tag:blogger.com,1999:blog-2031071943178978556.post6345287802850042452..comments2023-12-03T22:29:11.592+00:00Comments on detuned radio: Friday Puzzles #71Unknownnoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2031071943178978556.post-20515937086468844862010-11-25T02:44:28.000+00:002010-11-25T02:44:28.000+00:00Regarding puzzle #87The puzzle feels very constrai...Regarding puzzle #87<br><br>The puzzle feels very constrained – moreso than a typical Nikoli<br><br>We can say (without using uniqueness)<br><br>that “at most one” path can go around the 1s – this has to be 10s<br><br>and “at most one” path can split the 15s – this has to be the 14s (else the 14s will split the 11s)<br><br>The 1s then have no choice but to stick to the left (can’t split any other pair of numbers)<br><br>and then the 2s and the 4s then have to go around (either side of) the 3s<br><br>I’m pretty confident of a “uniqueness” proof here – sending paths around convex corners would seem to preserve uniqueness as the “shortest remaining path” – assuming all squares are used?<br><br>Ronaldnoreply@blogger.comtag:blogger.com,1999:blog-2031071943178978556.post-13426546916137422962010-10-10T19:31:11.000+01:002010-10-10T19:31:11.000+01:00Cheers Thomas – actually your logic there is very ...Cheers Thomas – actually your logic there is very reminiscent of the <a href="http://en.wikipedia.org/wiki/Reidemeister_move" rel="nofollow">Reidemeister moves</a>. More than that, it has a base in logic that a computer would be able to check very quickly (not that I have the skills necessary to do this, or indeed any sort of any programming) – you are checking basic properties on pairs of pairs. I also think it is the right way to think about “wriggle room”. Most illuminating!<br><br>I’d have a feeling that systematically enumerating various possibilities might be a start on “proving” numberlink. At this stage, I’d be inclined to think that checking at most triples or quadruples of these transitive intersections might be sufficient. When I get a chance I’ll have a check over a few numberlink solutions and see if this applies…<br><br>Thomas Collyerhttp://blogs.warwick.ac.uk/tcollyer/noreply@blogger.comtag:blogger.com,1999:blog-2031071943178978556.post-20529790918797289072010-09-28T05:03:54.000+01:002010-09-28T05:03:54.000+01:00Unique.Great post, great puzzle.TheSubroUnique.<br><br>Great post, great puzzle.<br><br>TheSubro<br><br>Thesubronoreply@blogger.comtag:blogger.com,1999:blog-2031071943178978556.post-83320130756650768982010-09-26T15:58:28.000+01:002010-09-26T15:58:28.000+01:00Well, this one certainly feels unique to me, but I...Well, this one certainly feels unique to me, but I have the same misgivings and uncertainties about resolving uniqueness for numberlinks as you do.<br><br>The 11’s and 14’s together certainly force the general shape in the top right. <br><br>You get a little flexibility in where the four squirts out of the lower right, but as far as I can tell you can’t actually make the 1-5 part work if you send the 4 over the top.<br><br>Jacknoreply@blogger.com