Ohhhkay, Net is good; can get the bordered ones done pretty quickly.
But, I haven't yet managed to get any of the wrapping ones solved. I've got a few to a point of being hopelessly tangled in knots, with several squares blatantly not connectable with the rest of the configuration, but I haven't found any obvious starting points (like straights/Ts on the edges in the bordered version, for example), apart from occassionally-occuring straights between two end points. This makes it seem a lot more like trial and error (or randomly twisting things round and restarting again several times from the beginning for ages until stumbling over the correct solution) than anything involving logic. Am I missing some key point, or is the wrapping version really that ... random?
There are quite a few possible starting patterns you can look for in a wrapping grid. You're correct that a straight between two endpoints is one of them. Others include:
an endpoint surrounded on three sides by other endpoints (the centre one only has one direction it can point)
a corner piece surrounded on three sides by endpoints (the corner piece must have a connection on the remaining edge so as not to connect two endpoints into a dead end)
a T-piece surrounded on three sides by endpoints (again, it must connect on the remaining edge otherwise it just connects the three endpoints together)
two endpoints and two straights arranged in a 2x2 square with opposite pieces identical (considering both ways for one of the straights to point should convince you that the endpoints cannot possibly connect on either of the two sides that don't border one of the two straights).
Also, keep in mind that a corner piece is always connected on one side if and only if it is not connected on the opposite side; so if one of the above deductions allows you to deduce that some piece has a connection on a particular side, and the next piece in that direction is a corner, then you know the piece beyond the corner does not have a connection on the near side - which allows you to nail down its orientation completely if it's a T-piece.
There are others as well, mostly more complex forms of dead-end avoidance. Those are just the first few that sprang to mind. It's certainly not random guesswork - I wouldn't expect to ever meet a wrapping Net puzzle I couldn't find somewhere to start on.
Thank you! That clarifies several things I'd been doing instinctively in the bordered versions, that I hadn't extrapolated into conscious thought for the wrapping ones. I shall tackle them later. (Not now, not at work. Really not. Honest. I can resist. *cough*)
Now all I need is a "lock" option for tiles so I don't forget which ones were set that way for a reason darnit... ;)
But, I haven't yet managed to get any of the wrapping ones solved. I've got a few to a point of being hopelessly tangled in knots, with several squares blatantly not connectable with the rest of the configuration, but I haven't found any obvious starting points (like straights/Ts on the edges in the bordered version, for example), apart from occassionally-occuring straights between two end points. This makes it seem a lot more like trial and error (or randomly twisting things round and restarting again several times from the beginning for ages until stumbling over the correct solution) than anything involving logic. Am I missing some key point, or is the wrapping version really that ... random?
- an endpoint surrounded on three sides by other endpoints (the centre one only has one direction it can point)
- a corner piece surrounded on three sides by endpoints (the corner piece must have a connection on the remaining edge so as not to connect two endpoints into a dead end)
- a T-piece surrounded on three sides by endpoints (again, it must connect on the remaining edge otherwise it just connects the three endpoints together)
- two endpoints and two straights arranged in a 2x2 square with opposite pieces identical (considering both ways for one of the straights to point should convince you that the endpoints cannot possibly connect on either of the two sides that don't border one of the two straights).
Also, keep in mind that a corner piece is always connected on one side if and only if it is not connected on the opposite side; so if one of the above deductions allows you to deduce that some piece has a connection on a particular side, and the next piece in that direction is a corner, then you know the piece beyond the corner does not have a connection on the near side - which allows you to nail down its orientation completely if it's a T-piece.There are others as well, mostly more complex forms of dead-end avoidance. Those are just the first few that sprang to mind. It's certainly not random guesswork - I wouldn't expect to ever meet a wrapping Net puzzle I couldn't find somewhere to start on.
Now all I need is a "lock" option for tiles so I don't forget which ones were set that way for a reason darnit... ;)
And I just solved one, too *beam*