One conveniently easy problem (perhaps not puzzle) which your description of an open-ended puzzle reminds me of is to prove there can only be five (3D) platonic solids. How many regular polygons can fit around a point with angles summing to less than 360° (so that it's a polyhedron, not a plane tesselation)? Answer: 3, 4 or 5 triangles, 3 squares or 3 pentagons. Which turns out to be exactly the platonic solids which do exist.
Puzzle 5 here is one of my most fondly remembered from when I was a kid, which might make it one of my favourites.
no subject
Date: 2014-12-05 01:27 am (UTC)Puzzle 5 here is one of my most fondly remembered from when I was a kid, which might make it one of my favourites.
There's also the blue forehead puzzle in its various forms.