mariemuad Rated puzzle: EasyBest completion time: 12:37Time on first attempt: 18:17Used 'show wrong moves' Used 'check puzzle' when incorrect
I didn't need to use the X clues to do it
Posted 26th Apr 2016 at 11:50
Elisabeth Daily subscriber Rated puzzle: EasyCompletion time: 25:06
So did I, but it would have been far quicker if I had. Puzzle disappeared so this is my second attempt, no aids however!!
Posted 26th Apr 2016 at 21:12 Last edited by JoergWausW 26th Apr 2016 at 21:24
JoergWausW Daily subscriber Best completion time: 9:55Time on first attempt: 17:58
Usually I forget about the X - and regret it. This time I thought of it quite early, but had to fix a mixup of numbers. The third 2 in a 3x3 square couldn't be right... Got it this time and could finish the puzzle without starting over. Now I tried it again - it is indeed solvable without the X.
Posted 27th Apr 2016 at 08:59
Elisabeth Daily subscriber Rated puzzle: EasyCompletion time: 25:06
I wonder, is it possible to fix a puzzle so the 'X' has to be used to solve it? There are often different ways of solving a particular puzzle, but usually all restrictions have to be used otherwise there can sometimes be several solutions.
Posted 27th Apr 2016 at 12:56 Last edited by gareth 27th Apr 2016 at 13:01
gareth Administrator Daily subscriber Has not played this puzzle yet
See here for discussion on whether you need the X or not. I looked at this in 2010:
Ever since then all puzzles on PuzzleMix have worked that way. i.e. I test them using 'reasonable solving techniques' to make sure the X is used, and reject them if not. But for Killer Sudoku, there are so many ways you can solve the puzzle that this isn't an exhaustive check and it's inevitably going to be the case that from time to time you can solve without the X.
So here's the key bit: I always check that having the X can be of significant help in solving the puzzle.
But to answer Elisabeth's question, yes of course you could make the puzzles like that - you'd just need to run them through a brute-force solver (something that tries every possibility recursively) until you found whether they solved uniquely or not. However, that's not what I do (as per the links above).
Posted 27th Apr 2016 at 15:29 Last edited by JoergWausW 27th Apr 2016 at 15:50
JoergWausW Daily subscriber Best completion time: 9:55Time on first attempt: 17:58
I don't think you'd need a brute force solver. Just use a regular logical solver (if there is one) and don't allow to use the X. If it comes up with any solution, you'd know that it's not necessary. This way the solver is allowed to be smart, and you don't have to try every possible way recursively.
Edit: After reading the links I'd like to add that 'm sure you knew this - I'd like to add now, concerning the difinition of terms: To have an X in the name it could be enough that each number occurs just once in the diagonals. It depends on the author whether he wants to give this information or not.
A question might be: what's the percentage of all possible 9x9 Sudoku-grids that also match the X-rule? After knowing about this chance: what percentage of those does really "need" the X (no Killers)?
With the Killer Sudokus there are way more possibilities to construct a puzzle, because you have a lot of options using the same solution with different ways to arrange the extra boxes (and they don't need to be symmetrical... but I like it that they are, even though that this makes the number of possible puzzles smaller...)
Posted 27th Apr 2016 at 16:00 Last edited by gareth 27th Apr 2016 at 16:11
gareth Administrator Daily subscriber Has not played this puzzle yet
Hi JoergWausW,
A brute force solver does of course use elimination logic, since Sudoku is NP-complete and would be mathematically intractable otherwise. I didn't mean you would try solutions randomly - that would never work!
When people refer to brute force solving of Sudoku, they mean guessing a digit, making row, column and box eliminations, and then continuing. If you hit a contradiction, you undo your guesses until you can try a new one (thus the recursive bit). Of course, humans don't solve like this (unless the guess is just one or two deep, and they are stuck), so this 'brute force' approach contrasts with a nuanced human-like solver which tests the puzzle using logic someone sitting at home is likely to use. (Which is not to start by guessing the first digit, but rather use other observations)
Anyway, so since I made this change in 2010 I haven't seen this "don't need the X" comment since then.
So that's not bad, in over 6 years! ;)
Gareth, puzzlemix
Posted 28th Apr 2016 at 08:53
Elisabeth Daily subscriber Rated puzzle: EasyCompletion time: 25:06
My question was a bit naive; I knew there had to be some way of making 'X's necessary to the solution but expressed it rather badly!!
Yes, pretty good going, Gareth, I shall watch out now though for others:)
Posted 28th Apr 2016 at 16:14
JoergWausW Daily subscriber Best completion time: 9:55Time on first attempt: 17:58
Hi gareth, thanks for the clarification. But I didn't want to suggest (and didn't understand) that you were talking about a random solver.
My point was to express that there was a way to stop after the solver found the first solution - because I understood you would want to go on to check if it was the only way to get the solution.
I regret I don't have the time to study NP-completeness (seems to have some levels of recursively defined terminology...)
About the X-puzzles: Usually I forget the X (as mentioned above) and get stuck because of it. In these cases I would notice that the X wasn't needed. Too bad, this time I thought of it...
Maybe I'll go back over the older puzzles to check this now :-D
Posted 22nd Oct 2016 at 18:07 Last edited by Gostar 23rd Oct 2016 at 03:33
Gostar Rated puzzle: EasyCompletion time: 16:41
I did this good puzzle for the first time about April 2016. I've redone now in October, twice on the same day: after seeing the comments posted in April 2016, I wanted to try it without using the X. It seems that it is possible. A good puzzle anyway.
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Last edited by JoergWausW 26th Apr 2016 at 21:24
Now I tried it again - it is indeed solvable without the X.
Last edited by gareth 27th Apr 2016 at 13:01
Sudoku X and the diagonal challenge
And then on Killer Sudoku X:
Killer Sudoku X and diagonals
Ever since then all puzzles on PuzzleMix have worked that way. i.e. I test them using 'reasonable solving techniques' to make sure the X is used, and reject them if not. But for Killer Sudoku, there are so many ways you can solve the puzzle that this isn't an exhaustive check and it's inevitably going to be the case that from time to time you can solve without the X.
So here's the key bit: I always check that having the X can be of significant help in solving the puzzle.
But to answer Elisabeth's question, yes of course you could make the puzzles like that - you'd just need to run them through a brute-force solver (something that tries every possibility recursively) until you found whether they solved uniquely or not. However, that's not what I do (as per the links above).
Last edited by JoergWausW 27th Apr 2016 at 15:50
Just use a regular logical solver (if there is one) and don't allow to use the X. If it comes up with any solution, you'd know that it's not necessary. This way the solver is allowed to be smart, and you don't have to try every possible way recursively.
Edit:
After reading the links I'd like to add that 'm sure you knew this - I'd like to add now, concerning the difinition of terms:
To have an X in the name it could be enough that each number occurs just once in the diagonals. It depends on the author whether he wants to give this information or not.
A question might be: what's the percentage of all possible 9x9 Sudoku-grids that also match the X-rule? After knowing about this chance: what percentage of those does really "need" the X (no Killers)?
With the Killer Sudokus there are way more possibilities to construct a puzzle, because you have a lot of options using the same solution with different ways to arrange the extra boxes (and they don't need to be symmetrical... but I like it that they are, even though that this makes the number of possible puzzles smaller...)
Last edited by gareth 27th Apr 2016 at 16:11
A brute force solver does of course use elimination logic, since Sudoku is NP-complete and would be mathematically intractable otherwise. I didn't mean you would try solutions randomly - that would never work!
When people refer to brute force solving of Sudoku, they mean guessing a digit, making row, column and box eliminations, and then continuing. If you hit a contradiction, you undo your guesses until you can try a new one (thus the recursive bit). Of course, humans don't solve like this (unless the guess is just one or two deep, and they are stuck), so this 'brute force' approach contrasts with a nuanced human-like solver which tests the puzzle using logic someone sitting at home is likely to use. (Which is not to start by guessing the first digit, but rather use other observations)
Anyway, so since I made this change in 2010 I haven't seen this "don't need the X" comment since then.
So that's not bad, in over 6 years! ;)
Gareth, puzzlemix
Yes, pretty good going, Gareth, I shall watch out now though for others:)
thanks for the clarification. But I didn't want to suggest (and didn't understand) that you were talking about a random solver.
My point was to express that there was a way to stop after the solver found the first solution - because I understood you would want to go on to check if it was the only way to get the solution.
I regret I don't have the time to study NP-completeness (seems to have some levels of recursively defined terminology...)
About the X-puzzles: Usually I forget the X (as mentioned above) and get stuck because of it. In these cases I would notice that the X wasn't needed. Too bad, this time I thought of it...
Maybe I'll go back over the older puzzles to check this now :-D
Last edited by Gostar 23rd Oct 2016 at 03:33
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