, or More or Less, is a

logic puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the a ...

game from

Japan Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...

. Its name means "

inequality Inequality may refer to: * Inequality (mathematics), a relation between two quantities when they are different. * Economic inequality, difference in economic well-being between population groups ** Income inequality, an unequal distribution of i ...

". It is also spelled hutosiki (using

Kunrei-shiki , also known as the Monbusho system (named after the endonym for the Ministry of Education, Culture, Sports, Science and Technology) or MEXT system, is the Cabinet-ordered romanization system for transcribing the Japanese language into the Lat ...

romanization In linguistics, romanization is the conversion of text from a different writing system to the Latin script, Roman (Latin) script, or a system for doing so. Methods of romanization include transliteration, for representing written text, and tra ...

). Futoshiki was developed by Tamaki Seto in 2001. The puzzle is played on a square grid. The objective is to place the numbers such that each row and column contains only one of each digit. Some digits may be given at the start. Inequality constraints are initially specified between some of the squares, such that one must be higher or lower than its neighbor. These constraints must be honored in order to complete the puzzle.

Strategy

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. 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. A solved futoshiki puzzle is a

Latin square Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion o ...

Futoshiki in the United Kingdom

A futoshiki puzzle is published in the following UK newspapers: * ''

The Daily Telegraph ''The Daily Telegraph'', known online and elsewhere as ''The Telegraph'', is a British daily broadsheet conservative newspaper published in London by Telegraph Media Group and distributed in the United Kingdom and internationally. It was found ...

'' — Saturdays * ''

Dundee Courier ''The Courier'' (known as ''The Courier & Advertiser'' between 1926 and 2012) is a newspaper published by DC Thomson in Dundee, Scotland. As of 2013, it is printed in six regional editions: Dundee, Angus & The Mearns, Fife, West Fife, Perths ...

'' — daily * '' i'' — Mondays through Fridays * ''

The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...

'' — Saturdays * ''

The Times ''The Times'' is a British Newspaper#Daily, daily Newspaper#National, national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its modern name on 1 January 1788. ''The Times'' and its si ...

'' — daily

Notes

{{Reflist Logic puzzles Latin squares Japanese board games