Puzzle 354 X-Sums Sudoku

I had in mind to write a few X-Sums and Killer Sudoku over the next few days, which led me to digging around in my notebook and spotting a puzzle or two that I don't think I'd published anywhere.

Actually I think this one was in the same batch as a similar post I made last year.  I think I originally wrote that batch for someone I care about very deeply and who particularly enjoys X-Sums Sudoku.  Last year’s  post was the better puzzle I think, but I certainly enjoyed myself re-solving this one just now and it certainly seemed too good not to share.

Obviously 2020 hasn't been the best year for many people, but 2019 was also a pretty miserable year for me, and off the back of that I had a period in February this year, before the pandemic set in where I was feeling particularly hurt, betrayed, ignored, unloved, unappreciated and unencouraged.  Maybe that wasn't (and isn't) exactly true, but it certainly felt real enough at the time and was a really overwhelming wave of sadness.  One of the nicer things to happen after that was receiving a message from Simon Anthony, who offered to do a video on one of my puzzles.  Mark, who is a good friend, was very generous with his comments in the ensuing video, which features the puzzle from that same post.  

The whole thing was a kind gesture, as perhaps even back then, pre-pandemic, it was clear that the puzzles that I like to write and the puzzles I enjoy are generally in a very different direction from the puzzles that they like to feature on the channel.  With that in mind I suppose that I'm not surprised that's pretty much the last I heard from them, despite our previous history.  As I've said before, that's not a complaint on my part, it's fair enough, they've moved on and have their own audiences to worry about.  I am certainly appreciative of the gesture when I was at a really low point.  

It was certainly in marked contrast from any support from the WPF, for whom I was half killing myself to write a report trying to provide clarity in trying to classifying sudoku variations.  Looking back, it was a good report and something that I suppose I'm proud of - But equally, it turns out that that was something the WPF didn't take seriously (either in trying to produce it - or then subsequently using when finished), and that the wider community was more or less entirely indifferent to, and so it's hard to conclude that all that effort wasn't entirely in vain.

I felt a similar overwhelming wave of sadness again over the Christmas period - here in London Christmas has more or less been cancelled and I've had to try and cope by myself as best I can.  If I'm being completely honest there have been times where I have not coped at all.  Part of my sadness is that to me, the puzzling community feels as distant now as it ever has - previously it has been somewhere where I could draw a sense of appreciation, strength and support - and I just don't get any of that any more.  I should say that there's no real point or criticism I'm trying to make here, dearest reader, this is just how life goes and sometimes things just move on.  It's more a case of making some observations and trying to process and untangle some knotty threads that have been bringing me down for what is probably a period of over 2 years now.

Better out than in I suppose - I hope my dearest readers have had a happier year than I have.  Enjoy!

    #354 X-Sums Sudoku – rated 6/10 [Hard]

All puzzles © Tom Collyer 2009-20.

Puzzle 353 Sudoku

Sometimes it turns out that you aren't always everyone's flavour of the month.  As always,  I suppose I'll have to make my own fun, and as always I am very grateful for the company of my dearest readers.

So here the intended idea is a little bit obscured by having to add in a couple more givens than I'd have liked, in order to guarantee uniqueness.  This unfortunately gives a few easy-ish placements to start off, maybe lulling you into a false sense of security.  Which is a pity for the flow of the puzzle, but such is life.

Anyhow all I'll say with this puzzle is that if you're looking for dead-or-alive ambiguity you'll know it when you see it, dearest reader.  After that the puzzle will flow quite nicely, even if I do say so myself.  Enjoy!

    #353 Sudoku – rated 9/10 [Very Hard]

All puzzles © Tom Collyer 2009-20.

Puzzle 352 Sudoku

So here's a puzzle with an idea on a recent theme.  I'd say the execution is reasonably good, but as I'm working mostly by hand it doesn't quite feel polished to its true potential.  It's still doable if you don't get the idea, but fair warning, it might be a bit of a slog.  Failing that it's probably very guessable.  But I have more faith in you than that, dearest reader.  Enjoy!

   #352 Sudoku – rated 8/10 [Very Hard]

Update: I might downgrade this from a 9 to an 8 as I've just realised the intended pattern used is very similar to the original Phistomefel pattern, which perhaps is a bit easier to spot and make use of...

All puzzles © Tom Collyer 2009-20.

Reflections on Intersections, Naked and Hidden.

There's no puzzle in this post I'm afraid, but a few random thoughts.  Some more to do with me, and some more generally on Sudoku Theory.  I'm afraid if you're more interested in one things rather than the other, dearest reader, then you'll just have to bear with me this time.

---

Firstly, something that has been playing on my mind a bit recently was the announcement of a Cracking the Cryptic sudoku book via a kickstarter campaign.  This does look very exciting, and I've paid up my $19 USD to secure a copy for whenever it's ready.  The money they've raised to date is phenomenal and it's exciting to see exactly where Mark and Simon can take Sudoku, particularly when you compare that with what the WPF has been able to achieve.  All the best to them!

And yet when I look at the list of the contributors, it's a bit like seeing all the cool kids running off to play their cool kid game, without being invited.  Don't get me wrong, it's their book and their channel and they can do whatever they like, I have no problem with that.  And I do get that the puzzles I create aren't really the sorts of puzzles that get their viewers' pulses racing, so there's no real reason why I would be included.  And the authors on that list certainly include a few of my favourite authors so absolutely no complaints there.  I suppose the crux of the matter is simply that I'm kidding myself a bit to look at that list as a "Who's Who" of the best sudoku authors.  From that point of view I can console myself with the company of many more of my absolute favourite sudoku authors who didn't make the cut.

I'll leave things there - I do feel a bit better for simply expressing my feelings on the matter to you, dearest reader - I suppose all I'm really saying is that it would have been nice to have been asked.  As presumptuous as I'm sure that sounds to even my most dearest of readers.

---

Moving on, I've been thinking a little more on some of the recent posts and discussions on this blog, particularly to do with intersection theory.  The news thing from that front is that I've created this resource to help any of my interested dearest readers to easily visualise the addition and subtraction of rows, columns and 3x3 boxes.

https://docs.google.com/spreadsheets/d/1dTAJNB-U-5d8bxwFsWwyVHEU9xAGiBf3mjMmUboHzFI/edit?usp=sharing

I've also started fleshing out a list of references which might become the basis of a more permanent article I might put together as and when I get my head around this stuff even more.

Fred's recent comment gives me some hope that there might be some kind of multiplication we can work into this algebra of constraints, but I haven't really given much more thought to it than that.  If anyone else gets there before I do I'd be most interested to hear about it!

---

The final item of business is simply to reflect that all this discussion holds my interest because it's fundamentally about linking different areas of a sudoku grid to each other in interesting ways.  We had started off by thinking about these as partitions of cells, but I did want to discuss something more along the lines of a partition of digits.

At the danger of stating the complete obvious, hidden pairs/triples/etc using a subset of the digits 1-9 are exactly the same thing as naked septuplets/sextuplets/etc, and vice versa.  The way I thought about it was like this:

• Suppose you have a naked triple of 3 cells in a row whose possible candidate placements are some of 1,2,3.  That means there a 6 cells left in the row, and 6 digits which we haven't been able to place - i.e. we have the very definition of a hidden sextuplet.
• Now suppose you have a hidden triple of digits 1,2,3 - each of which can only go in some or all of 3 different cells in a particular row.  This means that for each of the 6 remaining cells, we only have 6 possible digits from which we can choose from - i.e. we have the very definition of a naked sextuplet.

The conclusion is that which ever way you look at things, hidden or naked, you end up making identical deductions.

My next thought is that the naked point of view (i.e. looking at which digits are possibilities for given cells) I've always - perhaps mistakenly - viewed as the basis for some of the more advanced techniques when compared to the hidden point of view (i.e. looking at which cells are possibilities for given digits).

I say perhaps mistakenly because I think I realise now this is probably a misconception I've picked up trying to follow discussions of advanced sudoku solving techniques, where computer assistance is de rigueur and grids are very conveniently displayed with all the possible candidates automatically displayed - an approach to sudoku solving which generally leaves me very cold.  When I tend to solve, the more cells in the grid I label with pencilmarks, the less I generally enjoy solving a puzzle.

Anyhow, the link between naked and hidden and partitions and so on reared its head to me again when I came across Bob Hanson's website, discussing:

• Bent naked subsets (in particular Y-wings)
• Intersection ideas briefly
• Intersection ideas in more detail

As I'm sure you can pick up from the somewhat dated web-design, in some sense all of this way of thinking is not particularly new - indeed it's been around nearly as long as sudoku mania (dating back to 2004) itself has.  My interest remains in thinking about these things from different perspectives.

There's a bit more there for me to get my head around, particularly with a link to almost locked sets (ALS) and what he describes as almost locked ranges, but I want to finish with the two rules that Bob outlines with relations to bent subsets:

1. If a bent naked subset contains one and only one candidate k that is present in both of its nonintersection subdomains, k can be eliminated as a candidate in any cell that sees all the possibilities for k in the subset.
2. When there is no common value k in the two nonintersecting regions of a bent naked subset, the subset behaves as a standard naked subset. That is, candidate k can be eliminated from any cell that can "see" all cells of the subset containing k.

What I'd like to try and work out and see if there's a "hidden" point of view for "naked" subsets that span intersections of a row/column with a box, in the same kind of pleasing way that can alternatively view so-called Schroedinger's cells via intersections as a kind of semi-Phistomefel arrangement.  Again if anyone else gets there before I do, I'd be most interested to hear about it!

The MSLS: Revolutions

Wait. 

I've seen this. 

I stand here, right here, and I'm supposed to say something.

I say, "Every grid with an intersection of partitions deduction has a multi sector locked set, Tom"

A little while back I published a difficult puzzle as a kind of tribute to what I consider one of the greatest Sudoku puzzles of all time.  This puzzle was first published in 2008 in the Botsu Baku section of what was nikoli.com.  Sadly, nikoli.com and its many, many gems are no longer with us, but I do have a screenshot or two in my private records so that there is at least some archive of these puzzles.

To make initial progress with this puzzle, you can place a 3 in R9C6 and 9's in R3C5 and R5C8. And then you grind to a halt.

I suppose it should come as no surprise that this is a puzzle that Cracking the Cryptic has picked up on previously, as wonderfully meticulous as they are.  The position after these three placed digits seems to be where they've picked up on this.  [As an aside, I can't say why they picked up on this non-symmetrical version of the puzzle, to which there isn't the usual attribution - but I'd be interested to hear more about that].  Simon goes on to describe the technique required as a so-called Schroedinger's cell.

R4C1 is identified as the Schroedinger's cell, which seems the natural choice as the ensuing what-if analysis makes use of the fact that the only candidates in R9C5 are 1 and 2.  This mirrors the original explanation given by nikoli in the corresponding solution replay back in 2008, as it happens.  My interpretation of the logic is something like:

• If R9C5 is not a 1, then this means the 1 in Row 9 must go in R9C3.
• This implies the 1 in Column 1 must go in R4C1.
• Equally, if R9C5 is not a 2, this means that R4C1 must be a 2.
• Therefore the only candidates for the Schroedinger's cell R4C1 have to be 1 and 2

The puzzle then continues by noting that the only place for a 4 in Column 1 is at R2C1.

One observation with my interpretation is that we didn't use the fact that the only candidates for R9C5 were 1 and 2.  If R9C5 was neither 1 nor 2, then we'd have to conclude that R4C1 was simultaneously a 1 and 2.  Which, despite all this Schroedinger adjectival being thrown about, is still a contradiction, and so we also deduce that the only candidates for R9C5 are 1 and 2 anyway.

So why not observe that R9C5 is also a Schroedinger's cell?  The logic is something like:

• If R4C1 is not a 1, then this means the 1 in Column 1 must go in R1C7.
• This implies the 1 in Row 9 must go in R9C5.
• Equally, if R4C1 is not a 2, this means that R9C5 must be a 2.
• Therefore the only candidates for the Schroedinger's cell R9C5 have to be 1 and 2

The symmetry is beautiful!  But either way there is still something of the if-this-then-that, or even trial-and-error about this deduction.  Maybe we could make this slightly more satisfying:

 

Let's consider Row 9 and Column 1 simultaneously, which I've circled purple.  Within these 17 cells, we need to place two 1's and two 2's (noting that we already have a 6 placed at the intersection).

Now let's think about where we can possibly place this set of four digits within the confines of the purple cells?

• We can have at most one each in the two cells I've circled red
• We can have at most two cells in the cells I've circled orange (noting that these four cells are contained in one box)
• We can't have a 1 or 2 anywhere else!

Therefore, we can conclude that the "at mosts" are also "at leasts", and subsequently that the only two candidates in each red circled cell have to be 1 or 2.  If either cell was anything other than a 1 or a 2, then we could not fill up Row 9 and Column 1 with their full complements of 1s and 2s.  Put another way, this little trick that unlocks a masterpiece from 2008, is nothing other than an example of MSLS, as first described in 2012.  Which I think is rather extraordinary!

So dearest reader, what are we to make of all of this?  All the recent discussion regarding Phistomefel's theorem, its further generalisation as Fred's intersection theory, its further generalisation as Trevor Tao's "9D Wonkyfish" - as well as Sam Cappelman Lynes' exposition of this in the language of SK Loops and MSLS has certainly got me thinking.

Sam himself said that there is no formal definition of MSLS that is agreed upon, so I thought (at the risk of probably reinventing the wheel) it might be worth sticking my own neck out, and having a fumble in the dark with my own interpretation.

I see MSLS as being a generalisation of hidden pairs/triples etc.  The idea being that we are trying to find areas of the grid where we have:

1. A subset D of the digits 1-9, considered with a multiplicity M, which then makes up a set of (at most) M copies of D.  Let's call that repeated set S, and we'll say that it has a total of N digits to be placed.
2. A collection of (perhaps slightly more than) N cells into which the N (possibly repeated) digits of S need to fit into.
3. The idea then is that the digits in D squeeze out all the other candidates from those cells because there is no room for anything else.

To highlight the generalisation, suppose you have a row where you are looking to place the digits 1,2,3 - and you know that the 1 can only go in C4,9, the 2 can only go in C2,4,9 and the 3 can only go in C2,4.  Then you have a set of three digits (1,2,3), and only three cells in the row in which you can collectively place them.  The hidden triple deduction then lets you say that the possible candidates in C2,4,9 can only be 1,2,3 - and that any other digit can be eliminated as a possibility.

This is easy enough to see in the confines of a single Row (or Column, or 3x3 Box come to think of it) where we don't have the complication of repeated digits.  After all a hidden triple, whilst sometimes very difficult to see when solving by hand, is nevertheless viewed as an elementary sudoku solving technique.  What I find fascinating is that Phistomefel, Fred and Trevor have helped teach us that there are deeper structures within Sudoku, inherited from Latin squares, that link together multiple instances of different rows and columns, and to which we can apply the same kind of thinking.  These structures go beyond the naive understanding that we are simply looking to place each digit from 1-9 both at least once in each Row, Column and 3x3 Box in isolation, and indeed at most once in each Row, Column and 3x3 Box in isolation.

The examples from the Tatooine puzzles (we discuss sunset here), as well as Sam's puzzle (as discussed in Reloaded) involve rather large sets of "hidden" digits with multiplicity that somehow need to be squeezed rather tightly into similarly sized sets of cells within the grid, and both the digits and the cells can be hard to see on the face of it.  The main point of all the recent progress we have made, dearest reader, is to help better visualise when we might be in a situation to uncover one of these hidden multi-pairs, multi-triples or multi-quads.  

I don't think we will ever need anything bigger than quads, in much the same that we never really any thing beyond the 4-way x-wing, a.k.a. "Jellyfish".  In fact, I think the correct way of thinking about all of this is that x-wings, swordfish and jellyfish are basically hidden multi-singles.

I'll begin to conclude.  Hopefully with Revolutions, I have been able to demonstrate that hidden multi-sets don't always have to be big and intimidating beasts.  Once I revisited the nikoli puzzle with the MSLS framework in mind, I was surprised by the simplicity of the deduction - potentially even easier than x-wings and swordfish, and certainly no more difficult.  

Equally interesting is that within this simplicity lies something else that I haven't been able to grasp in terms of intersection theory alone - and I think it's because now we're mixing in 3x3 boxes alongside rows and columns.  As I've hinted previously, I do have other ideas about how this might equivalently end up, but on that note, dearest reader, I'm going to leave things there and simply say I much prefer Sudoku to Column Dance.

The MSLS: Reloaded

"And now here I stand, because of you Mr. Stalder, because of you.  I'm no longer an agent of this system, because of you.  I've changed.  I'm unplugged.  A new man, so to speak, like you, apparently free."

"Congratulations."

"Thank you."

So I was originally going to add one more post on this topic, but this morning it's become clear there's the opportunity to add two related posts, and add in more neat nods to pop culture I enjoy.

This one was prompted by last night's video on cracking the cryptic, which is very much presenting the MSLS interpretation of the discussion.  I'm not entirely sure whether Simon actually reads this blog, or gets the information via separate conversations he may (or may not!) be having with Sam, but in the videos he is vaguely referencing conversations between myself and Sam.  My discussions with Sam have only happened here on this blog, so one way or the other they have to be the source.  I haven't heard back from Simon since pointing him in the direction of Trevor Tao's wonderful video, which I'm sad to say has not (to date) even had a vague reference on cracking the cryptic, so I can't say for sure whether it's a conscious decision to present this theory from one angle, or whether he is simply unaware of the extent to which all this discussion is influenced by many different contributions, Trevor’s certainly not withstanding.

Anyhow, I hope at least that my dearest readers will agree that all this stuff is far too interesting to not explore in plenty of detail and from multiple different angles. 

On to business.  Sam has come up with a wonderful puzzle which I'm pretty sure has been designed to completely bamboozle scanraid.  And it does.  For reference:

• The video is here: https://www.youtube.com/watch?v=uvTV_Wivxmo
• You can play the puzzle here: https://app.crackingthecryptic.com/webapp/dqTM27jm3P

However, I’d like to present it to you again with a bit of colouring in:

As I'm sure all my dearest readers are aware, this looks very much like one of Fred Stalder's examples as discussed in a previous post.  To recap:

• Here's my post: https://tcollyer.blogspot.com/2020/09/puzzle-350-sudoku.html
• Here's Fred's original post: http://forum.logic-masters.de/showthread.php?tid=1811&pid=32019#pid32019

The punchline to all of this is that instead of doing all the elegant MSLS stuff that Simon does in the video, you can instead make the following (simpler!) observations:

1. Thanks to Fred, we know that the digits placed in the blue cells plus a copy of (1-9) are precisely the same digits that need to be placed in the red cells.
2. There are 15 red cells with odd digit givens, and 10 red cells with no givens
3. There are 6 blue cells with even digit givens, and 4 further even digits in the copy of (1-9)
4. Therefore the 10 empty red cells must contain 10 even digits.

As Sam has pointed out on a youtube comment discussion, Fred gives you even more than that, but the observations above are all you need to serenely solve a diabolical-rated sudoku.

That's all for now folks - I still have one further follow up on this subject, again linking together some of the subject matter I've been discussing recently.

There shined a shiny demon, in the middle of the road

And I made the first grid that came to my head

Just so happened to be

The best grid in the world

It was the best grid in the world

Look into my eyes, is it easy to see?

One and One go where?

Two and One must be?

It was destiny

More on this one later, especially for my dearest readers whose memory might not go back quite as far as 2008, but also for all my dearest readers who have enjoyed the recent discussions.  

And although this is just a tribute to a legend of nikoli.com, I also think it's one of the better Sudokus I've ever put together.  For whatever that's worth.  Enjoy!

   #351 Sudoku – rated 8/10 [Very Hard]

Edit: I'm having second thoughts about the rating of this puzzle.  I initially thought I wouldn't have the balls to put something like this into a sudoku competition, because people might end up guessing anyway.  But on second thoughts (see the comments for more thoughts), maybe I would.  In which case that 10 might get downgraded to an 8 or 9.

All puzzles © Tom Collyer 2009-20.

Tatooine Sunsets and Partitions of Latin Squares

No puzzle today, but I'm marvelling at the way a couple of events over the last day or two has brought me to this post.  I am very excited about all of it, and I'm probably going to have a bit of trouble keeping this post clear and coherent, so let me first post the main link to this video by Trevor Tao, which is a demonstration of unbelievable genius sudoku solving.

• Tatooine Sunset Sudoku and the 9-Dimensional Wonkyfish

I wouldn't recommend jumping straight into it however, so I'm going to try and post a little bit of background material first.  I'm now going to work backwards.

Today (9th October) I was about to write this post, and then I saw Sam Cappleman-Lynes comment on my previous post regarding Phistomefel's theorem being equivalent to SK Loops, and so I am wondering if the Fred's generalisation, and the further generalisation I am about to try and explain, are in fact equivalently explained using some impenetrable notation in a dark corner somewhere over on http://forum.enjoysudoku.com/.  Maybe we'll find that out later, dearest reader.

Now let's jump back to the beginning.  My attention was piqued over on Cracking the Cryptic by a pair of videos where both Mark and Simon solved the same puzzle by Philip Newman, which comes with the name Tatooine Sunset:

• Mark's guessy solve is here: How I "Cheat" at Sudoku
• Simon's more methodical solve is here: How NOT To Cheat At Sudoku!
• For reference, the puzzle is also discussed here: http://forum.enjoysudoku.com/tatooine-sunset-tatooine-sunrise-t38180.html

I watched Simon's video on Wednesday night (7th October), and saw there were an awful lot of swordfish going on, together with some triples, and that everything was hinting at some extraordinary underlying structure to this puzzle.  I messaged Simon to say that there was something sort of Phistomefel-ly with the givens in the 4x4 region of the grid between Rows 2-5 and Columns 2-5 (A).  I also saw there was something else going on with some more regions: namely those between Rows 7-8/Columns 2-5 (B), Rows 2-5/Columns 8-9 (C), and then Rows 7-8/Columns 8-9 (D).

This clearly suggested a Fred style partition, grouping together Rows 169 to define one part of the partition, and Columns 167 to define the other.  The 9 cell set (E) defined by the intersection of these rows and columns is absolutely fascinating, as it is where the breakthrough in this puzzle is made, after you're done with all the fishing around.

Fred's theory tells us that the set of digits placed in those 9 cells, plus 3 extra copies of 1-9, are equal to the set of 36 numbers placed in the four regions A, B, C and D described above.  I'd even got as far as noticing that the digits 5,7,9 occur exactly 3 times each in that ABCD area.  Which implies that the set E cannot contain the digits 5,7,9, since:

E + 3 x (1-9) = A + B + C + D

and the 3 copies of each digit on the right hand side are exactly accounted for by the 3 sets of 1-9 on the left.  This felt like an exciting deduction, and I'd even managed to have the idea that this was in some sense equivalent to swordfishes, because as Fred has told us, swordfishes are  one thing that can be explained by this intersection theory.

At that point I think I'd have been left scrabbling around not knowing what to do next.  It was as if I had some of the picture, but not all of it, and I had no idea what I was looking for.  However fate then smiled upon me. 

On Thursday night (8th October), as I was googling "tatooine sunset sudoku" to try and find the enjoysudoku forum post again, I noticed a link to Trevor Tao's video.  [I'm so excited by all of this I am only going to mention in passing that I *think* Trevor may well be the brother of the Fields Medal winner mathematician, Terence Tao].  I also messaged Simon about this video on Thursday, so I'm kind of hoping we might be seeing a video on this in the next week or so.  Simon certainly has a talent for clear exposition than I can only dream about!

Trevor's genius observation was that the right way of thinking about this puzzle is not via Fred's inersection theory, and a partition into 4 regions of the grids, but instead to partition rows and columns into 3 (which he does via colours in the video) to end up with a 9 region partition of the grid.

In case you are too lazy to scroll up to see the link to Trevor's video, I'm going to post it again.  I can't get over how unbelievably elegant this generalisation of Fred's already very elegant intersection theory actually is!

• Tatooine Sunset Sudoku and the 9-Dimensional Wonkyfish

The video skips over some of the details a bit quickly, so I'm going to add a couple of observations.

1. I'm not entirely convinced using the same colours to partition both the rows and the columns is necessarily helpful.  When playing around with this in my notebook, I'm labelling the columns ABC and the rows DEF.
2. I also don't think displaying the dual view of the 9 resulting intersections as exactly the same grid as the original Sudoku puzzle is all that intuitive.  Whilst the two are linked, they do behave very differently.  In my notebook I drew a 3x3 array of the partition something like this:
   DA DB DC
   EA EB EC
   FA FB FC
3. On the other hand there are some advantages to the colouring, as it does highlight some of the beautiful structures underlying this puzzle - firstly that the red rows/red columns intersection is entirely occupied by givens, which is also the case for the blue rows/blue columns intersection.
4. More than that, the digits in the red intersection and the digits in the blue intersection have no overlap!  And this imposes further structure into the dual 3x3 array because now it means that, for example, red rows/blue columns is the same set as blue rows/red columns.  In other words it's Fred's intersection theory working together simultaneously over 3 different 2x2 partitions!
5. What this then means is that you can play a weird sudoku-like game (albeit one with repeated symbols!) in this dual 3x3 array to then try and solve the sets of digits in each of the 9 intersections, noting that each complete set of 3 rows or 3 columns must contain 3 complete copies of the digits 1-9.
6. For this particular puzzle, this game is by no means trivial.  The step where Trevor places two 8's and two 1's in the green rows/green columns intersection (having first observed that having three of either is impossible) is quite subtle, and relies on some pigeonhole principle style reasoning.  For example, if you only have one 8 then this implies three 1s, which we have already seen is impossible.  And vice versa.
7. It's also worth observing that to solve the sets of digits within the dual 3x3 array, you still need to make some reference to the original grid.  It's not easy!
8. When you have solved the dual 3x3 array, using all this information to solve the puzzle is also not easy.  You'll need to mark up quite a few triples in the grid, noting that cells in some of the intersections have only 4 possible candidates, before you can finish the solve.  As in Simon's video, the techniques used after this are simply hidden singles and naked singles, but let me say this again, to actually spot these after all of the above, well, it's not easy!

Puzzle 350 Sudoku

So before I really get started, I wanted to draw the attention of my dearest readers to a really remarkable puzzle I've come across in the last day or two, courtesy of 胡蒙汀(Hu Meng Ting) from China.  I'd probably give this one an 8/10 for difficulty on my scale.

https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000474

Scanraid rates this as a diabolical grade puzzle requiring all sorts of fiddly techniques to get through.  But it is also rendered much easier by a quick application of the so-called Phistomefel's theorem.  This, to the best of my knowledge, is first discussed here.  It's also been picked up and popularised by various cracking the cryptic videos, which I am too lazy to link to but I'm sure all my dearest readers are either already familiar with or else can find for themselves.

For various reasons, Hu's puzzle does not seem to getting the attention I believe it deserves in the logic masters community.  To me, this seems to be the first instance of a puzzle that really makes good use of the solving technique.  Previous versions of puzzles that have attempted to incorporate it have always had equivalent shortcuts using much easier solving techniques, and people had speculated whether this was of any practical solving interest.  Now we know!

Reading on in this thread I was pleasantly surprised to see a generalisation of the theory by Fred Stalder, which is well worth reading as well.

This will also help with another really remarkable puzzle, also courtesy of courtesy of 胡蒙汀(Hu Meng Ting).  This one easily gets a 10/10 for difficulty, and maybe even an 11 for the sheer genius of the puzzle

https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=00048U

This one is unsolvable by scanraid, and is certainly not easy even when you are armed with both the theory, and the equally remarkable thread of hints to get you going - there is a lot of work to do to get through this puzzle, but it is just about doable.  I find this fascinating as what it really means is we are now shining a light on some of the hidden complexities underlying the structure of sudoku.  

Anyhow, I am very grateful to cdwg2000 for sharing these puzzles and the theory and I shall certainly keep an eye out for anything else that they share, hoping that they haven't been discouraged too much.

All this talk of new and exciting theory has also made me a little bit nostalgic.  I am going to offer up nothing related to this particular subject (although I'd invite my dearest readers to take another look at one of the classics on the 2020 edition of the UK Sudoku Championship if you're interested).  Instead I feel like I've got a pretty nice execution of an idea that once upon a time was done to death.  Enjoy!

    #350 Sudoku – rated 3/10 [Easy]

All puzzles © Tom Collyer 2009-20.

Puzzle 349 Masyu

Here's another Masyu I've put together, because why not?  it's definitely one where some of the required techniques are starting to spill over into trial and error type things, especially if you haven't seen them before. Enjoy!

    #349 Masyu – rated 7/10 [Hard]

All puzzles © Tom Collyer 2009-20.

Puzzle 348 Doppelblock

So once again I find myself wondering if a post is particularly well advised or not, but I've had a belly full of being made to feel bad about things.

In recent weeks I'd dabbled back on to a couple of discord servers, namely the puzzler club and cracking the cryptic.  I'm not really sure those discord servers are a particularly healthy way to have spent my time - whilst both represent some kind of community of like minded individuals, neither has given me the impression of being friendly or caring too much about individual users.  Having apparently withdrawn myself from the puzzling community a month or two back, it does feel like a mistake to have dipped my toes back in to those particular waters.

Anyhow, I found myself on the receiving end of a particularly snarky comment suggesting that I might be overestimating how interesting and useful my comments were, which seemed to me to come with an additional nasty implication that it would be better for everyone if I simply kept quiet.  Naturally I wondered if I had done something to offend this individual who had taken it upon themselves to speak on behalf of the group, but private enquiries with the individual in question bore no response beyond apparently blocking my messages.  I suppose that confirms the fact I have offended them in some way, although I'm none the wiser as to why.

This initially made me very frustrated, and in no small part angry.  And whilst this individual has succeeded in getting me to throw away logins and delete discord, and they can congratulate themselves on that, I have also taken this opportunity to see this one instance of a block, and re-raise that to a double block.  

The rules to this puzzles go something like this.  In each row and column, you need to place the numbers 1-6, and shade the other two cells.  The clues outside the grid give the sums of the numbers in cells between the two shaded cells (which maxes out at 21 for everything, and hits 0 when they are adjacent).  In other words it's similar to sandwich sudoku.  

All that's left to say to all my dearest readers who do still care in some way about what I have to say, enjoy!

    #348 Doppeblock – rated 5/10 [Medium]

All puzzles © Tom Collyer 2009-20.

Not a Friday Puzzle

Here's a Masyu I put together, because I really enjoy putting Masyu puzzles together.  There are a few moments where you'll need to watch your step if you aren't so familiar with genre, and maybe even if you are.

By the way, I've updated how I rate the difficulty of my puzzles.  You can read more about it here, if that kind of thing floats your boat.

Enjoy!

    #347 Masyu – rated 5/10 [Medium]

All puzzles © Tom Collyer 2009-20.

A small correction to the record

As much as I have tried my best to avoid having conversations about the puzzling community, it seems that I am still the subject of whispers and rumours.  This is something that I ought to find amusing and pathetic in equal measures, and I definitely do, but something about it is still bothering me a little bit.  So here goes, better out than in.

It seems as if there is a perception that one of the reasons I have been previously critical of the WPF is as follows.  At a time, I coveted the role of being the WPF's sole paid employee (misleadingly titled "Director").

This is ridiculous for any number of reasons, but here are two very good ones:

 - I have posted numerous times that my opinion is that those anywhere near the organisation of competitions they are responsible for should not also participate.  I enjoy(ed) participating in sudoku and puzzle competitions for many years, particularly at the world championships, and I have stated several times that I don't think the Director should participate competitively.  My supposed desire to be Director at any point in time directly contradicts what I have stated several times.

 - The WPF doesn't pay nearly enough compared to my current full time job to really consider this worth doing on anything other than a part time basis.  Having previously volunteered my time as the competition director of the Sudoku GP in 2016, I know this would have to mean changing my current employment arrangements, or else being miserable because I had no spare time.  Neither of these options as ever struck me as being attractive.

I should have thought the true reasons I have previously been critical of the WPF are entirely self-evident.  If that's not the case, then too bad, all that stuff is something I have zero interest in revisiting.  To absolutely clear, my current opinion of the WPF is this: I do not give a flying focaccia about the WPF.

All I'd like to add is that it is my opinion that the source of this particular rumour is either a liar or a fantasist.

Thoughts on copyright and online puzzle applets

I'll start by saying this is a subject that I remain a bit unsure about and I am going to be careful not to come to too many conclusions.  If there's one thing I'd like to tell my dearest readers before carrying on, it's that if you are going to use internet tools to make versions of my puzzles, please can you do me the courtesy of telling me you have done so, and (as per the licence of puzzles published on this blog) please can you ensure that you (a) credit me and (b) provide a link to the licence each time you share a link.

Puzzle Sprints: pilot version

The purpose of this post is to see whether I can manage to roughly approximate the halcyon days of the nikoli time trials.  The idea is for anyone who is interested to turn up to this blog at a fixed date and time, and then race to see who can get the fastest solve time for a particular puzzle.  For the time being, the particular puzzle will very likely be a classic sudoku.

In retrospect this doesn't sound anything like a time trial.  Therefore I will call my version "Puzzle Sprints".

The way it will (hopefully!) work, at least initially, is as follows.

1. I will schedule a post at a fixed date and time with a link to a Google form, which contains all you need.  For the real thing, the fixed date and time will be advertised in advance.
2. The form requires you to be signed in to Google (in order for me to impose a limit of one response per participant).
3. Therefore, to participate you will need both a Google account, and to be logged into that Google account.
4. Once the form loads, you should see a short description, together with:
1. A link to the puzzle to be solved in an external online solver.
2. Space to enter your email and nickname.
3. A static image of the puzzle with the two answer keys marked.
4. Space to enter the two answer keys into the form.
5. To take part in the Puzzle Sprint, open up the link to the online solver and solve the puzzle.
6. Once you have solved the puzzle, come back to the form, and then enter in the corresponding answer keys.
7. When you are done, hit the "Submit" button.
8. Once you have submitted, you can click the "View Score" button to instantly see if the answer codes you submitted were correct.
9. After a certain amount of time has passed, I'll declare a cut-off and publish the results.

For those interested in this pilot version, please note there is absolutely nothing at stake here.  You are more than welcome to poke around, but for the next few hours after this initial post, it is highly unlikely you will be getting anything out of this, as I will be making plenty of edits and updates.  It is mostly for my own benefit for now.

Here is the link: https://forms.gle/WQYhioNFFfCiUC2TA

Once I am happy with the way things seem to be working (I will edit in a message to this effect within this post when I am happy), please do feel free to have a go.  If nothing else, submitting an entry to this pilot version is a good way for me to see who might be interested in this kind of thing.

There are several limitations to the approach as it currently stands.

• I don't like people having to log into Google to be able to do this.
• I don't like having to worry about collecting people's emails.
• Ideally there'd be some kind of self-contained and robust log-in system akin to things like nikoli, fed, croco and so on.  This would completely negate the need to use something like Google forms in the first place.
• I am not 100% satisfied with any online solving interface for the purposes of these Puzzle Sprints, where the emphasis is very much on speed solving.
• I don't want an undo function
• I don't want a trial and error function
• I do want much better pencil-marks
• I also want the online solver to directly interact with the form so there's no extra faff switching between solver and form.  (This is no longer an issue once you eliminate the need for a form...)
• If this were to ever get very serious, I would also want some way for winning solves to be verified.  (Most likely this would involve saving some kind of solve history and having replay functionality...)
• Now the cat is out of the bag, anyone can come along and imitate my idea.  

Not that anything I've described here is original, and I have no doubts any number of more talented people could execute this much better than I can but this is still something that I'd like to try and get off the ground on my own terms.  As per my other posts, I'd like to be able to do something positive again for my own benefit as much as anything else.  If people still insist on being negative about that (or anything else), then all I can say is that I'm done caring.  Such people are no longer of any interest to me.

There are the following advantages to the approach.

• Everything is more or less under my control.
• The format gets to the heart of what is really exciting about speed-solving.
• My reputation as a good puzzle author.
• My reputation as a good sudoku competition director.
• I am willing to eventually provide cash prizes (for UK based participants)

That's it for now.  I'm intrigued to see whether anyone is going to be interested in this.

Thoughts on the near future of this blog

So I put out some puzzles earlier today, and I called them Friday Puzzles because it happens to be a Friday.  However I don't think it's going to be a revival of a regular series of posting.  I suspect that whenever I do post a puzzle, I'll retain the numbering, but I won't be too bothered about things if the day in the week happens not to be a Friday.

There are a couple of things to look out for in the near future of this blog.

The first thing will be an exploration of my interest in ratings systems.  Generally the ratings systems used in the likes of Football, Tennis, Chess, various computer games all leave at least something to be desired, and I have some ideas which might go some way to addressing these short-comings.  There is a lot of good, freely available, data in the results of various puzzle and sudoku competitions covering a good period of time, and so this is probably where I'll make a first go of things.  Needless to say this will be strictly unofficial, in association with no-one other than myself, and on a just-for-fun basis. 

My exact mechanism might need a few goes to get the details exactly right, and will probably reveal its own set of shortcomings, but I am excited to be giving that a go in the coming weeks.  I'll probably put out a blog post outlining some of the theory behind my ideas as well.

My second idea is to revive something like the old Nikoli.com time trials, whereby I'll put out a puzzle at a given time, and then anyone who happens to be around races to register the first finishing time, which i affectionately remember being referred to as a "1get".  This won't be a 100% polished experience without any further expertise and collaboration, but on the other hand I think plenty is achievable with the likes to google forms and pzv.jp.  I'd probably look to be handing out some kind of prizes to UK participants at least.  Note that this would be purely on my own behalf, and not as part of any organisation.

My third idea might look to start some kind of a puzzle club that eventually ends up replacing regular puzzles being posted here.  This may well feature sudoku variations that are on the harder end of the difficulty scale, and that may cross over the "solves like" criteria of the "What is a Sudoku?" view of the world.  Maybe this gets splits up into seasons, or even just over the course of a year, and again with some kind of self-funded prizes being up for grabs.  This is probably the least developed idea I have for now, and I can certainly see it ending up down one of many possible initial choice of routes.

Time will tell as to how far are get with any of those three ideas, but I am quite excited by the idea of doing things on my own terms and seeing what happens.  It feels like reviving the spirit from the good old days a bit, and i think will help me feel a bit better about the puzzling world.  Hopefully that will end up being the case!

Friday Puzzles #303

So by now more or less everyone has heard of Cracking The Cryptic.  Lots of the puzzles featured these days are what I'd describe as curiosities, sometimes with strange mish-mashes of constraints paired together to produce interesting solving gimmicks, sometimes with constraints and solving mechanics that go way beyond anything that resembles classic sudoku.  In any case they represent sudoku variations probably wouldn't retain much in the way of interest once the initial novelty had worn off.  Not that it isn't great to see so many different people I'd never heard of before producing these interesting novelties of course!

One idea that does seem to have a few more legs appeared in a more fiendish form that presented below.  Ahaupt's idea is for you to construct an irregular grid from a regionless start to the puzzle, using clues which give the sums of numbers to be placed in each of the cells the clue sees in both the horizontal and vertical directions up to the border of a marked region, including the cell the clue is contained in.

I think the idea is perfectly nice if you are given the courtesy of the irregular grid to start off with.  You end up with something that is related to Jigsaw Killer, where you combine Irregular Sudoku with Killer Sudoku, but something that I think is a little bit nicer, and with enough differences to warrant calling it a separate Sudoku variation.  I'll call it Signpost Sums Sudoku.

The trade-off with Signpost Sums is that you no longer have the cages represented visually, which is a bit of an inconvenience, but you do have the comfort that you don't have to scan across different regions when looking at the sums, and you get the possibility of having some of the now implied cages to be overlapping.  As each of the sums are entirely contained within one region, it means that you still get to keep the no-repeats condition with the sums.

I've tried a puzzle using a normal 3x3 box layout, and whilst possible I don't think it was all that enjoyable.  Instead I've gone with a couple of irregular grids, one a warm-up, and one towards the harder end of difficulty you might see at a well-balance competition.  I'm kind of hoping I've taken enough care with the clues and testing this myself for these to have come out uniquely, but if not I'm sure one of my dearest readers will let me know soon enough.

Enjoy!

    #345 Signpost Sums Sudoku – rated easy(ish)

    #346 Signpost Sums Sudoku – rated medium

All puzzles © Tom Collyer 2009-20.

Leftover 2020 UKSC Puzzle

Here's a leftover puzzle from the 2020 UK Sudoku Championship.  I had thought to keep it in reserve for future years, but I think Sam has already seen it and he might want to take part.  Anyhow the reason this wasn't included was because Sam's puzzle was much better.  Not that this one is bad or anything though.  Enjoy!

    #344 Diagonal Sudoku – rated medium

All puzzles © Tom Collyer 2009-20.

Thoughts on my place in the puzzling community

This post is going to be a bit of an outpouring, in lieu of my withdrawal from the puzzling community for as long as it takes to get my mojo back.

Once upon a time the puzzling community represented a place I could go to be myself, a place that boosted my self-esteem and, as I grew in confidence, a place that I felt able to contribute towards in a meaningful way.  More recently it seems to be a place that represents personal frustration, conflict with others, a sense of being unappreciated and a feeling that I have to constantly explain myself, self-censor and reign myself in.  It's a place that I've realised is causing me a lot of personal trauma, and a place from which I would be better off taking an indefinite break from.

I have a number of wonderful friends from the puzzling community who I will, of course, stay in touch with, and for whose support I am very grateful for.  In that sense, great friends are great friends, regardless of them being half way around the world or of them also being part of the puzzling community.

The purpose of this post is not to point fingers or apportion any blame.  Indeed, I am aware that I am at fault in any number of way, and that also a lot of this is all in my head - the point is that none of that seems to be of any comfort to me.  The reason why I am writing this is to try and arrive at a place of peace with myself, by laying out some of my experiences as I see them, and to try to "show" my current state of mind rather than to "tell" or explain it.

Doing this in a public way may not seem like the best of ideas, but the way I see it is there is a certain comfort in propagating my thoughts out into the great ether, not knowing exactly who will see it, but perhaps being surprised by how people might react it to, be that in a positive or a negative way.  So I'm going to crack on regardless, with no other agenda, and if people are still offended then I'm done with caring about that - they don't get to dictate my interpretation of my experiences any more.

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.