Arukone

Rules

Some cells in the grid are marked with numbers; each number appears exactly twice and no cell contains more than one number. For each pair of identical numbers, draw a path that connects those two numbers. The paths must go through orthogonally adjacent cells. Each cell may be visited by at most one path and may be visited at most once by that path. (It is permissible for a cell to not be visited by any path.)

(Rules and example from PGP IB)

Rule variations

• Alphabets (or any symbols) can be used instead of numbers.
• In some puzzles, it is required that all cells be used by a path.
• In some puzzles, it is required that no path occupy 2x2 areas.
• Multi Arukone: From WPC 2019/Round 10. There are more than two copies of the same symbol. The example on the left is from WPC 2019 IB.

History of the puzzle

Due to the simplicity of the rules, this puzzle has been independently developed multiple times.

Henry Dudeney's (USA) 1932 book Puzzles and Curious Problems include an example of this puzzle.

On Nikoli the first appearance is on volume 17 (1987) under the name ナンバーリンク ("Number Link"). The puzzle was by 野木一生 (Kazuki Nogi).

On Puzzler it was 1989 under the name of アルファベットコネクション ("Alphabet Connection"). The name Arukone comes from the contraction of the longer name. It was inspired by Sam Loyd (USA)'s "Quarrelsome Neighbors" puzzle, published in 1897.

Appearances in the past WPCs

• WPC 2019/Round 3 (Permaculture hybrid with Pentominous) by Silke Berendes
• WPC 2019/Round 10 (Multi Arukone) by Sebastian Matschke
• WPC 2018/Round 7 by Jiří Hrdina
• WPC 2017/Round 16 by Rohan Rao
• WPC 2016/Round 12 by Matúš Demiger
• WPC 2014/Round 6 (Classic, Toroidal)
• WPC 2014/Round 11 (Diagonal Number Link)
• WPC 2014/Round 12 (Toroidal)
• WPC 2013/Part 7
• WPC 2012/Part 7
• WPC 2011/Part 1
• WPC 2010/Part 3 (Tapa Connection)