The New Sudoku Players' Forum

[champagne]

HI Champagne

Champagne wrote:
As written before applying a uniqueness rule to a puzzle with multiple solutions can lead to one of the solutions.
When I read the TDP description, I noticed some implicit uses of the uniqueness property. It is likely the case for these puzzles.
As noticed eleven, no logical rule can give you an elimination in the area where are the multiple solutions.

EDIT: I had a look to the puzzle 600.
It is clear that the final step is to count valid solutions, having solved what can be solved.
By chance, this puzzle has only 5 solutions.
In this forum, this is not called a logical elimination

I have plenty of code sequences counting the solutions of a puzzle. This is the best approach to extract unavoidable sets from a solution grid. But this is another story.

I disagree with the fact that the solutions found are illogical. The solutions are fully logical. They are not accepted on the site simply because they are chains of contradiction that use the basic technique. When a logical chain proves that a candidate leads to a contradiction, this contradiction is valid for all solutions of the puzzle, not just one in particular. All deletions made with an AIC are also valid for all solutions.

Paolo

?????? I see nothing in relation with my statement.
EDIT but I have nothing against the fact that part of a puzzle with multiple solutions can be solved with logical eliminations. The limit is in the area where you have multiple solutions

[Ajò Dimonios]

Hi Champagne.

My bad English probably didn't make me understand what you meant.
For me, proving that a candidate leads to a solution, while being the final part of the logical process, is a logical process. When you say "It is clear that the final step is to count valid solutions, having solved what can be solved" is exactly what is done in the single solution puzzles that lead to the final test "the fateful STTE". The same is done with multiple solution puzzles with the variant that "there are more than one fateful STTE".

Paolo

[champagne]

Hi Champagne.

My bad English probably didn't make me understand what you meant.
For me, proving that a candidate leads to a solution, while being the final part of the logical process, is a logical process. When you say "It is clear that the final step is to count valid solutions, having solved what can be solved" is exactly what is done in the single solution puzzles that lead to the final test "the fateful STTE". The same is done with multiple solution puzzles with the variant that "there are more than one fateful STTE".

Paolo

STTE means Singles to the end, in other terms, the simplest rule (last in row, column box cell or hidden single in row column box) leads to the final "unique" solution.
Believe me, when you have several solutions, you have in the simplest case to make a guess leading to the first solution, then to make the complementary guess and see the second solution. No elimination rule can be applied.

Making a guess and checking if it leads to a valid solution is a logical process, I's not classified as a "solving rule" but it is widely used by puzzle creators and to check if the puzzle has a unique solution. As I apply the uniqueness property in my solver, the preliminary step is to check that the puzzle is a valid sudoku (unique solution)

[Ajò Dimonios]

It is clear that if we mean by solving a puzzle, the use until the end of elimination rules, this cannot be the case for a multiple solution puzzle.
The process of solving a multiple solution puzzle cannot be unlike the process of solving a single solution only the logical elimination of candidates because otherwise it would get stuck to the point where it is not possible to exclude any candidate because all the remaining candidates in the scheme are present in at least one solution.

Paolo

[eleven]

For example this "puzzle" looks like multi-solution but it isn't.

Code: Select all

....12.3
4.134..2.
..423..1.
..21.34..
.3..1...4
24..2...1
3.34....2
11...234.
.2...413..

....12.34.134..2...423..1...21.34...3..1...424..2...13.34....211...234..2...413..


(the grid is wrong formatted, this way you have two 1's at the beginning of row 8)
Interesting puzzle. Obviously it can't be unique with all the deadly patterns.

It must have either 0 or 5! (120) solutions. You can choose any digits in an arbitrary unit. If it solves it, all permutations would lead be a solution too.

To show then, that it has no solution, is neither basics nor hard.

[eleven]

EDIT: I had a look to the puzzle 600.
It is clear that the final step is to count valid solutions, having solved what can be solved.
By chance, this puzzle has only 5 solutions.

...8.7...4...3...5.23...86...56.93............1.385.9..........67.....191.4...5.6
Can you post them please ? oops this is 660 ...

[champagne]

It is clear that if we mean by solving a puzzle, the use until the end of elimination rules, this cannot be the case for a multiple solution puzzle.

This is AFAIK the common understanding of the expression "solving a puzzle" in this forum and this is why puzzles with multiples solutions are not accepted. However, when a solver does not have a set of rules solving a sudoku, it uses the brute force as escape lane or it stops.

[champagne]

EDIT: I had a look to the puzzle 600.
It is clear that the final step is to count valid solutions, having solved what can be solved.
By chance, this puzzle has only 5 solutions.

...8.7...4...3...5.23...86...56.93............1.385.9..........67.....191.4...5.6
Can you post them please ?

Hi eleven,
I did not check, this is what is written in the comments of the solution. As I stop with my code at the second solution, I don't have the tool to do that without more coding. My interest for puzzles with several solutions does not push me to do more coding.

[eleven]

Now i looked at the right puzzle (600).
.....4.3.2.......9..6...7..9....3.1..736...8..6.5.......1.2.4...5....6.......9...
Robert is a very good solver, and he knows, why he stated, that this would be a multisolution puzzle.
This was his hint, that if you arrive at a uniqueness pattern, be aware, that the pattern can lead to solutions too.
This puzzle is a game for advanced solvers with a lot of time or those, who try to look, what solvers make of guesses.

[SpAce]

Try these two puzzles in Hodoku:

.9...2...6..4....3..5..628....8....4.1...........27........341...65.43.2..9.1..76
.9...2...6..4....3..5..628....8....4.1...........27........341...65.43.24.9.1..76

The second puzzle is the same as the first, but has an extra clue 4 in r9c1. The Hodoku score I got for the first puzzle is 390 and for the second 2816.
...
Well I did find (using my own solver) an easy solution to my second puzzle using the ALS-XZ rule eliminating a different candidate. Hodoku didn't find this easy solution, so maybe I need to re-tune it someway.

No re-tuning necessary. Hodoku does find a single-step ALS-XZ solution if you use "Find all steps". Even so, the UR solution available in the first puzzle is much easier to spot than the ALS-XZ (Hodoku sees the difference as 200 points; I'd say it's more). So the theory is valid for those two puzzles as well, even if not so drastic as with the classic example.

(Btw, even if you move ALS-XZ to the top of the non-basics hierarchy, it will only increase the point difference in the default paths. The reason is that Hodoku uses 7 other ALS-XZs before stumbling on the effective one, so the cumulative score remains high (2856). Thus you have to manually pick it to get the single-step solution right away.)

[StrmCkr]

Early and partly updated er ratings did not have als techniques in it this solution path when the rating issues was first pointed out, as these move sets often perform more or identical eliminations as the urs (same with m-rings) giveing slightly higher ratings when moved lower in hierarchy for both n1 n2 puzzles. Which meerly hides the effectness lower rating of uniquess techniques when solutions are assumed/pre proved by puzzle provider and they are used..

Hence my suggestion from long ago of a three fold rating system (ill have to dig for the link)
here

[Leren]

I have a pragmatic approach to considering whether one puzzle may "harder" than another. Let the forum participants comment.

So Mystery Puzzle 26 was a morph of n2 and Mystery Puzzle 27 was a morph of puzzle n1.

Those who looked at these puzzles may be in a position to comment on whether they found one "harder" than the other.

Leren

[SpAce]

So Mystery Puzzle 26 was a morph of n2 and Mystery Puzzle 27 was a morph of puzzle n1.

Nice! I totally missed that. A very good example of the principle! Removing the redundant clue(s) from Puzzle 26 drops the Hodoku rating by almost 3000 points. More importantly, the SER drops from 7.2 to 4.5. Obviously it's the same difference between 26 and 27.

Those who looked at these puzzles may be in a position to comment on whether they found one "harder" than the other.

I think the SER difference between those two puzzles is quite indicative of the actual difference for a typical manual solver. If someone claims otherwise, they have no clue (pun intended). Of course there's no difference if one refuses to use uniqueness methods, but that's a personal choice and irrelevant in the big picture. (It requires a certain level of masochism to voluntarily drop the most fun and elegant tools from one's palette.)

An even bigger difference between the two puzzles is in their OTP potential. One (27) was a trivial one-stepper with an almost immediately obvious solution, and the other (26) was practically impossible to solve with one step. Hodoku claims it can pull some one-step net solutions for the latter, but they don't seem to make much sense. It tends to get confused with complicated nets, claiming imaginary links. (I leave it up to others to decide whether my unorthodox solution counts or not.)

[Leren]

Here is another pair of puzzles:

..3....9...78....6.6......1............45....45..61..7..81.926.9....3........8.1.
..3....9...78....6.6......1............45.1..45..61..7..81.926.9....3........8.1.

Adding an extra clue 1 to r5c7 raises the Hodoku score from 912 to 3188.

The corresponding Hodoku scores for n1 and n2 were 742 and 4738. The scores for the n1 and n2 morphs were 742 and 3578.

Successive scores for some other morphs of n1 were all 742 but for n2 were 4888, 3398, 3428, 4968, 4258, 3728 etc

I guess we can say that the oldies are the goodies, but an exact Hodoku score for a hard puzzle is a bit of a lottery (or maybe I don't know enough about Hodoku to keep the scores consistent)

Leren

PS No I'm not crazy, the Hodoku scores for the four rotations of n2 were 4738, 3398, 3548 & 4818.

[Ajò Dimonios]

If we want to have a fair comparison between the two difficulties of the two puzzles, only the methods that do not impose uniqueness must be set on the Hodoku solver, excluding the "uniqueness" methods. This reverses the difficulty. The n1 has a score of 3952 and the n2 has a score of 3338. This can be seen as a demonstration as the introduction of uniqueness methods defines something different from what is commonly understood as the resolution of a sudoku, that is, a similar solution path to what the creator of the puzzle identified when he demonstrated the uniqueness of the solution.
Paolo