Thoughts on "What is a Sudoku?"

Throughout much of last year, and early parts of this year, I wrote a report which tried to survey the wide and varied landscape of sudoku variations, in order to give guidance and clarity to both the organisers and the solvers of sudoku competitions.

The original report can be viewed here.

To cut a long story short, I lay out some principles to help determine whether a puzzle "looks like" a classic sudoku, and whether it "solves like" a classic sudoku.

It was submitted to the World Puzzle Federation, who have also published a PDF version here.

I'm sure my dearest readers will be heartened to hear that:

Vladimir and Prasanna are reviewing past WSCs to see how they fit within the report and the WPF will then analyse the results and move forward on any potential actions, including but not limited to a potential breakdown of percentages of different categories provided by the report that a WSC should ideally target having.

Looking back, it's clear that writing this report caused me all sorts of personal trauma, and I took the decision to hand it over to the WPF, to not look back, and to not be involved with whatever the WPF choose to do with it going forward.

On the other hand, since finishing the report (I think it was February) I have had some time to reflect on some related issues.

1. People do care about this question, and it is important

One response from those who actively choose to engage with my work - a response I general take as being irritatingly patronising, even if that's not the intention - is that no-one really cares about this question, that people know a sudoku when they see one, and that an exercise in trying to survey the landscape of sudoku variations is a waste of time.

This attitude more or less comes from solvers who are equally at home at the WSC as they are at the WPC.  To simplify the argument in the terms of my report, the most important thing for them is that if a puzzle "looks like" classic sudoku, then they can't really understand why people wouldn't want to solve the puzzle as part of a sudoku competition.

One recent response to this might be some anecdotal evidence relating to the WPF's 2020 Sudoku Grand Prix competition, Round 5, with puzzles provided by authors from India.  The following anonymised comments are not my own, and nor were they comments that I went out of my way to solicit to persue any kind of agenda.  They simply reflect the experiences and feelings of several seasoned sudoku solvers.

"Still a lot better than me. I broke every puzzle I tried and even made an error in one puzzle (or the answer key, didn't bother checking which)"

"I thought most of the latter "sudokus" were more puzzle like and wouldn't fit the definition of a sudoku in the report Tom released earlier this month. It's pretty disappointing that we had a competition that rewarded the best guessers. I don't know if I'll bother with any more GPs this year."

"I had some hard time there too in that round. Didn't go smoothly I must say. Also had to guess in some puzzles. After finishing I had a feeling that I did horribly"

"At least you all scored a few points. After breaking three puzzles and having had to guess on two, I decided that I had enough and gave up altogether."

Reading all of that gives me the impression that even seasoned puzzlers did not enjoy this set of puzzles in the whole.  I will add that whilst there were certainly some very enjoyable puzzles that did appear on the round, it seems the less enjoyable ones have dominated this feedback.  If you'll allow me to go further, I'd say that it's because not enough consideration was given to how some of the puzzles were "solving like".  Perhaps the experience might have been improved if these puzzles solved more elegantly and without the need for guesswork.  In general I would also add that a lot of people also feel that if they want to solve sudoku variations, then a lot of the enjoyment comes from that puzzle "solving like" classic sudoku.

My point here is not to single out a particular GP round - apart from anything else it happens to be the most recent sudoku competition I can think of.  My point is to rebut some of this criticism of irrelevance.  In summary, I think there is great value in trying to put in to words explicitly what a lot of people have been feeling for a long time.  Namely, these concepts of whether a puzzle "looks like" classic sudoku and whether it "solves like" classic sudoku.

If you still feel that I'm stating the bleeding obvious, then I humbly ask in response: why has it not been stated anywhere before this report?

2. It's OK for sudoku variations to "look like" classic sudoku but not "solve like" classic sudoku

Another reason why people look to dismiss the report as irrelevant comes from a place of fear, that by calling out some kind of dividing line between what does and does not "solve like" classic sudoku is somehow going to consign a whole raft of creative/innovative/different/etc sudoku variations to the dustbin of history.  To give the devil his due, this isn't a groundless fear.  There is a certain minority within WPC community which seems to hold a special kind of disdain reserved for anything remotely looking like sudoku.  To simplify the argument a little bit, the feeling is that because there are sudoku competitions separate from puzzle competitions, anything that "looks like" a sudoku should be separate from any kind of puzzle competition - which would mean that variations that "look like" but do not "solve like" classic sudoku are potentially in danger of not having a home anywhere.

I can't say I fully understand this attitude, given that a WPC fad in recent years is to dedicate entire rounds to variations of one type of puzzle or another (Tapa, Snakes, Skyscrapers, Kropki).  Different puzzlers have different preferences, and certainly I've heard people that they don't much enjoy one or more of those types, but it never seems to be quite as strong a feeling as that reserved for sudoku.  I have never heard anyone say that Kropki puzzles do not belong at the WPC.  Admittedly there isn't such a thing as the WKC, but then again I don't see the existance of a separate competition as being sufficient grounds for some kind of puzzling apartheid.

From my observations within the WPC community it seems that, for some, this disdain comes from a sense of snobbery arising from the general popularity of sudoku; and for others it comes from a place of insecurity that they can't solve it competitively quickly.  I don't think that quite gets to the bottom of the double standards though, and I'd be interested to hear other perspectives.  Maybe people don't want to feel as if they are being tied down to just one type of puzzle.

Returning to the main point, I certainly don't want anyone to consign any puzzle to any kind of dustbin, and so I appreciate that it is worth discussing the puzzles which "look like" classic sudoku, but do not "solve like" classic sudoku.  In my opinion they have a place in both puzzle competitions and in sudoku competitions, but that the current way in which this happens is not particularly satisfactory.

I think it is fine to have sudoku competitions where you have all kinds of weird and wacky variations where the constraints and solving logic contain all sorts of novelties.  However I think that organisers of these competitions have to be more straightforward and transparent about this, and actually tell solvers that some of these puzzles do not particularly "solve like" classic sudoku.  Once organisers make this communication, they will have to accept the consequence that these kinds of competitions will not be as popular as those where the sudoku variations can be said to "solve like" classic sudoku.

On the puzzle side of this division, I also think it is fine to have puzzle competitions with the odd sudoku variation here or there.  Maybe you could have an entire round of them as well - I don't see any problem there.  The sudoku variations don't necessarily have to all be weird and wacky puzzles where the logic is far departed from "solving like" classic sudoku either - I don't see any problem in having conventional and well established sudoku variations in a puzzle competition.

Indeed, the fact that classic sudoku isn't featured in each and every round themed as "common/standard/classic puzzle types" absolutely baffles me.

3. It is perfectly possible to be creative/innovative/think outside the box with sudoku variations that do "solve like" classic sudoku

This is more a side point from the discussion above.  I was tempted to think this goes without saying, but on reflection I think it's clear that it doesn't.  Some people think that puzzles can only be interesting if you keep pushing the boundaries of rules and constraints in some kind of fetishisation of novelty.  

That argument is patently nonsense - and whilst I'm tempted to leave things there, I will add a bit of nuance by conceding that sometimes it takes a highly skilled author to pull off something fresh and interesting within the confines of the familiar.  I think it's fair to say that whilst there might be increasing numbers of sudoku authors, the number of them that I regard as having this level of ability is a number that I can still count using my fingers.

My own view is that innovation for the sake of innovation is more or less useless unless you pay some regard to whether your new creation solves nicely or not.  In fact it might be worse than useless if people are turned off because of these innovations - which is  something that I hope won't start happening with the Sudoku GP for example.  And that's not to say that I don't welcome any kind of innovation or exploration.  I'd just say that a little bit of self-discipline and self-critical evaluation certainly wouldn't go astray, particularly if you are introducing your creations straight into a competition.

4. Sudoku *is* an exceptional puzzle (for now)

In the discussions above, I've almost taken as given that there is some weird division between sudoku and puzzles.  When you step back and think about this idea, it's absolutely bizarre.  Sudoku and variations are simply a subset of logic puzzles - there is not really much more of a division to talk about besides deciding if something "looks like" a classic sudoku or not, and even then that separates "sudoku variation" puzzles from "not sudoku variation" puzzles.  The general category of puzzles includes both of these subcategories.  That said, because some sudoku competitions have historically sneaked in the odd puzzle here and there that didn't really "look like" sudoku I think it was still worth stating explicitly.

This historical curiosity aside, the main reason that this weird division nevertheless exists is because the WPF decided back in 2006 that there should be a competition for sudoku (i.e. the WSC) entirely separate from the WPC.  Looking at the numbers, this division seems to have been a success in one sense, which is to say that the WSC seems to be more popular than the WPC, and there are more solvers of the Sudoku GP than there are of the Puzzle GP.  On the other hand, this weird division has given birth to an increasing tension between sudoku and puzzles, a tension that the WPF has only half-spotted.  Me writing this report was supposed to put a lid on things, but as far as I'm concerned what has really happened with everything I have thought about and learned about, if I'm allowed to mix my metaphors, is that the lid has come off a can of worms.

As such I will end with an invitation for all those who do not share my belief that there is any kind of tension to perhaps reconsider their point of view.

There is clearly an appetite amongst solvers in general to maintain the exceptional status sudoku enjoys relative to other types of puzzle - no other type  of puzzle enjoys remotely near the levels of worldwide popularity that sudoku does.  As this is the case, the WPF is going to tread water unless it begins to maintain a clearly communicated distinction between its sudoku and its puzzle competitions.  If your sudoku competitions are going to be dominated by puzzles that don't much "solve like" classic sudoku, then I think inevitably  you are going to end up with accusations that WSCs are little more than mini WPCs.  And if that ends up being the case, I think you have completely missed the point of having a separate WSC in the first place.   

Moreover, this does not - in any way - contradict any of what I've written in point 2 above!  It is still possible to accomodate all forms of sudoku variations within competitions, be they sudoku competitions or be they puzzle competitions, as long as this is done with clear thought and communication.  This kind of clarity of thought and communication is what I'd like to see above everything else.

Of course, given that the WSC and WPC happen in the same week, there are plenty of people (including myself) who compete in both events and are more or less happy with the state of affairs.  Certainly there are many who really can't understand why anything would ever need to change.  I think that this point of view somehow manages to miss an obvious tautology arising from a self selecting bias.  Maybe that's fair enough and things should continue as they are for the benefit of exactly those people who enjoy things as they are, because after all, those people are enjoying things!  If that's the case, then maybe the WPF's audience will continue to be measured in the hundreds, or low thousands.  The success of Cracking The Cryptic, who now count in the hundreds of thousands, suggests this might be lacking in ambition.

So, will the WPF fudge together a compromise involving quotas and percentages without ever addressing the fundamental issues, and instead continue to have them bubbling away under the surface as the exceptionalism of sudoku slowly erodes away?  Time will tell - although I'll add that those issues have been bubbling away since at least 2008.  But if someone with a bit more clarity of thought, vision and ambition wants to step up and make something happen, then I might reconsider my decision to stay out of things.