Dots On A Plane

Alright, time for a new puzzle, its a bit of a weird geometry one I learned from Brandon, but its sort of neat:
Place 10 distinct points and 5 distinct lines on an infinite plane such that each line goes through exactly 4 points.

Fairly simple to word, note that the lines must be infinte and go through exactly 4 points so that having 5 points in a row does not count as two lines going through 4 points.

If you want to do a more advanced version, try to classify the set of all possible solutions to this puzzle, I still haven't done this but hopefully I will before I get around to posting the solution.


Anonymous said...

Maybe I"m missing the puzzle here, but isn't it obvious once you turn the problem around?

Take any 5 lines in general position (no 2 parallel, no 3+ lines crossing in a single point). They will define 10 intersection points total.
In Euclidean geometry, I think that should give you a complete description of all solutions.

Kory Stevens said...

Yeah, you have the essentials of it, at the time of posting I hadn't realised that the reverse problem is easy. I guess it would be best to reword the problem to obfuscate the situation a bit.