: Select all
`{4}    {27}   {69}   {59}   {1}    {3}    {67}   {256}  {8}    {369}  {5}    {8}    {7}    {269}  {269}  {1}    {236}  {4}    {1}    {27}   {36}   {58}   {268}  {4}    {9}    {2356} {357}  {8}    {9}    {356}  {2}    {36}   {7}    {4}    {56}   {1}    {356}  {4}    {1}    {89}   {3689} {69}   {2}    {7}    {35}   {7}    {36}   {2}    {4}    {5}    {1}    {36}   {8}    {9}    {59}   {1}    {7}    {3}    {29}   {259}  {8}    {4}    {6}    {36}   {36}   {4}    {1}    {7}    {8}    {5}    {9}    {2}    {2}    {8}    {59}   {6}    {4}    {59}   {37}   {1}    {37} `

Either r2c8 or r3c8 must be a 3, as there are no other places for a three in that column. Therefore, r3c9<>3.

This leaves:
Code: Select all
`{4}    {27}   {69}   {59}   {1}    {3}    {67}   {256}  {8}    {369}  {5}    {8}    {7}    {269}  {269}  {1}    {236}  {4}    {1}    {27}   {36}   {58}   {268}  {4}    {9}    {2356} {57}  {8}    {9}    {356}  {2}    {36}   {7}    {4}    {56}   {1}    {356}  {4}    {1}    {89}   {3689} {69}   {2}    {7}    {35}   {7}    {36}   {2}    {4}    {5}    {1}    {36}   {8}    {9}    {59}   {1}    {7}    {3}    {29}   {259}  {8}    {4}    {6}    {36}   {36}   {4}    {1}    {7}    {8}    {5}    {9}    {2}    {2}    {8}    {59}   {6}    {4}    {59}   {37}   {1}    {37} `

Now we can find a forcing chain to finally place a number.

Here are the cells used in the forcing chain proof:
Code: Select all
` .  . 69 | 59  .  .  | 67  .  .  .  .  . |  .  .  .  |  .  .  .  .  .  . | 58  .  .  |  .  . 57 ---------+-----------+---------- .  .  . |  .  .  .  |  .  .  .  .  .  . | 89  .  .  |  .  .  .  .  .  . |  .  .  .  |  .  .  . ---------+-----------+---------- .  .  . |  .  .  .  |  .  .  .  .  .  . |  .  .  .  |  .  .  .  .  .  . |  .  .  .  |  .  .  . r3c9=5 => r3c4=8 => r5c4=9 => r1c4=5 r3c9=7 => r1c7=6 => r1c3=9 => r1c4=5Therefore r1c4=5, the rest solves easily.`
tso

Posts: 798
Joined: 22 June 2005

### Re: Trial and error

Jeff wrote:Tso

Sorry that I have posted an incomplete reply due to lack of time.

Your solution using forcing chains is just as 'trail and error' as Supertorpe's solution.

Supertorpe's 'trial and error' is a direct and obvious one, but yours is subtle and happened behind the scene. I agree that the forcing chains you used to deduce the number is logical and it just look so simple after the final chains are listed. However, I will find it hard to believe that you are able to pinpoint exactly the chains that would lead to a solution the first time every time, as we know that these chains do not follow a set patten. You would have to try a few or quite a few chains and follow them through to see which ones would give you a solution. If not, you would have to try again, and again.......... It is this chain finding process that is 'trial and error'.

With this grid, you don't have to use forcing chains. After removing the 3 in r4c8, there is a xy-wing in r4c5,c8 & r5c5,c9 which would give you 3 in a few places. Subsequently apply colours to 6s and the complete puzzle is solved.

Jeff,
I) The x-wing you specify does not exist. The cells you specify do not form an X-wing nor any other pattern that implies anything as you suggest, nor does it lead to anything else by itself:
Code: Select all
`{4}    {27}   {69}   {59}   {1}    {3}    {67}   {256}  {8}    {369}  {5}    {8}    {7}    {269}  {26}   {1}    {236}  {4}    {1}    {27}   {36}   {58}   {268}  {4}    {9}    {2356} {57}   {8}    {9}    {356}  {2}    {36}   {7}    {4}    {56}   {1}    {356}  {4}    {1}    {89}   {3689} {69}   {2}    {7}    {35}   {7}    {36}   {2}    {4}    {5}    {1}    {36}   {8}    {9}    {59}   {1}    {7}    {3}    {29}   {259}  {8}    {4}    {6}    {36}   {36}   {4}    {1}    {7}    {8}    {5}    {9}    {2}    {2}    {8}    {59}   {6}    {4}    {59}   {37}   {1}    {37} For clarity: .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  .----------+-----------+---------- .  .  .  |  . 36  .  |  . 56  . .  .  .  |  .3689 .  |  .  . 35 .  .  .  |  .  .  .  |  .  .  .----------+-----------+---------- .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  .`

II) You've put words in my mouth and then disagreed with them. I never used the words "trial and error" in criticizing Supertrope's solution. I mentioned "trial and error" in passing in regards to SadMan's Sudoku software which can be set to specifically use or not use both "forcing chains" and "trial and error". Based on what he has posted previously, I made the assumption that he'd be interested in Sudokus that can be solved with short forcing chains that his software misses. (Though in this case, his software doesn’t so much miss the forcing chain as it never gets to the point where these chains apply.) See his description of forcing chains. Clearly he does not agree with you that finding forcing chains are trial and error.

III) My criticism of Supertrope's answer was that it was NOT an answer to the question posted. June wanted to know "...the next logical step." She most likely KNEW the solution. Look here -- In this case, Hana posted the puzzle AND THE SOLUTION and asked "I need to find the next logical step!". Yet Supertrope gave essentially the same non-answer -- "try this, see if it fits." Supertrope, possibly because his English is not perfect, does not answer the question asked, though earnestly trying to help. Actually, what he suggested wasn’t even trial and error, as he *told* her which numbers would work. He simulated looking in the back of the book. The solution I gave was complete from the point at which she was stuck, as it wasn’t clear how far she had gone with candidate elimination. She was free to use just as few steps as she required. It doesn’t matter *how* I came up with *any* of the steps -- logic, asking a friend, guessing -- I answered the question posed.

IV) I cannot disagree more completely with your assessment of "forcing chains" = "trial and error". You say: "I will find it hard to believe that you are able to pinpoint exactly the chains that would lead to a solution the first time every time, as we know that these chains do not follow a set pattern."

Code: Select all
`1) These chains do not form a set pattern,2) You cannot find the solving chains the first and every time.3) Therefore, "forcing chains" are trial and error.`

Premise 1: We know no such thing. Forcing chains are no more or less a pattern than Swordfish, etc.
Premise 2: We know no such thing. You have not defined parameters to judge if this were true in any specific case. It is an broad statement.
Conclusion: Even if we stipulate that the two premises are true, the conclusion does not follow. These premises apply to EVERY OTHER tactic used, simple and complex. For instance, if I were to look for a simple x-wing and did not find it (whether or not one exists) -- then your logic proves that I have used trial and error. If I simply scan across the diagram to see if the 3 in the first two boxes will allow me to place a 3 in the third -- since I won’t have success each and every time I try this -- your proof makes this trial and error.

Your are proving that ALL solving is trial and error.

Everyone reading this post has at searched for an X-Wing or Swordfish or other pattern and:

-- didn't find one, looked elsewhere with another candidate, gave up and tried something else
-- didn't find one, looked elsewhere using a different candidate, found one, solved the puzzle
-- found one, but it didn't help because it failed to eliminate any other candidates, tried something else

Unless you solve Sudokus by an set-in-stone sequence of routines, you are using the same flavour of "trial and error" you claim I use to find "forcing chains".

Lets imagine your suggested x-wing were valid -- by what method did you find it that rises above trial and error? Why did you look for an x-wing? Why did you try it with 3s? How does it change the situation knowing that what you found was an error? How do you searched was more or less trial and error than the way I found the forcing chains? -- Neither of described the process we used to find our proof. Of course, since it turns out it *was* an error ... you must see my confusion, right? Am I to avoid x-wings now because *looking* for them can be considered trial and error?

Will you describe here the line that separates tactics that require trial and error to find from those that do not in such a way that will have general agreement?
tso

Posts: 798
Joined: 22 June 2005

I believe Jeff's message was that there was an XY-Wing (not just an X-Wing) in those cells.. I was skeptical as I spent quite a bit of time trying to see how it would work. Being new to these puzzles, I have a hard time reorienting ideas. In this case, the XY-Wing is formed by taking the cells proposed by Jeff:

r4c5,c8 & r5c5,c9

and setting X=5, Y=6, and Z=3. What that'll do is let you eliminate 3 from r5c5... The XY-Wing is actually easy to see with the clear version, Tso put up:

Code: Select all
` .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  .----------+-----------+---------- .  .  .  |  . 36  .  |  . 56  . .  .  .  |  .3689 .  |  .  . 35 .  .  .  |  .  .  .  |  .  .  .----------+-----------+---------- .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  . .  .  .  |  .  .  .  |  .  .  . `

It also helps simplify the puzzle a lot, and the XY-Wing is really no more trial and error than an X-Wing is... i.e. very simple forcing chains.

I hope this helps someone...

Erik
emalvick

Posts: 13
Joined: 01 August 2005

### The Next Logical Step

Tso

You can't even recognise an xy-wing. This raised the question that how many trials you needed to find the appropriate forcing chains. Short forcing chains such as x-wing, xy-wing, turbot fish and colours which have set patterns can be regarded as 'the next logical step'. The process of finding forcing chains from first principal fall into the 'trial and error' region, may not necessarily be 'the next logical step'.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff

From your comments to tso, and the length of time you have been a member on this forum, i doubt you fully understand the conditions and circumstances where forcing chains are considered as a logical approach.

You can't even recognise an xy-wing. This raised the question that how many trials you needed to find the appropriate forcing chains.

Well, it just seems to me that tso was more unaware than unable to recognize xy-wing. Even if that isn't so, the ability to recognize an xy-wing is definitely not inversely proportional to how many trials he needs to find the appropriate forcing chains.

I have seen the discovery and evolution of several sudoku techniques since joining this forum. I believe tso was the first one who introduced 'forcing chains' to this forum. Just in case u missed it in tso's previous post, here's the link again: http://forum.enjoysudoku.com/viewtopic.php?t=834. It was thereafter adapted and accepted by many others.

I sense hostility directed to tso in your last post, and that you are using his mistake as your advantage to put him down. Personally, i don't think ALL of one's opinion are to be dismissed just because of a mistake he had made. Part (I) of what tso brought up may be wrong, but i think (II), (III) and (IV) are all great and clear explanation on his defense of the forcing chain technique.

Lastly, i'm not sure if you're aware, but the term 'trial and error' is very sensitive to sudoku players. To avoid ill-feelings, it is always better to research and read up a bit before you 'criticized' somebody's solving technique in your 1st post.
Bunnybuck

Posts: 15
Joined: 13 June 2005

### The Next Logical Step

Bunnybuck

Firstly, point taken. It can easily be taken the other way, but that wasn't the intention. A few messages were lost during the shutdown of the forum. The question arose when Tso said that Supertorpe's solution wasn't 'the next logical step' and I just offered my opinion without taking anything away from what Tso has done. After all, the ability to identify the appropriate forcing chains does differ from person to person. Some people may be able to 'read' these chains so well that 'trial and error' is never an issue. Personally, I don't have that ability but that's just me. Don't forget that the xy-wing is just another very simple chain. Sorry if that creates any ill-feelings. Great forum, great people, great discussion and have fun.
Jeff

Posts: 708
Joined: 01 August 2005

Bunnybuck: Thanks for defusing the situation.

Jeff: I read "xy-wing" as "x-wing" by oversight, then didn't bother to examine it closely as I assumed *you* had made a clerical error. Ooops, my fault.

You could have simply posted the xy-wing as better answer to the original question, we all would have been in agreement. We might also agree that the question "Which is the NEXT logical move?" rarely if ever has a definitive answer.

When I look for forcing chains, I ignore cells with more than 2 candidates, creating groups of connected cells, visually if possible, physically if the puzzle is more complicated. The method obviously has pros and cons, but it does explain why I might find a longer chain while overlooking this one. Not an excuse, just an explanation.

You have a point though. Though I have methods to find forcing chains, I haven't spelled them out. Many patterns have been presented in these forums without a step by step procedure showing how to look for them -- a description of the pattern is usually enough. But as the patterns become less specific and more general, the reader is more and more likely to be unable to reproduce the results. I certainly have been on the receiving end of that situation more than once. I'll see if I can codify what how I do what I do and post it soon.

I've always had a preference for using more general methods when possible rather than memorizing several specific instances of that method. (In trig, I couldn't memorize all the various formula -- I'd derive them from scratch when I needed them. It's slower, but I never had to worry about forgetting one during a test.) On the other hand, I *could* make a list of all possible forcing chains of length 4 or less -- there couldn't be more that a few million -- and give them all fish names!
tso

Posts: 798
Joined: 22 June 2005

Thanks for all the replies.

I caught a sick bug and so havent been on-line for a while but catching up has been very interesting.

First - I deliberately used the word logical - my husband had already solved the puzzle by trail and error but I wanted to find a more reasoned solution.

Second - Your arguments have convinced me that if all else fails forcing chains can form part of a logical solution.

Third - wow, Ive learned a lot!

Thanks again, June
Prunie

Posts: 5
Joined: 30 July 2005