The New Sudoku Players' Forum

[GONGORA]

I DON'T EVEN KNOW HOW TO POST A MESSAGE FOR MANY MEMBERS! SHOULD I POST IT HERE? PLEASE TELL ME WHERE DO I POST A GENERAL QUESTION?

HELP! I GOT STUCK WITH A SUDOKU PUZZLE...

WHILE FILLING IN NUMBERS... IS THERE A POSSIBILITY THAT YOU CAN GET TO THE POINT WHERE THERE IS NO MORE A SPACE WHERE LOGICALLY YOU "MUST" PUT CERTAIN NUMBER AND GO ON?

IN OTHER WORDS: IS THERE A POSSIBILITY THAT YOU CAN GET TO THE POINT WHERE YOU MUST CHOOSE BETWEEN TWO DIFFERENT NUMBERS... AND THERE ARE TWO EMPTY SPACES FOR THOSE ONLY NUMBERS?

THAT IS... IN ORDER TO CONTINUE, YOU HAVE TO PLAY IT "HEAD OR TAILS" AND PUT ONE NUMBER IN ONE SPACE AND THE OTHER NUMBER IN THE OTHER SPACE?

...IN THIS CASE... IS THERE A POSSIBILITY THAT, DOING SO, YOU CAN MAKE A MISTAKE AND LATER NEED TO ABANDON PLAYING BECAUSE YOU JUST CAN'T ADVANCE AND FINISH, BECAUSE FOR "THE ONLY SOLUTION" YOU SHOULD HAVE USED "THE OTHER" POSSIBILITY?

WOW! WHAT A QUESTION! THANKS FOR YOUR HELP!

[emm]

Yes, there are puzzles where this is a possibilty but these are not valid puzzles. If there's a place where you cannot logically put a number then it's guessing. Valid puzzles have only one solution and can be solved by logic without guessing.

You can guess if you want but if you need to guess then it means that the puzzle has multiple solutions and is invalid.

Guessing is different from Trial & Error which is a logical strategy. Pappacom puzzles do not require T & E, but there are other valid puzzles that do.

This is a good place to ask a general question but you don't need to write in CAPS - it makes it sound like you're either VERY DEAF or VERY CROSS!

[GONGORA]

HI em!
HI em!

Well. i'll write without caps for you... but its more difficult and much slower…
Are you awake? i am in Costa Rica, Central America...

Thanks for your reply... where are you located? i tried to get to see your profile but could not... this site is not easy at all!

From your answer I get: Valid puzzles have only one solution and can be solved by logic without guessing… but the puzzle i was trying was copied from the Sudoku site (i hope you can see it below)… But then how come I cannot find a logical way if I apply all rules to get a solution?



If you cannot see it, send me your direct mail address and I’ll send it by direct mail… my address is: Gongora@ice.co.cr

...

Yes, there are puzzles where this is a possibilty but these are not valid puzzles. Valid puzzles have only one solution and can be solved by logic without guessing.

You can guess if you want but if you need to guess then it means that the puzzle has multiple solutions and is invalid.

Guessing is different from Trial & Error which is a logical strategy. Pappacom puzzles do not require T & E, but there are other valid puzzles that do.

This is a good place to ask a general question but you don't need to write in CAPS - it makes it sound like you're either very deaf or very cross! :)

[emm]

Hi Gongora, Yes I am awake. I still find it really hard to do Sudoku when I am asleep! How about you? But no I cannot see your puzzle!

The best thing to do is to enter the original clues in a grid like this. Then we can help.

Code: Select all


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-------+-------+------
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I wonder which site you mean by the Sudoku site ?

[simes]

You can guess if you want but if you need to guess then it means that the puzzle has multiple solutions and is invalid.

Is that necessarily true? I think it's possible for a puzzle to have a single solution, but have no simple logical path to arrive at it.

Guessing is different from Trial & Error which is a logical strategy. Pappacom puzzles do not require T & E, but there are other valid puzzles that do.

So some puzzles that require T&M can have a single solution then? How is that different from the above case?

Simes

[emm]

Do we have the same definition of terms? It sounds to me like you don't consider T & E to come under the umbrella of 'simple logic'.

How is that different from the above case?

The two cases are different because T & E is not guessing. Guessing suggests random, haphazard stabs at possibilities. Logic, which includes T & E, suggests application of tested mathematical strategies. T & E is a logical strategy based on the principle of proof by contradiction. T & E does not compromise the validity of a puzzle - the need for guessing does.

I think it's possible for a puzzle to have a single solution, but have no simple logical path to arrive at it.

If a puzzle has multiple solutions then it cannot be solved by logic as there is not one certain place for each candidate. Is the reverse not true? If a puzzle cannot be solved by logic, including T & E, then at some point there must be a place in which more than one candidate is a possibility and the puzzle must have multiple solutions.

I have never done a puzzle that requires guessing. Maybe we should ask - can anyone produce a puzzle that is not solvable by logic and has one solution?

[MCC]

I believe that the difference between 'T&E' and 'guessing' comes down to the number of candidates in a cell.

When there are two candidates in a cell then T&E will show which of the two is the correct one.

When there are more than two candidates in a cell, then whatever candidate number you choose to continue with, will only lead to the elimination of that number (that's if the path is a dead end) and not to the knowledge of the correct candidate.

In my opinion, when there are two candidates 'T&E' and 'guessing' amount to the same thing.

[lunababy_moonchild]

In my opinion, when there are two candidates 'T&E' and 'guessing' amount to the same thing.

I think so too, since - it seems to me - that even if you only have 2 candidates to choose from, since you don't know which candidate it is you have to choose one at random, and see where it takes you. It's logical, imho, insofaras if it's wrong you know it must be the other candidate, so you're not exactly closing your eyes and sticking a pin into a group of numbers (guessing?) and hoping for the best, but it's not exactly 'it must be this because it can't go anywhere else'.

Anyway, who set the standard for the 'one solution, solve by logic only'? Is it a standard?

Luna

[udosuk]

I believe that the difference between 'T&E' and 'guessing' comes down to the number of candidates in a cell.

When there are two candidates in a cell then T&E will show which of the two is the correct one.

When there are more than two candidates in a cell, then whatever candidate number you choose to continue with, will only lead to the elimination of that number (that's if the path is a dead end) and not to the knowledge of the correct candidate.

In my opinion, when there are two candidates 'T&E' and 'guessing' amount to the same thing.

That's a quite refreshing point of view by MCC. However we also need to consider the following scenario: when there are two candidates in a cell, sometimes both of them won't lead to deadends, but to another point of "branching out" for more possibilities... e.g. 2x2=4 possibilities with 3 of them leading to a deadend. In that case it's not "simple trial and error" anymore.

How about the following description:

"Logical trial and error" means, from a cell with n candidates, n-1 of them will lead to contradiction/deadend without any need of more branching out. Thus we can safely and logically assume that cell must have the only remaining candidate. Whether we set n must be 2 is subject to debate...

(If we set n must not be 3 or more, do we have proof that all "valid" puzzle can be solved using basic logical steps and this "tool"?)

[emm]

Whether we set n must be 2 is subject to debate...

Yes, I can't see how the difference can be a question of how many candidates there are. If you have 3 candidates in a cell, theoretically you could use the same strategies/or not to place each one, in the same way you do with one or two. Is a forcing chain using 2 candidate-cells guessing? In another thread recently tso used naked triples in implication chains - it's all the same strategy.

I like this distinction from Lummox Jr in the Guesses thread.

In T&E, a trial candidate isn't considered "right" merely by placing it and finding no contradictions. T&E must either find a contradiction, or it must affirmatively place or fully eliminate a number by trial candidates in another set of cells.

A guess, on the other hand, tries a candidate and if it works, accepts it.

PaulIQ164 said this in the thread that's running along the other track Help With End Game

I suppose the difference between using T&E and guessing is the the guesser puts in a number he doesn't know to be correct, continues with the puzzle, and (if he's lucky) fills the grid, then says to himself "Ah! Finished!" and goes home. The T&E user would put in the number, fill the grid, and then go back and check the other possibility to make sure that didn't work too.

This implies a different modus operandi on the part of the solver. It also implies that guessing is subjective. When I run out of logical strategies I start guessing or when any old answer will do I am guessing. You on the other hand may do exactly the same thing as I did but with a logical strategy in mind.

(If we set n must not be 3 or more, do we have proof that all "valid" puzzle can be solved using basic logical steps and this "tool"?)

I want to know this too. In Help With End Game stuartn mentioned the possibility of a '9 guess' grid with a unique solution. Maybe we'll find out!

PS : I wonder if Gongora will come back!

[udosuk]

Although I don't know anything about the "9-guess grid", from the other thread I saw this post from tso where this 8-clue "dusumoh" is supposed to have a unique solution but requires a series of 15-20 guesses (as claimed by Bob the creator). So it's likely we could have a sudoku grid with similar "difficulty"...

[lviann11]

What I do is fill in all the possible numbers in each empty square and go through using the process of elimination. I come across the double number in two squares thing a lot... so I just circle one and work from there- if I get stuck then I know to go back and use the other one. It takes a long time for me to finish a puzzle that way but whatev... I just love to do them.

[GONGORA]

HI EM!

SORRY I forgot about caps... 'm telling you! Had great fun! I solved it! found a mistake i had made and worked on it for an hour... for me, it's a difficult one...

private direct e-mail is allowed here? Remember, send your address and i'll copy the difficult one... i solved it 'cause you assured me: no guessing allowed! and definitively yes, all can be solved without guessing! Thanks!

You forgot to tell me where are you located? I dunno your time zone... mine is (USA)EST + 2 in winter... +1 in summer...

Have a nice weekend!

Hi Gongora, Yes I am awake. I still find it really hard to do Sudoku when I am asleep! How about you? But no I cannot see your puzzle! :(

The best thing to do is to enter the original clues in a grid like this. Then we can help.

Code: Select all


 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
 ----+-----+-----
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-----+-----+----
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .


I wonder which site you mean by the Sudoku site ?

[GONGORA]

hi, everybody! ...i was about to log out, thought i should check my message to em... and found, with great joy, that a big enlightening discussion started! That's great...

Now, if you all allow me, i do type faster with caps... 'am not shouting... i'm counting with your "oh what the heck, let the guy do it" attitude! great::: Fine! Thanks!

AS FOR GUESSING AND T&E... LET THIS UNEXPERIENCED SPANISH SPEAKIN OLD, VERY OLD FELLOW SAY THIS: EVERY TIME I SEEM TO GET TO A DEAD END, I CHANGE THE WORKING SPOT AND TRY SOMEWHERE ELSE IN SAME PUZZLE... I PENCIL (JOT PROBABILITIES) MY WAY... A LOT... AND I ALWAYS HAVE FOUND A PLACE WHERE LOGIC TELLS ME: "THE ONLY NUMBER THAT CAN GO IN THIS SPOT IS n"... AND YOU MOVE ON... AND ALWAYS FIND ONE NEW SPOT WITH SAME LOGIC MESSAGE! SAME WITH YOU ALL? I'VE NEVER GOT TO THE POINT OF HAVING TO GUESS BETWEEN TWO or MORE OPTIONS! ...BY LOGIC: THERE CAN ONLY BE ONE SOLUTION... THE PERFECT LOGIC SOLUTION.
YOUR EXPERIENCE... A THOUSAND PUZZLES GRETAER, ALLOWS YOU AL TO BE ABLE TO STATE SAME STATEMENT? ...INTERESTING TO HEAR! HAVE A NICE WEEKEND!

...AND, em... DO NOT wonder which site I mean by the Sudoku site ? ITS: http://sudoku.com/ BYE-BYE!

[MCC]

My brain has gone on holiday and has taken a passport so it my be away for some time.

But in the meantime, using what's left.

Choosing a candidate from a bifurcate (or multifurcate?) position that leads to a solution, is a guess, with the proviso that the solver stops looking for another solution.

If the solver undertakes to look at the other candidate/s and their pathway/s and so therefore prove that the original choice was the only and therefore logical choice to make, then it can be called T&E.

It is also T&E if there are multiple solutions, so long, as ALL pathways are checked.

Just a thought.
If ALL pathways are not checked is it still a guess