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!!!
#105 Numberlink – rated easyAll puzzles © Tom Collyer 2009-10
#106 Numberlink – rated medium
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.
ReplyDeleteYou’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.
ReplyDeleteHmmm.
Thanks for two great Numberlinks.
ReplyDeleteI 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
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.
ReplyDelete