## Very Hard Classic Sudoku [WSC 2010]

### Very Hard Classic Sudoku [WSC 2010]

Whilst this is undeniably a Sudoku puzzle, its difficulty is the point of this discussion - it scores a diabolical grade of 494 at http://www.sudokuwiki.org/sudoku.htm. Note that very hard classic puzzles had also appeared at the WSC in each of 2006, 2008 and 2009, however the reason I've included this example from 2010 is because the WSC this year had an entire round of very hard puzzles which required guesswork to get through under time pressure.

### Re: Very Hard Classic Sudoku [WSC 2010]

In my oppinion, someone who claims to be a sudoku champion should be able to solve

**all**9x9 standard sudokus, even with quite difficult logic.### Re: Very Hard Classic Sudoku [WSC 2010]

(Throughout this post, "standard solving techniques" refers to singles, line-box interactions (pointing/claiming) pairs, triples, quads, X-Wings, swordfish and jellyfish)

- Using standard solving techniques, no numbers can be placed

- Furthermore, using standard solving techniques, no potential candidates can even be eliminated from a cell, that is:

- Whatever cell and whatever number you choose as the starting point for a guess will lead to zero progress - using standard techniques, it cannot be proved or disproved without immediately making another guess.

Faced with such a puzzle for the first time, I doubt anyone could solve it without several hours to spare and a mountain of eraser residue. This is clearly unsuitable for competition, and, in my opinion, a total waste of time even outside of a competition.

The puzzle, for those who care, can be found at http://www.sudokusnake.com/goldennugget.php

I think this is unreasonable. Take the sudoku known as "Golden Nugget". It has the following characteristics:

- Using standard solving techniques, no numbers can be placed

- Furthermore, using standard solving techniques, no potential candidates can even be eliminated from a cell, that is:

- Whatever cell and whatever number you choose as the starting point for a guess will lead to zero progress - using standard techniques, it cannot be proved or disproved without immediately making another guess.

Faced with such a puzzle for the first time, I doubt anyone could solve it without several hours to spare and a mountain of eraser residue. This is clearly unsuitable for competition, and, in my opinion, a total waste of time even outside of a competition.

The puzzle, for those who care, can be found at http://www.sudokusnake.com/goldennugget.php

### Re: Very Hard Classic Sudoku [WSC 2010]

This is a nice ideology, but impossible practically. The ones who are able to solve these hard classics (or even harder than the example posted here), will never win by solving it, because it is much faster to guess the solution. Thus, probably even the players who are able to solve it logically will prefer to guess the solution to be well ranked... It's not possible in a competition to reward players who are able to solve these kind of puzzles. That's why I think it's not suitable for a competition.

Fred

### Re: Very Hard Classic Sudoku [WSC 2010]

It depends exactly what we mean by solve.

Many solvers only consider something to have been solved "logically" if at each stage of solving the puzzle, the solver is 100% confident that the number placed is part of the solution. Nevertheless, from a competition point of view, the only thing that matters is whether the final solution is correct or not.

I think it is fair to say there is a certain amount of skill involved in guessing efficiently, and I think this is the point of view that was trying to be expressed by this round in the 2010 WSC. I would be very happy to hear more from someone involved in the organisation to add more to this.

The two problems which come to my mind are as follows:

- These puzzles are generally agreed to not be particularly fun to solve.

- The reward for solving these puzzles is highly variable.

The example that comes to mind to highlight this variability was the one off world record round in 2009. The winning time was 3 minutes and 6 seconds, by Vincent Bertrand of Belgium. Of course this is a great achievement - solving a "suitable" hard puzzle from a newspaper in this time would be impressive enough - but if I were to analyse this in more depth I find it difficult to conclude that Vincent did something special that was beyond the capability of anyone else in the room, beyond making the right choice about where to guess. There were many other great solvers in that room who were not as fortunate in their choice of where to guess.

[Unfortunately I do not have a copy of the 2009 puzzle]

Many solvers only consider something to have been solved "logically" if at each stage of solving the puzzle, the solver is 100% confident that the number placed is part of the solution. Nevertheless, from a competition point of view, the only thing that matters is whether the final solution is correct or not.

I think it is fair to say there is a certain amount of skill involved in guessing efficiently, and I think this is the point of view that was trying to be expressed by this round in the 2010 WSC. I would be very happy to hear more from someone involved in the organisation to add more to this.

The two problems which come to my mind are as follows:

- These puzzles are generally agreed to not be particularly fun to solve.

- The reward for solving these puzzles is highly variable.

The example that comes to mind to highlight this variability was the one off world record round in 2009. The winning time was 3 minutes and 6 seconds, by Vincent Bertrand of Belgium. Of course this is a great achievement - solving a "suitable" hard puzzle from a newspaper in this time would be impressive enough - but if I were to analyse this in more depth I find it difficult to conclude that Vincent did something special that was beyond the capability of anyone else in the room, beyond making the right choice about where to guess. There were many other great solvers in that room who were not as fortunate in their choice of where to guess.

[Unfortunately I do not have a copy of the 2009 puzzle]

### Re: Very Hard Classic Sudoku [WSC 2010]

Thanks - that one gets a slightly higher diabolical rating of 559 at http://www.sudokuwiki.org/sudoku.htm

### Re: Very Hard Classic Sudoku [WSC 2010]

In some of the posts so far, you mix "guessing" with "trail and error". I think, we should clearly distinguish between these two, because they are two different solving techniques, both feasable in some situations. To clearify:

While "guessing" is not a logical method, "trial an error" is. In fact you cannot distinguish "trail and error" from any other logical solving method. Think of a sudoku, which has 80 givens and only one cell left. You can use "trial and error" to solve this sudoku: Try 1 - doesn't fit, try 2 - doesn't fit, ... try 8 - doen't fit, try 9 - yeah! Contrary, whenever you solved a sudoku with "trial and error" you can replace this by a logic solving technique. The technique developed might include lot's of preconditions and is probably not usefull, but it's still logic.

What I want to say is, that I wouldn't exclude some sudokus by a list of solving techniques. One never knows if someone finds a completely new solving technique (none of us ever dreamed of yet), which makes this sudoku an easy one (such things happend, for example in the realm of fences puzzles). I would ask, that points are distributed fairly (by using enough testsolvers) and contests (and rounds) are not unbalanced with some sudokus overshadowing the rest.

To summarize: I would not reject (or select if you want to have a more positive view on it) any puzzle by certain (more or less arbitrary) conditions (which might be subject to change), but by results from testsolving and clear constraints on contests (balanced rounds, balanced contest, fairly distributed points etc.).

- Guessing means, that one puts a more or less random number in one cell and continues to solve. The result might be, that you will finish with a wrong solution or in case you guessed right, with a correct one.
- Trial and error means, that one carefully selects one cell and continues to solve with all possible values left for that cell. From here various possibilities arise: It's possible that one (or more than one) other cell has always the same number, independent of all values tried for the first cell. Then you know that number for sure and you can continue with that new number. Or you might be able to solve the sudoku with one of the values. Then you've got at least one solution. (As a side note: In case, a sudoku has more than one solution, this is the only way to find a solution.) More possibile outcomes exist, but it's not the place to discuss them all.

While "guessing" is not a logical method, "trial an error" is. In fact you cannot distinguish "trail and error" from any other logical solving method. Think of a sudoku, which has 80 givens and only one cell left. You can use "trial and error" to solve this sudoku: Try 1 - doesn't fit, try 2 - doesn't fit, ... try 8 - doen't fit, try 9 - yeah! Contrary, whenever you solved a sudoku with "trial and error" you can replace this by a logic solving technique. The technique developed might include lot's of preconditions and is probably not usefull, but it's still logic.

Well, if you include this sudoku in a contest with other less difficult classics and distribute fair points, you've got some sudokus with points not larger than 100 and one with, say 5000 points. In that case, the contest is clearly unbalanced and I would reject it therefore. If the whole contest would feature only such puzzles, it would be ok for me to include them. (Just in case: If only one round consists of such sudokus and all other rounds are "normal" it's still an unbalanced contest or the points are not distributed fairly.)Feadoor wrote: ↑Thu 03 Jan, 2019 10:10 amI think this is unreasonable. Take the sudoku known as "Golden Nugget". It has the following characteristics:

- Using standard solving techniques, no numbers can be placed

- Furthermore, using standard solving techniques, no potential candidates can even be eliminated from a cell, that is:

- Whatever cell and whatever number you choose as the starting point for a guess will lead to zero progress - using standard techniques, it cannot be proved or disproved without immediately making another guess.

What I want to say is, that I wouldn't exclude some sudokus by a list of solving techniques. One never knows if someone finds a completely new solving technique (none of us ever dreamed of yet), which makes this sudoku an easy one (such things happend, for example in the realm of fences puzzles). I would ask, that points are distributed fairly (by using enough testsolvers) and contests (and rounds) are not unbalanced with some sudokus overshadowing the rest.

If you use "guessing" like described above, you will probably not solve the puzzle at all. If you use "trial and error" you will solve it and you probably might be much faster using this technique. In my oppinion, this is fair, because there is quite some skill requiered to find a good starting point for "trial and error" and from my experience stronger solvers are better here too.Fred76 wrote: ↑Thu 03 Jan, 2019 2:39 pmThe ones who are able to solve these hard classics (or even harder than the example posted here), will never win by solving it, because it is much faster to guess the solution. Thus, probably even the players who are able to solve it logically will prefer to guess the solution to be well ranked...

That's true, but should not be a reason to remove them completely from a world championship. Sometimes you've got to do stuff that doesn't make fun, if you want to be a champion.

That again is something, I would move to the testsolving stage: If the times from the testsolvers differ too much, that is a sign, that the puzzle is unfair and should not be included in a contest. (At the moment I'm preparing the puzzles for the German Sudoku Championship and I dropped one puzzle for exactly this reason - it was solvable without trial and error and as far as I know the testsolvers did not use trial and error). On the other hand, it's thinkable, that sudokus exist, where you are better of using trial and error and still solving times are not much variable. I would not want to reject these puzzles from a contest.- The reward for solving these puzzles is highly variable.

To summarize: I would not reject (or select if you want to have a more positive view on it) any puzzle by certain (more or less arbitrary) conditions (which might be subject to change), but by results from testsolving and clear constraints on contests (balanced rounds, balanced contest, fairly distributed points etc.).

### Re: Very Hard Classic Sudoku [WSC 2010]

Hi Berni, thanks very much for your thoughts.

The main issue I have with the description of trial and error as a logical technique is the observation that, if you are fortunate from a speed solving point of view, you get lucky and don’t hit an error. Although I am not 100% certain, I can’t imagine that record time for 2009 involved much error and exhausting all possible cases from a carefully selected bifurcation point - the difficulty of the puzzle coupled with the speed of the solve suggest this is very unlikely.

I would agree that there is certainly a difference between a haphazardly chosen guess and a more considered system of trial and error. I’d also expect there to be a correlation between top solvers and top guessers, simply because if you can “logically” (not the right word strictly speaking but I hope my meaning here is clear) solve faster then you should be able to get through cases faster too.

However, there is still a great amount of variability. Maybe there are several a priori promising places to make your guess, and one in particular is helpful in cracking open the puzzle and you get it first time. Maybe someone else has to go through several branches of trial and error before they get anywhere. We can argue to a certain degree over the amount of skill at play, however I don’t think it is possible to argue there is no small amount of luck in play too.

From that point of view, a round of harder classics coukd bsaid to be in some sense fairer as the luck, should, on average, balance itself out. Not that on average guarantees everything. It is still possible (although less likely) for an individual solver to have a run of lucky (or unlucky) guesses through a series of such puzzles. And exactly the same reasoning applies to your test solving - it should be picked up given enough testers, but it is not impossible for all of them to get lucky

The main issue I have with the description of trial and error as a logical technique is the observation that, if you are fortunate from a speed solving point of view, you get lucky and don’t hit an error. Although I am not 100% certain, I can’t imagine that record time for 2009 involved much error and exhausting all possible cases from a carefully selected bifurcation point - the difficulty of the puzzle coupled with the speed of the solve suggest this is very unlikely.

I would agree that there is certainly a difference between a haphazardly chosen guess and a more considered system of trial and error. I’d also expect there to be a correlation between top solvers and top guessers, simply because if you can “logically” (not the right word strictly speaking but I hope my meaning here is clear) solve faster then you should be able to get through cases faster too.

However, there is still a great amount of variability. Maybe there are several a priori promising places to make your guess, and one in particular is helpful in cracking open the puzzle and you get it first time. Maybe someone else has to go through several branches of trial and error before they get anywhere. We can argue to a certain degree over the amount of skill at play, however I don’t think it is possible to argue there is no small amount of luck in play too.

From that point of view, a round of harder classics coukd bsaid to be in some sense fairer as the luck, should, on average, balance itself out. Not that on average guarantees everything. It is still possible (although less likely) for an individual solver to have a run of lucky (or unlucky) guesses through a series of such puzzles. And exactly the same reasoning applies to your test solving - it should be picked up given enough testers, but it is not impossible for all of them to get lucky

### Re: Very Hard Classic Sudoku [WSC 2010]

Indeed. That's a well-known problem from science. The solution there is to say, we want to err in not more than (say) 1 out of 100 cases. Since long I want to calculate the number of testsolvers you need to achieve this level... But I never did it, yet.detuned wrote: ↑Fri 04 Jan, 2019 6:23 pmFrom that point of view, a round of harder classics coukd bsaid to be in some sense fairer as the luck, should, on average, balance itself out. Not that on average guarantees everything. It is still possible (although less likely) for an individual solver to have a run of lucky (or unlucky) guesses through a series of such puzzles. And exactly the same reasoning applies to your test solving - it should be picked up given enough testers, but it is not impossible for all of them to get lucky

### Re: Very Hard Classic Sudoku [WSC 2010]

berni wrote: ↑Fri 04 Jan, 2019 10:05 amIf you use "guessing" like described above, you will probably not solve the puzzle at all. If you use "trial and error" you will solve it and you probably might be much faster using this technique. In my oppinion, this is fair, because there is quite some skill requiered to find a good starting point for "trial and error" and from my experience stronger solvers are better here too.Fred76 wrote: ↑Thu 03 Jan, 2019 2:39 pmThe ones who are able to solve these hard classics (or even harder than the example posted here), will never win by solving it, because it is much faster to guess the solution. Thus, probably even the players who are able to solve it logically will prefer to guess the solution to be well ranked...

I understand and I agree your point about difference between guessing and T&E, but I maintain that I think it is much faster to solve this sudoku by guessing (even if your 1rst guess is wrong) than solving by logic, including T&E.

I think nobody is able to solve this sudoku in a competitive solving time using standard techniques. For this one, sudoku explainer (SE) propose to solve it by using:

52 x Hidden Single, 2 x Naked Single, 3 x Pointing, 1 x Swordfish, 1 x Turbot Fish, 15 x Forcing Chain, 1 x Bidirectional Cycle.

By using non-standard techniques as T&E, I'm not sure you'll get a competitive solving time either, I disagree with you concerning this puzzle.

I haven't taken part in WSC 2010, but I think the same problem occured at WSC 2011 (hard classic round) and in 1rst round of sudoku GP 2014.

If nobody among author, organizers or testers is able to explain how a sudoku can be solved (including T&E technique) in a decent competitive time without using guessing, I think this sudoku should be rejected from the competition.

Here, I disagree, too. For 2 reasons:

- People concerned by WSC form a "small community" [WPF director], it means that most of players have no sponsor, they have to pay to attend the competition, there is no prize money, rewards for best players only consists of good reputation among this small community. I would say 95% of the players are there to have fun to solve sudoku. This point could be enough for the organizers to select puzzles that are potentially fun to solve.
- But the second point is more important to my eyes: it is the author point of view. As an author, if I created 2 puzzles of same types and similar difficulty, I'll always chose the one that I think is the more fun to solve for a competition. It is my task as an author, to create puzzles that can be fun to solve. Now the question, is it possible to create hard classic sudokus that are fun to solve? Until a certain point, I would answer yes.

Consider for example this one: http://sudokuvariante.blogspot.com/2015 ... e-n73.html It is graded 563 on http://www.sudokuwiki.org/sudoku.htm, but the only techniques that are needed are the 6 first basics. Nobody from my testers (included Bastien and Tiit) solved it in less than 6 minutes (it was used in a competition in 2015). And I had good feedback regarding how fun it was to solve it.