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The best 3D brain teaser puzzles require logic and spatial awareness to make an exciting game of skill. From Kanoodle to Hanayama, here are the good ones.
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
Deductive methods solve this problem by building a set of half-spaces that describe the interior of the geometry. These half-spaces are used to describe primitives that can be combined to get the final model. [7] Another approach decouples the detection of primitive shapes and the computation of the CSG tree that defines the final model.
The book Winning Ways for your Mathematical Plays also contains a detailed analysis of the Soma cube problem. There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections: these are easily generated by a simple recursive backtracking search computer program similar to that used for the eight queens puzzle .
Geometric constraint solving is constraint satisfaction in a computational geometry setting, which has primary applications in computer aided design. [1] A problem to be solved consists of a given set of geometric elements and a description of geometric constraints between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle ...
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
Rubik's cube: a popular puzzle that involves 3D mental rotation. Mental rotation is the ability to mentally represent and rotate 2D and 3D objects in space quickly and accurately, while the object's features remain unchanged. Mental representations of physical objects can help utilize problem solving and understanding.
The T-puzzle, a T shape can be assembled with the four pieces on the left. The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle , two right trapezoids and an irregular shaped pentagon .
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