TetraVex
Tetravex is a type of puzzle game in which you have to arrange a lot of square pieces into a large square. Each of the four sides of a part is labeled with a number ( ancient Greek τετρα = four, Latin vexo = shattered). Adjacent pages must have the same number in the solution order.
strategy
With n parts there are n! possible arrangements; with 9 parts this is 362880. There can be several or no solutions. There are also 362880 × 40 = 14515200 different play options for a 9 × 9 Tetravex. The number 362880 is the number of possibilities for arranging the stones: since each stone has four sides on which all 10 digits can fall, there are 40 (four sides by 10 digits) different possibilities for each arrangement.
A simple backtracking strategy would be to fill the fields of the solution square with parts from one corner to the opposite one. If two different numbers come to lie next to each other, the last part placed is replaced by an alternative. If there is no longer any alternative, the assignment of the field that was edited penultimate is replaced, and so on. This way, not all possible combinations have to be laid out in full.
A heuristic to possibly limit the problem size is to identify edge and corner parts. For example, if a part has a 7 at the top but no other part has a 7 at the bottom, then this part must be placed at the top of the solution square.
variants
Usually 9 parts are played. There are also often 4 or 16 puzzles. A non-square arrangement is also possible. Since new parts are required for every game, Textravex is mostly implemented as a computer game. Usually the numbers from 0 to 9 are used, but any pairs can be used, including colors, pictures or vocabulary.
Implementations
The oldest implementation as a computer game comes from Microsoft Windows Entertainment Pack 3. Another version is an open source game for GNOME . There are also versions as browser games.