Listener 4131 - Carte Blanche en Tore by Ten-Four

[cluelessJoe]

Easiest one of the year for me by a long chalk. Am I getting smarter, or are these Listeners getting simpler?

[AHearer]

Yes, Rogue-Elf, I found that was the easiest way to do it. It was only after solving it that I looked on the web for solutions, and the variety of results I found there only served to reinforce my sympathy for John Green when he checks the submissions. He must be hoping for a low number of entries. Maybe that's why the bars have to be entered -- they will be easier to check and might filter out a number of incorrect grids before the final step.

[kwyjibo]

I cold solved about half before I managed to find a possible fit and then it all started to fall into place. I think it's good to throw in a real stinker every now and then but it took a long time to get going.

[midazolam]

I have drawn two different grids using only straight lines that are completely different, not just mirror symmetry. I am sure there are more. Using only black ink will be very confusing for JEG.

[bellabee]

Rogue-Elfe and AHearer - do you think it's necessary to submit the 3D version[s]? I'd have thought pretty rough geometry in 2D would show that the theme had been grasped sufficiently. I'm thinking of sending it in this time as i'ts been such a slog but have stopped submitting them regularly. I also think Mr G will have a huge post bag for this one for that very reason. I certainly hope so!

[bellabee]

i meant...it's... [easy to make little blunders isn't it - you may be right about the bars idea]

[Zabadak]

Didn't really tackle this until today - too many other things to do over the weekend that precluded the kind of sustained effort this thing needs. Far too much cold solving, and I've ended up with a grid that looks like a 1960's TV with the horizontal hold on the blink (and lots of scrap paper). At least since it's a blank you can just print off as many 15x15 grids as you want, in any size, and unless you want to submit, that's enough. I've decided that completing this one is satisfaction enough without having to plough through producing a neat version. I have thought of buying a stale ring donut, writing all over it, and sending that in, but it probably wouldn't be appreciated.
Well done to everyone who persevered to the end - and a slightly envious well done to those of you who gritted your teeth and decided not to bother.

[AndrewG-S]

I thought this was fabulous, but then I am sitting in the sun in Cape Town looking over sunset on the Atlantic so it is hard not to enjoy anything!! Found the final piece particularly enjoyable - took a little while to work out the solution. Luckily as I knew I couldn't print I started and finished this on squared paper with the grid in the centre, which was a big help. There are clearly multiple solutions, which is odd.

[bellabee]

i would have thought my last posting might have produced some warning sounds by now ['pretty rough geometry' indeed!] - luckily i have a retired maths professor as a near neighbour who has now enlightened me as to the very precise nature of this final problem.so the pretty diagram i found on the net will not do at all! - i thought i detected a degree of schadenfreude after speravi's generous tip the other week... but maybe i'm imagining things. anyway, it's very bad of the editors to smuggle maths at this level into what is a very difficult word puzzle in itself.

[tilbee]

Bellabee, there is of course a 3D solution but this involves forming a torus from the grid, which is not required. A 2D solution using the original grid is adequate, but not sure how to demostrate the correctness of this without labelling the lins ?

[tilbee]

..or even lines.

[bellabee]

hello tilbee - i'm replotting my little diagram now that i understand the problem more fully but it is difficult to keep track of everything and i'm still not sure how geometrically precise the exits and entries should be. i'm too far into this now to give up without a struggle though. what i hadn't understood is what was meant by 'connected........to every other dot'!!!!!!!!!!

[midazolam]

bellabee, the solution to the preamble's spiel about the four dots can be found here.

http://www.boost.org/...oc/planar_graphs.html

[bellabee]

thanks midazolam, it's an ideal aid to visualise the problem - i'd be too embarrassed to tell you what i originally thought 'it's impossible to connect more than four dots....' meant. but i've just had my first ever seminar on 'connectivity' and i think i might be getting somewhere with my lines. reading up on 'graph theory' on the net - it might as well have been in greek!

[Zabadak]

Here's an interesting question. If you presented a 3-dimensional solution, would the lines be straight?

[borealis]

Whew. Tough but increasingly enjoyable. A hugely impressive construction - thank you, Ten-Four. To those who have a dozen or more clues - don't give up, start fitting 'em in. As Midazolam implies above, there are features which give you a toe-hold.

Zabadak - surely not; get out your doughnut and a ruler and give it a go! Of course if you leave your wrapped 2D surface (the surface of the doughnut) you can do it, but that would take a needle and thread rather than a pen and ruler......

[TheBear69]

For a surface such as a torus or a sphere, the analog of a straight line segment is a geodesic and is defined as a curve connecting two points with minimal path length. If you connect two such points with a geodesic and then 'flatten' the surface (in this case restore the original grid) at least some of the 'lines' will no longer be straight. Conversely if you connect the grid points with straight lines and then bend the grid into a torus, the resulting 'lines' will be neither straight nor will they be minimum length. (For a spherical example, consider the latitude lines on a map of the earth. They are straight lines, but as any pilot knows, the shortest path between two points with same latitude is not along the latitude but rather the great circle path connecting the points.) So an optimal solution to the puzzle would be with curves, not straight lines, but I'd be shocked if straight lines were marked wrong.

[Philoctetes]

Still plodding my way through the interminable cold-solving, so really unqualified to comment. But, looking at the geometric discussions on here, does this puzzle fit in with the guidelines on the level of knowledge required? Is this the sort of thing they teach at school these days?

[Zabadak]

Hi Philoctetes. The geometry only comes in once you've ploughed through all those cold solves, though they do warm up a it after a while as things begin to fall into place.

As to whether they teach it anywhere, they didn't when I was a lad, and I even had trouble working out how four dots on a piece of paper can be joined like the preamble says - but then I had them arranged in a square. Turns out you can do it with one dot in the middle of a triangle of dots.
For those of you with Yiddish as a second language: Torus? Tsouris!

[Zabadak]

That should be ...do warm up a bit...

[Zabadak]

For The Bear69 - cheers, that's what I thought, only you put it so well!