The Art of Puzzles: Cave & Nurikabe

So I've had two of my wackier puzzles published as part of Oddity week over at GM puzzles.  Here's the Cave and here's the Nurikabe.  And yes, you do bloody well have to prove your solutions are unique!

Friday Puzzles #160

This Nurikabe seemed like a good idea at the time. Enjoy.

    #192 Nurikabe – rated easy

All puzzles © Tom Collyer 2009-12.

Friday Puzzles #158

This one goes out to those 13 wonderful facebook fans I have.  Yes, that's right, as many as 13!  I don't think I've plugged that for a while, so why not scroll down a bit and click that like button.  What's the worst that can happen?

By the way, on the plugging theme I cannot recommend more highly the super-duper UKPA beginners contest I put together.  12 puzzles for you to have a go in the time frame of a month - and you don't even have to do them all in one go.  Feel free to keep coming back and  submitting your answers at your own knowledge.  And then see how you did at the end of month.  That's something I can't manage to offer my dearest readers here!  What exactly do you have to lose, eh?

Right, it turns out I do have a limit on my own shame, so I'll get straight onto this week's puzzle.  Nurikabe, with a little bit to think about, in my own slightly fiddly and time-honoured fashioned.  Enjoy!

    #190 Nurikabe – rated medium

All puzzles © Tom Collyer 2009-12.

Friday Puzzles #151

Delayed, I'm afraid, until Sunday.  I was toying with the idea of putting out something old, or perhaps something that may or may not end up being used for the UKPA Open - but I think the safest bet is to simply wait until I can actually put out something new.  Sorry!

EDIT: better late than never.  Here's a Nurikabe which will hopefully have a couple of head scratching moments.  Enjoy!

    #182 Nurikabe – rated easy

All puzzles © Tom Collyer 2009-12.

Friday Puzzles #150

Well it's the last Friday of Lent, and writing as I have been - from waaay back in the past - this week's puzzle suddenly seems something of an anti-climax. The theme isn't quite perfect and it's not a hugely challenging puzzle either. Mind you, I've never been one for milestones in terms of week numbers, so perhaps I'll do something better for the three year thing coming up. Enjoy!

EDIT: No, nothing's broken with the puzzle this time round, but I have to raise two points.  First blogger have decided to suck harder than a Texan trying to retrieve a golfball stuck in a hosepipe and have apparently ballsed up the commenting "feature".  Ever since google decided to change its privacy policy, all sorts of shitty little bugs have been rearing their ugly heads with the service.  Even before that, they couldn't get something simple like putting time-stamps on the comments in the correct time zone.  I can only hope the reason for the current comment downtime is they are fixing this.

Anyhow, blogger may provide they provide a free service, but so do many others without causing me the need to rant.  And where better to rant than into the vast vacuums of tinternet.

Second point.  Lent doesn't end on Good Friday (thanks pub quiz at The Pilgrim) and so this leaves me in something of a pickle for next week.  I'll think of something, I'm sure.

    #181 Nurikabe – rated easy

All puzzles © Tom Collyer 2009-12.

Friday Puzzles #142

I’ve not done a decent Nurikabe for a while, dearest reader, and nor have I used my favourite Nurikabe pentomino for a while!

In some Terribly Exciting News, this blog also has a nice new presence on facebook. Have a look here, and if you like, sign up for some facebook based prompts. If nothing else, it should inform you more reliably than RSS when I make an actual update as opposed to a place-holder.

So yes, onto the puzzle. Fairly steady progress, but watch your step. Bit of trivia, remove the 4 and 5 clues from the bottom left, stick in a 6 where it ought to go, and you end up with a similar – although I suppose ultimately easier – puzzle. Enjoy!

    #173 Nurikabe – rated medium

All puzzles © Tom Collyer 2009-12.

Friday Puzzles #131

Some more book-keeping dearest reader, before we begin. Last week’s broken slitherlink will soon be fixed; indeed last week’s unfinished WPC reports will soon be completed. Oh – and there are a few more pages that I’ll be adding to the links section on the right, which I haven’t updated in quite some time.

I’m feeling a little bit drained and tired and ill this week, a combination of factors ranging from Eger withdrawal to bluffing my way through the proof of the wonderfully titled “tube penetration lemma.” Perhaps not one to google, that.

Anyway, this week a Nurikabe. I’ll be honest and say whilst I tested on paper, I didn’t do it on the png (which I never used to do, but actually catches more errors than you’d think it would). On the other hand there’s plenty of bite to the puzzle, and there’s even something of a theme going on. As well as my word that this isn’t in fact broken, touch wood. Enjoy!

    #161 Nurikabe – rated hard
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #128

I’m running about as low on inspiration for a spiel this week as my laptop is its battery charge. Here’s a Nurikabe puzzle. It feels a little contrived but perhaps I’m just a little tired. Enjoy.

    #158 Nurikabe – rated medium
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #124

I’m afraid this week’s puzzle is also going to be a bit delayed, new laptop and all, perhaps until later tomorrow. Whatever happened to my time management!?

EDIT: After much delay, here is the puzzle. It’s another Nurikabe, a type for which I don’t think I’ve quite nailed my own individual style. On the other hand it means that I come up with lots of slightly quirky puzzles. But then I don’t know exactly how I should be rating them. I think for the sake of beginners I’ll leave this as a medium. Enjoy!

    #154 Nurikabe – rated medium

All puzzles © Tom Collyer 2009-11

Friday Puzzles #117

I’m feeling a little below par and not really up to making up the usual half-arsed spiel for a Friday entry. So I’ll let this little Nurikabe speak for itself – I’m quite pleased with the claustrophobic sort of logic you’ll need with this one. Enjoy!

    #147 Nurikabe – rated medium

EDIT: Fully interactive version of this puzzle, as kindly powered by Otto Janko’s Java web application can be found here.

All puzzles © Tom Collyer 2009-11

Friday Puzzles #106

So this is the post to make up for an absence of anything last Friday. This might have been the Great Wall sudoku that I came up with on the coach to and from – you guessed it – the Great Wall, but it turns out that was broken and I want to give that a little more time to fix it to do things justice.

Instead, you’ll have to make do with one of my trademark slightly quirky Nurikabe puzzles. It’s generally plain sailing, but watch out for the odd moment. Enjoy!

    #133 Nurikabe – rated easy
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #102

I wonder whether this puzzle will end up being particularly remarkable or not – it’ll end up proving a point to me one way or the other. Enjoy!

    #128 Nurikabe – rated medium
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #99

This week’s puzzle is a Nurikabe, but with a slightly novel feel to it. If you initially flounder, don’t panic, it is still definitely an easy. Enjoy!

    #125 Nurikabe – rated easy
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #88

So this started off being vaguely themed, and now it’s just quite hard. Not as hard as I’d intended, but that’s life. Enjoy!

EDIT: this used to have 2 solutions. Now it has one.

    #114 Nurikabe – rated medium
 

All puzzles © Tom Collyer 2009-11

Friday Puzzles #81

First up – I’ll post this week’s puzzle – which is a fairly gentle nurikabe. It’s been a while since I had a nice and easy puzzle so I hope this pleases the more casual of my readers!

    #107 Nurikabe – rated easy
 

All puzzles © Tom Collyer 2009-10

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But let’s move on. I want to discuss the numberlink puzzles from last week, and in particular make a few remarks about uniqueness of puzzle. As regular readers know, my approach to numberlink uniqueness is to find a solution to given array of clues and then try and establish its rigidity.
The first puzzle I’ll discuss is #106. Here is the solution:

The first intuition I have about numberlink rigidity is the idea of “unnecessary wrapping”. The general idea is to suppose you have a pair of clues A, and another pair of clues B – and draw the straight line between these two clues. If these two straight lines intersect, then it is clear that one of the solution lines joining the clue must wrap around the other solution line. Conversely, alarm bells should be ringing with any candidate solution if the straight lines are disjoint and yet one solution line wraps round the other.

It is a quick check with this puzzle to see that there is no such unnecessary wrapping. I haven’t rigorously proved to myself that this means the solution must be rigid, but I’d be very surprised if this wasn’t the case (with a few highly symmetric exceptions). Ok, fine, I haven’t got anything more to add to this at the moment so let’s move on.

Here’s what I had in mind (in black) with the original #105 I posted, together with (in red) where things go wrong:

So there are a couple of points to consider here. Firstly, look at that pair of 2’s, and the amount of what I’ve just defined as “unnecessary wrapping” it does! There’s something more than meets the eye going on here. The initial idea for the break-in to this puzzle was with the 1’s and the 5’s. A little spatial reasoning quickly suggests that one of the solution lines must go via the top-left of the grid, and the other along the bottom edge – so that the cluster of 3/4/6/7 is avoided.

A little more inspection reveals that the 1’s would be causing all sorts of difficulty with the 6’s if it went out top left, so the 5 goes round the top left. It was here that I made the mistake. I thought there was only one way for the 5 to get past the 4 and the 6, but completely overlooked the obvious route as marked in red. This was how I fixed the puzzle – by closing up the gap (and adding a 13th pair of clues):

This alteration made the puzzle a little easier than intended. The 3/4/6/7/13 are now essentially forced. A by product of this is that it forces the 2 to squeeze the “wrong” side of the 1. This is a bit of “logic” that only came in to play later in the original – but essentially reveals the origin of the “unnecessary wrapping” of the 2. The given clues in the puzzle are acting as blocks to the paths, which must channel in between them, with the obvious restriction that there are only so many paths that can fit into a small space. So once the 2 goes round the back of the 1, it also has to go round the back of the 8 and the 9.

The rest of the puzzle is then fairly trivial.

What I find interesting with this puzzle is that actually it wasn’t too hard to find a sketch framework to logically prove the solution is the only one. Ok, I’ll hold my hands up with the stupid oversight with the 5’s, but the fix was essentially minimal and still retains most of the features I wanted from the original puzzle.

Going back to #106, I think this one is much harder to make a start to the puzzle and go step by step in trying to establish forced paths. Instead, it isn’t too tricky to use a little metalogic (i.e. assuming uniqueness of the solution) to get the solution out – and then to do a quick check to see that this solution turns out to be rigid. Which is a completely different approach to things!

Anyhow, for all those numberlink fans out there, I hope this has provided a little food for thought.

Friday Puzzles #79

We’ve not had a Nurikabe puzzle for a while. I claim this is a medium, but it might really be a hard. The reason for this is that the solving path is logical enough and I don’t want to be putting off some of my readers who do love a good Nurikabe put don’t want to dip their toes into a “hard” puzzle. Give it a bit of perseverance and you will get there in the end…

Anyhow, not the worst puzzle I’ve ever done, and perhaps this was indeed the right outlet after my rather rushed talk on Wednesday. Enjoy!

    #104 Nurikabe – rated medium
 

All puzzles © Tom Collyer 2009-10

Friday Puzzles #75

A.K.A. Tom Collyer finishes unfinished business

A.K.A. Tom Collyer keeps his promises (at least sometimes, at any rate haha…)

A.K.A. Who needs a list of pentominos by the side of a puzzle anyway?

So this is a tough cookie. But it’s worth it, I promise you. 75% solves beautifully well, and the last quarter is a bit of a head scratch. If it’s too much of a head scratch, you can probably trust my good nature and use a few hinted shortcuts to finish the puzzle. Enjoy!

    #092 Nurikabe – rated hard

P.S. A few weeks back I eulogised about how great my Marathon puzzles for the LMI test were. As it turned out, the test was somewhat of a disaster, with a high proportion of broken puzzles and plenty of egg on my face. That said, there were still some rather good puzzles and you can probably expect to see a couple of them reposted on my blog on weeks when I’ve not got a spare mo to do a semi-decent puzzle.

Anyhow, the Heyawake was actually broken – which made me die more than a little inside because if you skipped over the contradiction the mistake implied, it was in my opinion the best of the three puzzles. I did fix it, but it’s not the same :(.

    #093 Kakuro – rated hard

    #094 Masyu – rated hard

    #095 Heyawake – rated hard

All puzzles © Tom Collyer 2009-10

Friday Puzzles #63

There was a neat little trick I put in last week’s generally well received nurikabe puzzle that I’ve decided to play with a bit this week too. I haven’t really had time to turn this one up to 11, but this at least remains a difficulty level above from your standard 10×10 size puzzle.

Edit: This version slightly modified from what appeared on Friday

    #077 Nurikabe – rated medium

All puzzles © Tom Collyer 2009-10

Friday Puzzles #62

It’s been a while since I’ve done a nurikabe puzzle, although I seem to recall that I always seem to have a bit of a moan about how my nurikabe aren’t quite up to the highest standards. This, as opposed to something like my Masyu puzzles which I believe are as good as anything bar juno. It’s a similar story here – this puzzle has quite a nice “solving flow” to it, but it’s not quite as polished as I think it could be – which is not to say I didn’t give it my best shot! Nevertheless, I think this is a pretty nice idea, and will certainly have you scratching your head for at least a moment.

Interestingly, I’ve seen my traffic drop off a little bit in the last couple of weeks, which coincides with the end of the Warwick term. I’ll be keeping going throughout this summer period, but for now, enjoy!

    #076 Nurikabe – rated hard

All puzzles © Tom Collyer 2009-10

Friday Puzzles #52

Well, I’ve made it through a week going at a rate of a puzzle a day. Let me tell you it’s pretty hard going, and I have big respect for MellowMelon for going as long as he did at that rate. I’m now only 2 weeks behind where I’d like my indexing to be – and so you can look forward to a couple more puzzles coming between now and next week. As an added bonus, I’ve seen my weekly traffic increase somewhat. Although I can’t be quite sure whether this is entirely because of the increased rate of publication, bearing in mind the potentially new audience I mentioned my site to at the WSC [And yes, that report IS coming!!!].

One thing I’ve found is that the stricter deadline made my creativity a little forced, and that was definitely the case yesterday, where the nurikabe – as a solve – was pretty lame. When will designers learn that disguising messages into their puzzles doesn’t please anyone? Enjoy!

    #062 Nurikabe – rated medium

All puzzles © Tom Collyer 2009-10