This category groups puzzles made like its component parts, where the aim of the game is to reproduce certain figures. Soma Cube made by Piet Hein, Solomon Golomb's Pentomino and the aforementioned Tangram and "Anker-puzzle" are all examples of this kind of puzzles. In addition, all puzzles where a certain number of pieces are to be placed in order to fit them into the apparently too small box belong to this category.
The image on the right shows a typical Hoffman Puzzle with the packing problem. The aim is to pack 27 cubes with A, B and C side lengths in a box A + B + C side length, except for two constraints:
1) A, B, C must not be the same
2) The smallest of A, B, C must be larger than (A + B + C) / 4
One possibility could be A = 18, B = 20, C = 22 - then the box should have 60 × 60 × 60 dimension.
Modern technologies, such as laser cutters, allow the creation of two-dimensional puzzles made of wood or plexiglass. Recently this technology became predominant to design several new puzzles with an extraordinarily decorative geometry. This uses a large number of subdivision possibilities for repetitive figures.
Computers allowed a great leap forward in the design of new puzzles. The computer also allows an exhaustive search for solutions: with its help, a puzzle can be designed to have few possible solutions and consequently becomes seemingly impossible.
The use of transparent materials allows the creation of puzzles where the parts must be stacked on each other's top. The aim is to generate a model, or specific color combinations, to assist in the solution.
For example, a puzzle consists of disks where its varying angular sections are colored differently. The disks must be stacked so as to generate a circle of color (red -> blue -> green -> red) around the disks.
Some examples are: