, or More or Less, is a

logic puzzle A logic puzzle is a puzzle deriving from the mathematical 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 W ...

game from Japan. Its name means "

inequality Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * ...

". It is also spelled hutosiki (using

Kunrei-shiki is the Cabinet-ordered romanization system for transcribing the Japanese language into the Latin alphabet. Its name is rendered ''Kunreisiki rômazi'' in the system itself. Kunrei-shiki is sometimes known as the Monbushō system in English bec ...

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

). 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 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. An example of a 3×3 Latin sq ...

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 national British daily broadsheet newspaper published in London by Telegraph Media Group and distributed across the United Kingdom and internationally. It was f ...

'' — 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 1821 as ''The Manchester Guardian'', and changed its name in 1959. Along with its sister papers ''The Observer'' and ''The Guardian Weekly'', ''The Guardian'' is part of the Gu ...

'' — Saturdays * ''

The Times ''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper '' The Sunday Times'' (f ...

'' — daily
Futoshiki igre

Notes

{{Reflist Logic puzzles Latin squares