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## Arukone (Number Link) Puzzles

I was alerted to this use of the Sudoku Grid in Yahoo! group’s Sudokuworld about a week ago for a completely different variation exercising mental pathways, which for me, are not well traveled. To make the sample puzzle clearer, I used a yellow path that included both endpoints. There will be 9 such yellow paths, (with none that cross each other,) and at least one blank square long so that all the squares are covered by the (unique) solution. Dark lines may also be used to connect like numbers.

My strategy is (“Get It Surrounded”) to start at the outermost Number (i.e. in a corner) and try to connect to its mate. Then work inwards. If the numbers permit, working from right to left, up to down or the reverse also helps. It is a bit irritating that multiple tentative paths are not easily displayed concurrently.

There are puzzle sites with either paired numbers or paired letters. The grids are anywhere from 5×5 to 16×16. In general, the larger the grid, the more difficult the puzzle is to solve.

Sites with Puzzles and/or Tutorials (in English) include:

Nikoli Number Link Puzzles. The tutorial is terse. Nikoli has 3 books published in Japan containing Number Link puzzles exclusively.

Arukone Puzzles. This site is created and maintained by Vegard Hanssen. It has puzzles in 5×5 and 9×9 and is graded for difficulty. The puzzles are printable and solutions can be displayed (but not printed).

Angela And Otto Janko’s German Puzzle Site, containing many kinds of riddles and puzzles, including Arukone puzzles. The tutorial and strategy section is very concise.

A Wikipedia Article about Number Link Puzzles is likewise quite brief.

Finally, Tim Halbert’s Number Link Site contains an archive of Number Link puzzles (which was generated daily until May 2006). According to Halbert, not all puzzles in the archive have a unique solution. This site also uses the strategy based on working from outside in, to avoid crossed paths. He indicates that Excel can be used as a solving grid, once the numbers are entered. Printing a puzzle out on paper (even multiple times) to solve portably is also a good option.