Bridges ( Jap. 橋 を か け ろ , from Japan - “build bridges”) is a logic puzzle developed by Nikoli and published in 1990. The player’s task is to connect the island with lines, and the number of bridges must match the number indicated on the island [1] .
The puzzle is also known by other names, among them Hashiwokakero [1] , Bridges , Chopsticks , Ai-Ki-Ai .
Content
History
“Bridges” became the second puzzle of Nikoli, and it was invented by the reader under the pseudonym Renin ( Jap. れ ー に ん ) in 1990. The game, as one of the first puzzles of Nikoli, played a role in popularizing the readers section of the magazine [2] .
Rules
Initially, the figure shows the number in each circle, depicting the island. It is necessary to connect the islands with bridges in the form of straight lines according to the following rules [1] :
- The number in the circle corresponds to the number of bridges at the island.
- Between any two islands there can be no more than two bridges.
- Bridges must be horizontal or vertical, and cannot cross other bridges and islands.
- Islands must be connected so that from any island you can get to any other.
Mathematically, a puzzle can be described as a search for a connected flat graph, which can have at most two edges between two vertices [2] .
Solutions
To obtain the first bridges in the puzzle, the following solutions can be applied. If the number corresponds to the maximum number of bridges, then all bridges can be drawn. For example, if it is an island with the number 8, or if it is an island with the number 4, which is located in the corner of the playing field. At the same time, part of the bridges can be drawn if the number indicated on the island is 1 less than the number of possible bridges. For example, if a corner island has the number 3, then at least one vertical and one horizontal bridge exist and can be noted [1] .
After the bridges are created, the possible options for building others are changed. So, if the number of bridges to the island already corresponds to its number, then more bridges cannot be created, and this means that there are no bridges in the corresponding directions leading to other islands. In addition to this property, the bridges that are created intersect the playing field, thus dividing the other islands, between which bridges can no longer be, since they should not intersect. The fact that from each island can eventually be reached by any other, is used in more complex cases - for example, when interconnected groups of islands should not remain isolated [4] .
Notes
- ↑ 1 2 3 4 Bellos, 2017 , p. 18.
- ↑ 1 2 Bellos, 2017 , p. nineteen.
- ↑ Bellos, 2017 , p. 21, 226.
- ↑ Bellos, 2017 , p. 18-19.
Literature
- Alex Bellos . Puzzle Ninja: Pit Your Wits Against The Japanese Puzzle Masters: [ eng ] . - CPI Group. - UK, 2017. - 268 p. - ISBN 978-1-78335-136-7 .