## November 26, 2010

### Friday Puzzles #80

More Numberlink this week. Over the week I’ve pretty much convinced myself the solutions I have in mind really are the only ones, and I’ll go into this more maybe with an edit to this post in a few days. What I’ll say for now is this. I reckon the second is a much nicer puzzle than the first, but the first was definitely more easy for me to convince myself of uniqueness.

This seemed rather strange to me on second inspection, as it turns out that it has a few properties that I had previously thought might have been barriers to uniqueness. In particular, it fails a test I’ve devised to check whether if you have one solution, then you can only have one.

This test was something I came up with when inspecting the second puzzle again. I haven’t rigorously proved this to myself but it does make intuitive sense. The second puzzle does pass this test.

Anyhow, my apologies for being so cryptic – but be assured dearest reader that I am only because I don’t want to spoil the solving experience, and also with the promise of explaining all in a few days time. Until then, enjoy!

UPDATE (II): PUZZLE 105 EARLIER CAME WITH A SPECIAL OFFER OF MANY POSSIBLE SOLUTIONS FOR THE PRICE OF ONE!!!

All puzzles © Tom Collyer 2009-10

### 4 comments by 1 or more people

1. #### term

Assuming one may leave cells empty, and assuming I’m not missing a mistake in my solution, No. 105 leaves lots of wiggle room in the left side of the board, which makes for a non-unique problem. In one possible arrangement, this leaves open a U-shaped area below the lowermost three, the cell under the leftmost four, and the cells to the left of the a 4-cell long line connecting the two threes.

26 Nov 2010, 06:20

2. You’re very right – I think I’ve got what you have in mind. That’s very strange – if that one was going to break down somewhere, I didn’t think it’d have been there… although I suppose in retrospect there are some warning signs with how the 3 and the 7 interact with each other.

Hmmm.

26 Nov 2010, 12:53

3. #### TheSubro

I had been spending lots of time working on these types and I couldnt have been happier seeing two great ones to play with on a day off in America. Had fun with both. Keep em coming – as its hard to find good ones out there.

TheSubro

27 Nov 2010, 01:14

4. #### mathgrant

Holy crap, a symmetrical 10×18 Numberlink. I’d never have the patience to build one of those. o_o; Very beautiful to solve, though.

03 Dec 2010, 16:29

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## Information

Welcome to the blog of current UKPA sudoku champion, two-time Times national sudoku champion and general logic puzzle fan Tom Collyer.

Home of the original Friday Puzzles, each Friday I publish a 100% original and handmade logic puzzle, inspired by the world-famous Nikoli company.

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