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The block-stacking problem is the following puzzle: Place identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang. Paterson et al. (2007) provide a long list of references on this problem going back to mechanics texts from the middle of the 19th century.
The best known example is the Conway puzzle which asks for the packing of eighteen convex rectangular blocks into a 5 x 5 x 5 box. A harder convex rectangular block packing problem is to pack forty-one 1 x 2 x 4 blocks into a 7 x 7 x 7 box (thereby leaving 15 holes); the solution is analogous to the 5x5x5 case, and has three 1x1x5 cuboidal ...
Pieces used in the Conway puzzle. Conway's puzzle, or blocks-in-a-box, is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway.It calls for packing thirteen 1 × 2 × 4 blocks, one 2 × 2 × 2 block, one 1 × 2 × 2 block, and three 1 × 1 × 3 blocks into a 5 × 5 × 5 box.
Nurikabe (hiragana: ぬりかべ) is a binary determination puzzle named for Nurikabe, an invisible wall in Japanese folklore that blocks roads and delays foot travel. Nurikabe was apparently invented and named by the publisher Nikoli ; other names (and attempts at localization) for the puzzle include Cell Structure and Islands in the Stream .
Famous examples include the number of ways to place n non-attacking rooks on: an entire n × n chessboard, which is an elementary combinatorial problem; the same board with its diagonal squares forbidden; this is the derangement or "hat-check" problem (this is a particular case of the problème des rencontres);
An initial configuration. A solution. Shikaku is played on a rectangular grid. Some of the squares in the grid are numbered. The objective is to divide the grid into rectangular and square pieces such that each piece contains exactly one number, and that number represents the area of the rectangle.
For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle : The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...
A-C are axis oriented - parallel to axes of the light blue "floor" and also examples of. [1] E shows a maximal empty rectangle with arbitrary orientation In computational geometry , the largest empty rectangle problem, [ 2 ] maximal empty rectangle problem [ 3 ] or maximum empty rectangle problem , [ 4 ] is the problem of finding a rectangle of ...