Futoshiki
Encyclopedia
or Unequal is a logic puzzle
game from Japan
. Its name means "inequality". It is also spelled hutosiki (using Kunrei-shiki
romanization
).
The puzzle is played on a square grid, such as 5 x 5. The objective is to place the numbers 1 to 5 (or whatever the dimensions are) such that each row, and column contains each of the digits 1 to 5. Some digits may be given at the start. In addition, inequality constraints are also initially specifed between some of the squares, such that one must be higher or lower than its neighbour. These constraints must be honoured as the grid is filled out.
Once the table of possibilities has been determined, a crucial tactic to solve the puzzle involves "AB elimination", in which subsets are identified within a row whose range of values can be determined. For example, if the first two squares within a row must contain 1 or 2, then these numbers can be excluded from the remaining squares. Similarly, if the first three squares must contain 1 or 2; 1 or 3; and 1 or 2 or 3, then those remaining must contain other values (4 and 5 in a 5x5 puzzle).
Another important technique is to work through the range of possibilities in open inequalities. A value on one side of an inequality determines others, which then can be worked through the puzzle until a contradiction is reached and the first value is excluded.
Additionally, many Futoshiki puzzles are promised to possess unique solutions. If this is strictly true, then regions of the form
A . B
. . .
B . A
cannot be present, unless an inequality or pre-filled number can specify which of the two numbers is B and which number is A.
A solved Futoshiki puzzle is a Latin square
.
and in The Daily Telegraph
, and daily in The Times
and also in the Dundee Courier.
Logic puzzle
A logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in Wonderland...
game from Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
. Its name means "inequality". It is also spelled hutosiki (using Kunrei-shiki
Kunrei-shiki
is a Japanese romanization system, i.e. a system for transcribing the Japanese language into the Latin alphabet. It is abbreviated as Kunrei-shiki. Its name is rendered Kunreisiki using Kunrei-shiki itself....
romanization
Romanization
In linguistics, romanization or latinization is the representation of a written word or spoken speech with the Roman script, or a system for doing so, where the original word or language uses a different writing system . Methods of romanization include transliteration, for representing written...
).
The puzzle is played on a square grid, such as 5 x 5. The objective is to place the numbers 1 to 5 (or whatever the dimensions are) such that each row, and column contains each of the digits 1 to 5. Some digits may be given at the start. In addition, inequality constraints are also initially specifed between some of the squares, such that one must be higher or lower than its neighbour. These constraints must be honoured as the grid is filled out.
Solving the puzzle
Solving the puzzle requires a combination of logical techniques. Numbers in each row and column restrict the number of possible values for each position, as do the inequalities.Once the table of possibilities has been determined, a crucial tactic to solve the puzzle involves "AB elimination", in which subsets are identified within a row whose range of values can be determined. For example, if the first two squares within a row must contain 1 or 2, then these numbers can be excluded from the remaining squares. Similarly, if the first three squares must contain 1 or 2; 1 or 3; and 1 or 2 or 3, then those remaining must contain other values (4 and 5 in a 5x5 puzzle).
Another important technique is to work through the range of possibilities in open inequalities. A value on one side of an inequality determines others, which then can be worked through the puzzle until a contradiction is reached and the first value is excluded.
Additionally, many Futoshiki puzzles are promised to possess unique solutions. If this is strictly true, then regions of the form
A . B
. . .
B . A
cannot be present, unless an inequality or pre-filled number can specify which of the two numbers is B and which number is A.
A solved Futoshiki puzzle is a Latin square
Latin square
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column...
.
Futoshiki in the United Kingdom
The puzzle is published every Saturday in The GuardianThe Guardian
The Guardian, formerly known as The Manchester Guardian , is a British national daily newspaper in the Berliner format...
and in The Daily Telegraph
The Daily Telegraph
The Daily Telegraph is a daily morning broadsheet newspaper distributed throughout the United Kingdom and internationally. The newspaper was founded by Arthur B...
, and daily in The Times
The Times
The Times is a British daily national newspaper, first published in London in 1785 under the title The Daily Universal Register . The Times and its sister paper The Sunday Times are published by Times Newspapers Limited, a subsidiary since 1981 of News International...
and also in the Dundee Courier.