*Nurikabe*

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## February 03, 2012

### 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!

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All puzzles © Tom Collyer 2009-12

## November 18, 2011

### 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!

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All puzzles © Tom Collyer 2009-11

## October 28, 2011

### 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.

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All puzzles © Tom Collyer 2009-11

## September 30, 2011

### 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!

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All puzzles © Tom Collyer 2009-11

## August 12, 2011

### 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!

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**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

## June 03, 2011

### 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!

All puzzles © Tom Collyer 2009-11

## April 29, 2011

### 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!

All puzzles © Tom Collyer 2009-11

## April 08, 2011

### 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!

All puzzles © Tom Collyer 2009-11

## January 21, 2011

### 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.**

All puzzles © Tom Collyer 2009-11

## December 03, 2010

### 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!

All puzzles © Tom Collyer 2009-10

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.