Hashiwokakero (橋をかけろ Hashi o kakero; lit. "build bridges!") is a type of logic puzzle published by Nikoli. A logic puzzle is a Puzzle deriving from the Mathematics field of Deduction. Nikoli is also a village on the island of Lefkada Nikoli (ニコリ nikori) Co It has also been published in English under the name Bridges or Chopsticks. It has also appeared in The Times under the name Hashi. The Times is a daily national Newspaper published in the United Kingdom since 1785 when it was known as The Daily Universal Register. In France, Denmark, the Netherlands, and Belgium it is published under the name Ai-Ki-Ai. This article is about the country For a topic outline on this subject see List of basic France topics. The Kingdom of Denmark ( ˈd̥ænmɑɡ̊ (archaic ˈd̥anmɑːɡ̊ commonly known as Denmark, is a country in the Scandinavian region of northern Europe The Netherlands ( Dutch:, ˈnedərlɑnt is the European part of the Kingdom of the Netherlands, which consists of the Netherlands the Netherlands The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those
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Rules
Hashiwokakero is played on a rectangular grid with no standard size, although the grid itself is not usually drawn. Some cells start out with (usually encircled) numbers from 1 to 8 inclusive; these are the islands. The rest of the cells are empty.
The goal is to connect all of the islands into a single connected group by drawing a series of bridges between the islands. The bridges must follow certain criteria:
- They must begin and end at distinct islands, travelling a straight line in between;
- They must not cross any other bridges or islands.
- They may only run perpendiculary. In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent
- At most two bridges connect a pair of islands.
- The number of bridges connected to each island must match the number on that island.
Solution methods
Solving a Hashiwokakero puzzle is a matter of procedural force: having determined where a bridge must be placed, placing it there can eliminate other possible places for bridges, forcing the placement of another bridge, and so on.
An island showing '3' in a corner, '5' along the outside edge, or '7' anywhere must have at least one bridge radiating from it in each valid direction, for if one direction did not have a bridge, even if all other directions sported two bridges, not enough will have been placed. Obviously, a '4' in a corner, '6' along the border, or '8' anywhere must have two bridges in each direction. This can be generalized as added bridges obstruct routes: a '3' that can only be travelled from vertically must have at least one bridge each for up and down, for example.
It is common practice to cross off islands whose bridge quota has been reached. In addition to reducing mistakes, this can also help locate potential "short circuits": keeping in mind that all islands must be connected by one network of bridges, a bridge that would create a closed network that no further bridges could be added to can only be permitted if it immediately yields the solution to the complete puzzle. The simplest example of this is two islands showing '1' aligned with each other; unless they are the only two islands in the puzzle, they cannot be connected by a bridge, as that would complete a network that cannot be added to, and would therefore force those two islands to be unreachable by any others.
History
Hashiwokakero first appeared in Puzzle Communication Nikoli in issue #31 (September 1990), although an earlier form of the puzzle appeared in issue #28 (December 1989). Nikoli is also a village on the island of Lefkada Nikoli (ニコリ nikori) Co
See also
References
- Puzzle Cyclopedia, Nikoli, 2004. This is a list of major puzzles published by Nikoli. Terms in parentheses are published English titles for the various puzzle types ISBN 4-89072-406-0.
- Nikoli's English page on Hashiwokakero
- Generator and Solver