Futoshiki
Futoshiki ( Japanese 不等式 futōshiki , German ' inequality ' ) is a logic puzzle in the shape of the Latin square . It was developed in Japan around 2001 and has been distributed and publicized in Great Britain by the Guardian since 2006 .
As usual with this type of puzzle, the game is played on a square grid. The aim is to place the numbers in such a way that each row and column contains exactly one of each digit. Usually a few digits are given at the beginning. The specialty of the Futoshiki are the comparison characters "<" ( smaller sign ) and ">" ( larger sign ) placed between some fields , which determine that the value of the field must be higher or lower than that of its neighbor. These inequality relations must be taken into account in order to solve the puzzle and thus all must be fulfilled in the end.
Solution strategy
As with Sudoku , the basic rules of the Latin square apply: Each number appears exactly once in each row and each column. This limits the number of possible values for each position, as do the inequalities.
So the first step in solving the puzzle is to list possible values based on non-duplication and inequalities within rows and columns. Then AB elimination can be useful, in which subsets are identified within a line, the value range of which can be determined. For example, if the first two fields within a row must contain 1 or 2, then these numbers can be excluded from the remaining fields. Likewise, if the first three fields are 1 or 2; 1 or 3; and must contain 1 or 2 or 3, then the remaining fields must contain other values (4 and 5 in a 5 × 5 puzzle). Another important technique is to work through the possibilities of open inequalities. One value on one side of an inequality constrains the other. For example, there can never be 1 on the “greater than” side, as it represents the absolutely smallest element in the puzzle. A chain of inequalities can be followed through the puzzle until a contradiction is reached and thus a value is excluded.
literature
- Kazuya Haraguchi: The Number of Inequality Signs in the Design of Futoshiki Puzzle . In: Journal of Information Processing . tape 21 , no. 1 , 2013, p. 26-32 , doi : 10.2197 / ipsjjip.21.26 .
Web links
Individual evidence
- ↑ If you were seduced by sudoku, prepare for futoshiki fever. In: The Guardian . September 30, 2006, accessed October 19, 2019 .