Solving with Excel

Advanced methods and approaches for solving Sudoku puzzles

Postby MC » Fri Mar 18, 2005 4:38 am

OK, that time I definitely logged in before hitting "Post reply". I can only assume that, if you take too long, the system assumes you've left.

Pappocom - I can remember that, in the first puzzle I found, the cell in question was row 3 or 4, column 4 or 5 and the choice was between 7 and 8, as I recall, and the puzzle was about 50% complete. That doesn't help you much, though. Would you be prepared to send me only the Fiendish puzzles as published in T2 from 2, 3 and 4 weeks ago? I went for a wide timescale to be sure of hitting the mark. This reduced field should still cut it, I think.

It was very gracious of you to try to intercede; however, the phrase "I don't mean to upset you..." is very similar to "With all due respect..." or "I hear what you say, but..." in that all 3 are often the precursor to the exact opposite. Hence the fact that I'm wide awake at 3:36 in the morning, extremely angry.
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Postby Guest » Fri Mar 18, 2005 8:58 am

MC, apologies for any offence - I really don't mean to imply that you are a fool. However, you do keep asserting that even though a puszzle can be solved by logic alone, it is possible for another solution to exist somehow. This is an obvious contradiction in terms.
If the clues tell you that a cell contains a three by pure elimination of possibilities (i.e. it must be a three), any other value in that cell will clearly be in incorrect as it will directly contradict the clues. It's as simple as that. The original clues cannot be consitent with an incorrect guess.
This logic carries through the whole solving process, as each number derived by logic is a direct product of the original clues.
The only way more than one solution can be possible is if the complete answer cannot be derived by logic alone - in other words, if you have to guess. Even this does not necessarilly mean the puzzle has more than one answer.
The fact is that it is such an easy job to test if guessing is necessary, and by doing so you have proved that a puzzle has only one possible solution, I simply don't believe that the Times would make such an elimentary mistake in setting a puzzle. They may have of course, but this doesn't change the basic fact that if a puzzle is set correctly (i.e. the solution can be derivied by logic alone) then only one solution is possible.
As I say, none of this is personal - how could it be as I don't know you - so please don't take it as such. Who has the time? I'm afraid though that I will continue to try to find different ways to explain the flaw in your thinking until you realise that your position is illogical. This is the first time I've used a forum, so please forgive me while I find my feet - I just don't think it does anyone any good to leave untruths uncontested in any walks of life, even such trivial ones!

Postby MC » Fri Mar 18, 2005 12:51 pm

Until you understand that I am not claiming that 2 alternative solutions can be arrived at by logical use of the clues but that, instead, the alternative (ie "wrong") one involves a guess at a critical point in the puzzle and yet still arrives at 1 - 9 in every row, column and box, then there is little point in continuing this discussion.

[Note from Administrator: Part of this post, largely on the subject of Netiquette, has been edited out, in an effort to keep the thread on-topic.]
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Postby simes » Fri Mar 18, 2005 1:23 pm

Netiquette and flame wars aside...

MC, I think you're missing the main point of IJ's argument. If I may try my own slant on explaining it...

To arrive at a solution by a logical series of steps, each time you put a number in a cell, you're saying "this number must be in this cell". If that number need not be in that cell, then it's not a logical step. So by the time you've completed the puzzle logically, you've said a particular number must be in each and every cell.

So if a specific number must be in each cell, then there can be no other number in that cell. Therefore, there can be no other solution. QED.

If a puzzle cannot be solved logically, then at some point you enter a number in a cell without any particular reason, and you could just as well enter a different number. This sort of puzzle could have more than one solution.

There, did that make it any better?

Oh yes, before I forget...:D
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Postby Pappocom » Fri Mar 18, 2005 1:25 pm

Let's say you are logically-solving a puzzle, and you prove beyond doubt that Cell X must contain 7.

You have done more than prove that it must contain 7 - you have also proved that it cannot contain any number other than 7.

Therefore, it is not possible to have a solution which has a different (non-7) number in Cell X.

- Wayne
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Postby Guest » Fri Mar 18, 2005 4:22 pm

Simes & Wayne - Bingo! Thanks for interceding there - and both very eloquently put... I'll obviously never be a teacher :o)

Postby MC » Fri Mar 18, 2005 5:36 pm

I know perfectly well how to solve these puzzles using logic alone. I also know perfectly well that there is, if you use logic alone, only one solution. I have not now, nor have I ever had, any problem with IJ's point.

However, as I said on another thread, people who haven't yet worked out the all the finer points of logic to enable them to solve the puzzles will, at some point, be tempted to guess and see where it takes them. Having been at that stage a couple or three weeks ago myself, I found I was having to guess one of 2 possible numbers in order to carry on. More often than not, these would lead to a dead end, with duplicates, and I had to re-trace my steps and try the other number to complete the puzzle. On 2 occasions, however, I found that both the numbers that I tried led to a "valid solution" in that each row, column and box contained one of each digit 1 - 9. One of these solutions was the "correct" one, that could have been arrived at had I known how, the other was "incorrect" but still "valid". Once a player discovers the finer points of logic required, he no longer needs to guess, and the issue therefore does not arise again.

Is that clear enough now?

Pappocom - this is what comes of hacking people's posts about and moving them about to create new threads. Other people cannot hope to understand why the "original" post in this thread was posted. As I said before, it's like walking in on a conversation half-way through. By moving the "original" post from its place in the "Trial & Error" thread, it looks as if, at first glance, I am maintaining that your puzzles do not have a unique, logic based solution, particularly if readers either don't bother to follow the post's argument properly or bother to find out where it came from originally. It was a perfectly logical adjunct to the T&E thread. On its own, it does not stand up to scrutiny very well, hence the misunderstanding that has arisen. Some of this misunderstanding is my fault, I guess, as I could not fathom why people did not understand my original premise. It only now occurs to me that, if others did not bother to read where this thread came from and the original discussion on the T&E thread, they can never really understand why I have been so adamant about this. I know where this discussion originated and why I posted it. Others don't.

Lastly, if IJ did not get to read my thoughts on Netiquette, then that is a shame. He surely needs the pointers I posted, otherwise he will end up about as popular as a pork pie in a synagogue:D
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Postby simes » Fri Mar 18, 2005 6:07 pm

MC wrote:I also know perfectly well that there is, if you use logic alone, only one solution. I have not now, nor have I ever had, any problem with IJ's point.

It seeems you do have a problem with IJ's point though. If the solution is solvable by logic, then it doesn't matter whether you actually use logic or not. There is only one solution. You could guess every cell, but there is still only one solution.

Oh well, I tried.:(
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