Friday 25 December 2015

Friday Puzzles #288

That moment when you realise Christmas Day is also a Friday!

Nothing too taxing today as this was rather a last minute affair, but watch your step!  Each of the four shaded regions follows a different rule:

  • odd
  • even
  • fortress
  • renban group
Merry Christmas to all my dearest readers, and as ever, enjoy!

EDIT: I'd managed to leave a couple of clues out.  This should make things a little easier!

    #328 Mini-Matchmaker Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Tuesday 15 December 2015

2015 WSC and Group Theory

I've yet to post any sort of championship report for the WSC/WPC held in Sofia in October. I might still get round to that soon!  But the rationale for this post comes from finishing off the broken/unsolved puzzles from my booklets recently.  I came across this gem of a puzzle.

This puzzle is actually taken from the instruction booklet - however it's not the puzzle itself which interests me, rather the phrasing of the instructions.  The Twin Regions in question are effectively extra regions, which are related by a cyclic permutation - and here is the crucial bit - which might possibly be reversed in order.

Now given the cyclic nature of the constraint, it was reasonable to assume that if the twin regions were not quite parallel rows/columns, then they would at least both go from top edge to bottom or left edge to right.  But if this is the case, then that cyclic permutation couldn't possibly be reversed!

And why is that, you ask?

Answer 1: Any orientation reversing symmetry of the regular nonagon is a relfection whose axis passes through a vertex and the midpoint of the opposite edge.

Answer 2: Lets label the cells in the 1st twin region ABCDEFGHI.  Any order reversing cyclic permutation has a fixed point!  This is bad for Sudoku because that means you will end up with two of the same number in a column.

And why is there a fixed point?  Well, this is because any order-reversing cyclic permutation is in fact a reflection of the set X, and because X has 9 elements, when you start pairing off the elements of X that define the reflection, you will always be left with one left over.  The fixed point!

Don't believe me about the reflection claim?  Well let's take the easy case: the order reversing cyclic permutation.


This pairs off (AI)(BH)(CG)(DF) and fixes E.  It's a reflection in E.

Now, we can get any other order-reversing permutation of X by taking this one and applying a (non-trival) order-preserving permutation.  This will move the fixed point from E, and rotate it round to another fixed point, which will then define another reflection.

Answer 3: The D_18 action on X has 9 distinct stabiliser subgroups!

Friday 11 December 2015

Friday Puzzles #287

Greetings all!  I've been a bit busy recently - not least because I have taken over the role of Competition Director of the WPF's Sudoku GP.  Exciting times indeed.

I have been posting for the Daily League once a fortnight for a while, as has Bastien on a Wednesday.  I think this means now at least we are posting on different weeks.  By-the-by, if you fancy yourself as an aspiring Sudoku author, then please do contribute!

Anyhow, only time for a classic this week.  Enjoy!
    #327 Sudoku – rated easy
All puzzles © Tom Collyer 2009-15.

Saturday 21 November 2015

Friday Puzzles #286

Well, I hope this was worth the wait.  I'm quite pleased with this one - Enjoy!
    #326 Very Odd Sudoku – rated easy
All puzzles © Tom Collyer 2009-15.

Friday 6 November 2015

Friday Puzzles #285

In celebration of George Boole's 200th birthday, and Bram de Laat's excellent Clone Or Extra Region Sudoku, I give you Clone And Extra Region Sudoku.  Enjoy!

Rules: the two shaded regions contain each of the numbers 1-9 exactly once.  Moreover, the same numbers go in cells with the same relative position in the two regions.
    #325 Extra Region And Clone Sudoku – rated hard
All puzzles © Tom Collyer 2009-15.

Friday 30 October 2015

Friday Puzzles #284

It's funny how a bit of bad news can get in the way of all the fun stuff you intended to do - like write a championship report  But never mind, some things never change and I still love a good masyu puzzle.  This one definitely gets filed under the category of watch your step. Enjoy!

EDIT: an early version of this puzzle was missing the clue in R3C2.
    #324 Masyu – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 23 October 2015

Friday Puzzles #283

Well I've been and gone to the world championships in Sofia, Bulgaria.  Expect some kind of write up in the next week-ish, although I'm not sure I have the heart or energy to go into the kind of detail I normally do.

Abbreviated results are:

WSC: 49th -- GBR-A: 8th
WPC: 45th -- GBR-A: 7th

I'm pretty happy with both sets of team results, just about happy with the WPC result and pretty disappointed with the WSC result.

Congratulations to our two new Japanese world champions Kota Morinishi (WSC) and Ken Endo (WPC).  Japan and Germany won the respective team competitions.

A new fixture during world championship week are the two WPF Sudoku and Puzzle GP finals.  I still have a few thoughts about these competitions which I will save for another post, but as a UK author for the 8th leg of the Sudoku I also had the honour of contributing two puzzles for this play-off.

One of them was a classic, which got selected.  Nothing hugely special, but it was probably at a medium difficulty level as opposed to my normal easy level.  I was a little disappointed that my variant didn't get picked, which was a hybrid Renban-Killer variant.  So instead I get to share it here with all my dearest readers!

Rules: numbers placed in cages don't repeat and sum to the given clue.  Numbers placed in shaded regions don't repeat and form a consecutive set.

    #323 Renban-Killer Sudoku – rated hard
All puzzles © Tom Collyer 2009-15.

Friday 9 October 2015

Friday Puzzles #282

I must say I feel even more under-prepared for the upcoming world sudoku and puzzle championships than I was for the comparative cake-walk that was the Times championship.

Hopefully this is a good omen.  Sadly it's not that great an omen for puzzles I've been writing recently.  The rules of anti-diagonal state that you can only place 3 different numbers on each diagonal.

Enjoy, anyway!
    #322 Anti-Diagonal Sudoku – rated easy
All puzzles © Tom Collyer 2009-15.

Sunday 20 September 2015

Championship Report: 2015 Times National Sudoku Championship

There was a time and place, dearest reader, when posts on this blog (and I really still do hate that word) were given titles of Radiohead tracks.  Whilst some things never change - such as hopefully the continuation of these reports - somethings do and so we'll all have to deal with a boringly functional title.

The build up to this year's championships was a little different from previous years, with organisation behind the scenes being handled by some Times admin staff; the usual suspects David Levy and Tony Corfe were to take over on the day.  There had been one major change however: in previous years the competition format meant that the grand finalists were the best 8 from solvers who had solved two preliminary sessions.  This year reverted to a much earlier format (going back to perhaps 2007 or 2008?) whereby solvers were entered into exactly one of two of the preliminary sessions and the best four from each session would make it through to the solver.

The letters through the post confirming entry were rather delayed, but this little bombshell was something that Mark Goodliffe for instance had initially missed.  I was not the only one pondering this little complication, as it soon became apparent that the top 3 qualifiers from last years competition - Myself, Mark and David Collison - along with two-time champion George Danker had all been entered into the afternoon session.  This seemed to be running the distinct danger of overloading one of the two preliminaries, which I think George took up with the organisers who then promptly asked both George and Mark whether they wouldn't like to take part in the morning session itself.

Anyhow, sticking to the afternoon session was entirely fine by me; I definitely like to have more rather than less sleep on a Saturday morning.  My trip down from Milton Keynes to London was very uneventful, the main highlight being that instead of trekking over to Tower Hill and walking over to Thomas More Square I could instead get the Northern line straight to London Bridge, emerge from its warren of tunnels and emerge at the base of that most delightful Qatari tribute to Barad Dur.  Having been suitably dazzled by that for a minute, I quickly located the shiny new News Corporation building, and decided to check in with the reception.  As it happened I was a little early, but not early enough to get any of the seats, so I decided to head to M&S and get some sandwiches and a bag of mints.

After returning we had to wait another 15 minutes before actually being let up to the top of Times Towers.  Some of the morning session had decided to stretch their legs, including 2013 champion Stephen Gerrard, as well as Mark and 2015's UK Sudoku Champion Heather Golding who I'd not realised was going to be there.  In retrospect it seems that the transfer of George and Mark to the morning session may have inadvertently lightened up the load for the afternoon!  This impression was further reinforced when I got to the top floor, and bumped into general UKPA hero Mike Colloby who had also been there in the morning.  After a good chat with him, and with George + his fiancee Sophie, I was able to digest a little information about how the morning session had gone.  There had been one particularly nasty puzzle, but the top 4 had ended up being Mark, George, Stephen and Mike.  Poor old Heather had had a bit of a nightmare, but those four certainly represented a strong half of the draw.

At this stage the following piece of trivia might help to explain my mind.  Having won in 2007, I made a stupid mistake in 2008.  I then went on to win in 2009 - and in 2010 then went on to make a stupid mistake.  In 2011 I made the grand final, eventually coming 3rd after freezing up in the final, but in 2012 made a stupid mistake (which agonisingly meant I could not go head to head with my great friend Rishi Puri).  In 2013 I stupidly missed the qualifiers so did not take part in the event.  In 2014 I made the grand finals, eventually finishing 2nd to Mark - perhaps you can spot what kind of forecast might logically be extrapolated for 2015?

With the addition of where I judged my form to be based on my performances on and fed sudoku (check out my results for Saturday 12th), combined the volatility that is inherent to the I think it is safe to say I wasn't expecting too much from myself this year.  That's perhaps not say that I didn't consider myself the favourite - I do most years - but when any one from eight can win over a set of puzzles where any solver might miss something or make a silly mistake I don't think any one individual can have an a priori probability of winning greater than say 40-50%.  With Mark in tremendous form, I think I had my own chances at 25-30%, a little lower than in previous years, where I had not really come close to winning anyway.

So on to the preliminary.  I'm not sure there's a huge amount to say, other than the quirky booklet format remained, which meant that the first thing you see is puzzle 8 (as opposed to puzzles 5, 6 or 7).  Having not apparently recovered from my shaky online solving from the morning, I made a shaky start to number 8 before deciding I'd leave the puzzle half way through and instead have a look at the others.  This was a good idea - puzzles 5, 6 and 7 were much more to my liking and i whizzed through them all with out any incident.  After staring at puzzle 8 for a bit, I went into panic mode and made a "bifurcation" (rest assured that I still love that particular word, dearest reader).  My first attempt met with a fairly quick contradiction; the other route slowly led to the resolution of the puzzle - and after a couple of minutes of very carefully checking the filled grid for mistakes, I handed in after 20 minutes.

Having gone back through both sets of preliminary puzzles, I hadn't missed anything overly difficult in puzzle 8 - just a simple case of a naked triple in box 2.  This seemed in contrast with the stinker (puzzle 3) from the morning session which I think only resolves using x-wings (although please correct me if I'm wrong), and certainly put Mark's finishing time of 22 minutes in a very good light.

At the end of the hour I was very relieved to hear I'd made it through to the grand final.  It also turned out that I was 10 minutes quicker than the next finishers - of whom there were 5 or 6.  Joining me in the final would be Andrew Dyson, David and Ned Walker.

As always, the preliminaries are over at 2pm with an hour's break before the grand final starts at 3.  As always I wasn't particularly hungry, but I forced down a bag of crisps and a chicken and bacon sandwich anyway in one of the meeting rooms.  This was actually reasonably relaxed, with plenty of good banter from Mark and Heather (who will be joining me and David McNeill in representing the UK at the World Championships next month) amongst others in the room.  Nevertheless the excitement does slowly build as the clock nears 3, with the inevitable return to competition.

I think it's safe to say that as we were taking our seats all I was really focused on was being pleased that I had a seat in the front row, which removes any temptation to be distracted by any of the other competitors.  It had turned out that in one of the preliminaries, David Balderson had handed in answers to the four puzzles spread over two booklets in a time that would have placed him in the top 4.  I am not sure whether this was the morning or the afternoon session, but having initially been left out of the final David B was then invited to be the 9th man in the final.  This was certainly the fairest resolution to this unfortunate state of affairs, and an option that I sometimes wish was open to us for the 2014 WPC.  But like I say, I wasn't paying too much attention to this.  On to the final.

I started by making a conscious effort to solve the puzzles in order this time.  And things started well!  Puzzles 9 and 10 were both done before 7 minutes were up.  I know this because there was a great innovation for this year's competition: screens displaying countdown timers!  I was solving with good rhythm and spotting the naked subsets almost immediately.  I thought the same was true for puzzle number 11, until I was about 2/3 of the way through puzzle, where a contradiction suddenly popped up from nowhere.  When this happens it is possibly a devastating blow to your solving, because not only is your rhythm thrown completely off kilter, but it also introduces the nagging doubt in the back of your mind that it is perfectly possibly for you to make a silly error somewhere along the line and be totally oblivious to making it - until, if you're lucky - it blows up in your face and you catch it.  If you're unlucky it blows up much later when you think you've correctly solved it, and it turns out you haven't.  This time I did manage to catch it, and after the inevitably temptation of spending a few seconds looking for a quick fix (there is almost never a quick fix) I had to go with the option of rubbing everything out.

Solving a puzzle for the second time can be a very odd experience.  Some of the time, because the memory of key solving steps are fresh in your mind, it can end up being reasonably quick and any time lost is minimised.  However what can equally happen with your confidence shaken is that you completely miss all the steps that you had previously made, worrying about the faint imprints still visible in the papers and wondering whether you might actually be able to use them as a shortcut back into the puzzle (Don't do that!!!). Happily my experience this time round lay somewhere between the two.  I was quite careful up until the point I reached the area of the grid that had yielded the previous contradiction, but on entering in different numbers with no contradiction the adrenaline started kicking in and the rest of the puzzle went into the grid in something of a rush.

Which just left puzzle number 12.  I'm not sure exactly what the clock was showing at this point, but I'm guessing this was roughly 15 minutes in.  What my intuition was telling me was that Mark might well be up with me so the gloves had to be off for this last puzzle and this had to go down as quickly as possible.  Maybe this was letting emotion get a little the better of me, because I got about half way in before my progress ground to a halt.  Panic mode definitely set in and I set about looking for good places to bifurcate.  When you've put yourself under pressure this can sometimes be harder than it should be: all you need to do is go looking for pairs, or else numbers which can only go in one of two places in a row/column/box.  My first attempt looked like it was about to come up trumps for me, until with about 10 empty cells a contradiction loomed large.

I have previously described my guessing technique as "shambolic" in an explanation of why I never used to guess.  What might previously have happened is that I would forget where I had started bifurcating and then simply repeat the same branch - however maybe it's the case that I am now older and wiser and my technique has sured up a little.  What I had done here was for the bifurcation ensure that any entered numbers were entered in lightly and then circled - meaning they can very easily be rubbed out.  In this case this was about 1/3 of the grid so this definitely helped me out.

What can also happen in these circumstances where one branch yields lots of sequential information before getting to the contradiction, is that the other branch gives you sod all and then you have to make another guess.  For a fleeting second I thought this might be the case here - however I soon spotted the next deduction and I was on my way.  I was fairly confident that no-one else had yet handed in as I was filling in the finale few empty cells, so all I had to worry about was the structural integrity of the lead in my pencil which had suddenly seemed to have failed right at the last, with the final number to be placed only going in at the third attempt.

There was no time for doing anything other than a quick empty cells check before handing in, shortly after 21 minutes.

As is traditional, the remaining ~40 minutes sat in silence waiting for everyone else to finish entails a special sort of purgatory.  I attempted to do some killer sudoku from the book in the Times goody bag, but by this stage I think my mental energies were spent and I just couldn't concentrate.  Instead I was mentally preparing myself for the seeming inevitability of having made a mistake.  Indeed, when the hour was up, nothing seemed to happen for about 5 minutes before David Levy announced they needed a further 5 minutes for the final results.  With the 9 of us sat in limbo, I announced that this was indeed a special sort of purgatory, and circulated my bag of mints whilst musing over the afternoon's football scores.

Eventually Tony and David came back, announcing the final results.  It turned out that 3 of the finalists had only solved 2 puzzles correctly, and that 2 of the finalists had solved 3 puzzles correctly.  When it came those who had all 4, with my name not having been mentioned coupled together with the fact I had handed in first, I permitted myself a celebratory punch of the air to confirm my 3rd victory!

And I suppose that pretty much concludes this write-up.  The new Times puzzle editor had made the effort to come to the prize giving, which was very good of him, although I'm ashamed to say I don't recall his name.  There was no one-on-one session with a photographer this time round - alas the picture in the paper has my golden envelope rather neatly blocking the 2014 WSC/WPC logo on my red polo shirt.  And because I'm neither hugely vindictive, nor looking for an "angle", I won't say anything about the journalist who tried to interview me.  With this write-up I firmly believe I have set the record straight!

P.S. If anyone has copies of the grand final puzzles, please let me know!

Saturday 19 September 2015

Friday Puzzles #281

A couple of pieces of bookkeeping firstly this week.  Firstly, last Saturday I managed to simultaneously not have a brain-freeze or make a mistake that I didn't catch, and in doing so took my 3rd Times Sudoku championship.  The write-up in the newspaper on Monday was spectacularly mediocre, and to make matters worse none of the puzzles were actually published.

To put this right, I will be putting together a trademark championship report.  I also have copies of the puzzles from both preliminary sessions, but if anyone happens to have the grand final puzzles I would certainly be interested in seeing those again.

Next piece of bookkeeping is I've been toying with a few hitori ideas this week, prompted by this excellent post on the UKPA forums.  Maybe I'll go with that for next Friday.

Anyhow, onto this week's puzzle, less than half an hour late!  Enjoy...
    #321 WINdoku – rated medium
All puzzles © Tom Collyer 2009-15.

Saturday 5 September 2015

Friday Puzzles #280

I'd like to tell you that this puzzle wasn't in the least bit frustrating to put together.
   #319 Anti-Knight Sudoku – rated medium
And on that bomb-shell:
    #320 Diagonal Sudoku – not rated
All puzzles © Tom Collyer 2009-15.

Friday 21 August 2015

Friday Puzzles #279

I dare you to tell me this is too easy.  I double dare you.

    #318 Diagonal Sudoku – rated easy
All puzzles © Tom Collyer 2009-15.

Friday 7 August 2015

Friday Puzzles #278

Classic Sudoku this week.  Writing a good classic is a very much under appreciated art - it's much easier to do a variant most of the time.  This one is OK but there's still plenty of room for improvement!
    #317 Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 24 July 2015

Friday Puzzles #277

Here's a Thermo Sudoku. Enjoy!
    #316 Thermo Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 26 June 2015

Friday Puzzles #276

It's that time of year.  Enjoy!
    #315 Big-Small-Even-Odd – rated easy
All puzzles © Tom Collyer 2009-15.

Friday 12 June 2015

Friday Puzzles #275

I haven't done a givenless arrow before.  Not the most amazing thing I've ever done - it's using all the standard arrow gimmicks but I've managed to cut down the number of arrows quite well, and you will need to watch your step.

Rules, if you don't know them, are: numbers in the circles are equal to the sum of numbers along the corresponding arrows.  Numbers can repeat along the arrows.

    #314 Arrow Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 29 May 2015

Friday Puzzles #274

Can you tell what it is yet?

(Don't talk to me about symmetry...)

    #313 Killer Sudoku – rated easy
All puzzles © Tom Collyer 2009-15.

Friday 15 May 2015

Friday Puzzles #273

So you think you're good?  Try solving this without R1C9 and R9C1 then come back and tell me you're good.

    #312 Even Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 1 May 2015

Friday Puzzles #272

I'm not quite sure I'm in a state to judge the difficulty of this puzzle any more. Enjoy!
    #311 Non-Consecutive Sudoku – rated hard
All puzzles © Tom Collyer 2009-15.

Thursday 16 April 2015

Friday Puzzles #271

Whilst I've been travelling far and wide across Eastern Europe this week, I've still managed to find the time to make a puzzle.  The initial idea for this was a lot cleaner but it didn't quite turn out to solve uniquely.  So I've fiddled with some of the clues a bit and now it is unique, but a little harder than intended.  Or at least that seemed to be the case to me whilst going through it on the train.

In case you needed reminding, consecutive pairs is much like consecutive, only not all the pairs are given.  Much cleaner in my opinion, and much nicer to look at.

    #310 Consecutive Pairs Sudoku – rated hard
All puzzles © Tom Collyer 2009-15.

Friday 3 April 2015

Friday Puzzles #270

Sometimes one needs the hammer to strike the stone to indicate the work is done.  Enjoy!
    #309 Irregular Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 20 March 2015

Friday Puzzles #269

Palindrome Sudoku this week.  I've now got to rush off to watch some clouds obscure the moon obscuring the sun.  Enjoy!
    #308 Palindrome Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 6 March 2015

Friday Puzzles #268

Windoku this week.  Better late than never!
    #307 Windoku – rated medium
All puzzles © Tom Collyer 2009-15.

Saturday 21 February 2015

Friday Puzzles #267

Well what do you know, it's not a Friday.  This week's offering is Eliminate Sudoku, a novelty (at least to me!) from the 2014 World Sudoku Championships, where the puzzle was supplied by Ko Okamoto of Japan.  Incidentally if I'm wrong about this and there is an earlier example, then I'd certainly like to be enlightened!  Anyhow, this for me epitomised everything an innovative new variant should be - something which isn't overly contrived or a departure from what the average Joe would know as sudoku, something which compliments the standard sudoku solving logic completely naturally, and something that when you think about it makes you wonder why someone hadn't come up with it before.

The rules are easy enough.  Numbers placed in cells with arrows must not repeat in the corresponding direction.  Enjoy!
    #306 Eliminate Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 13 February 2015

Friday Puzzles #266

Here's an easy Masyu. Enjoy!
    #305 Masyu – rated easy
All puzzles © Tom Collyer 2009-15.

Friday 6 February 2015

Friday Puzzles #265

I'm quite pleased with this Even Sudoku puzzle, although admittedly I'm feeling quite tired. Enjoy!
    #304 Even Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 23 January 2015

Friday Puzzles #264

A medium level puzzle, but only just bearing in mind I've never posted a Quadro Sudoku here before.  It's a slightly subtle odd/even style variant, where the solving flow is very much either on or off, so perhaps your enjoyment mileage may vary.  If you struggle, let me reassure you by saying these can get a lot harder!

Rules: No 2x2 block of cells may contain exclusively odd or exclusively even numbers.

    #303 Quadro Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 16 January 2015

Friday Puzzles #263

Fairly recently I had the honour of being asked to be one of Roland Voigt's weekly "experts " for his daily skyscraper puzzle project.  I am always in awe of anyone who tries to maintain any sort of daily puzzle project for any period of time, and this one is of particular note because in my opinion Roland is by far and away the world's leading authority on both solving and creating Skyscrapers puzzles.

Please take a look here:

I think eventually some commentary on my times will appear on Roland's blog - as someone who often struggles with a weekly schedule I am more than happy to be patient on this count!

Anyhow, skyscrapers this week.  Not too hard, not too easy.  Enjoy!
    #302 Skyscrapers – rated medium
All puzzles © Tom Collyer 2009-15.

Friday 9 January 2015

Friday Puzzles #262

So Consecutive Sudoku really annoys me because it always ends up solving as non-consecutive Sudoku - and any really cool combinatorial tricks end up being drowned out by the non-consecutive logic.

I believe it was Bastien who first introduced the idea of a Consecutive pair to the Daily League, and it's a really good idea.  I was quite tempted to stick with the ubiquitous bar notation for this puzzle in an attempt to reclaim it, but I will stick with what Bastien used for now.  Marked pairs of adjacent cells must contain consecutive numbers; there is no restriction on adjacent cells with no marking.  Enjoy!
    #301 Consecutive Pair Sudoku – rated medium
All puzzles © Tom Collyer 2009-15.

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