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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.
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
Furthermore, the disk to be moved is determined by the number of times the move count (m) can be divided by 2 (i.e. the number of zero bits at the right), counting the first move as 1 and identifying the disks by the numbers 0, 1, 2, etc. in order of increasing size. This permits a very fast non-recursive computer implementation to find the ...
The strictly jammed (mechanically stable even as a finite system) regular sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only π √ 2 /9 ≈ 0.49365. [6] The loosest known regular jammed packing has a density of approximately 0.0555. [7]
Tricky Towers is a physics-based tower building game puzzle video game that uses a form of the block-stacking problem as the central game mechanic. [2] It was released on digital distribution service Steam for Windows, OS X, and Linux, and for the PlayStation Plus service in August 2016, before being released on PlayStation 4 a month later.
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Given n cubes, with the faces of each cube coloured with one of n colours, determining if it is possible to stack the cubes so that each colour appears exactly once on each of the 4 sides of the stack is NP-complete. [8] [9] The cube stacking game is a two-player game version of this puzzle. Given an ordered list of cubes, the players take ...