Month: November 2007

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Arukone (Number Link) Puzzles

Arukone Sudoku

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.

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Roman Sudoku

Roman Sudoku

There is a continuing fascination with predecessor number systems like Roman Numerals. This Wikipedia site also discusses fractional notation and the subsequent use of the “zero” as N (standing for Null). There are sites which provide Arabic from/to Roman Numeral Converters and those that actually teach how to perform arithmetic operations using Roman numbers.

A little known function in Excel 2004 (maybe others) called roman(arabic_no,form) permits varying Roman Number succinctness. As the help facility notes: we have
0 for classic; 1, 2, 3 for more, more and more concise; and 4 for simplified. (Look up Excel Help for Roman form). In particular the number 499 has 5 (!) versions: CDXCIX, LDVLIV, XDIX, VDIV, and ID.

One of my favorite problems for Computer Programmers learning the C programming language (I taught this in the 1980s) was to write an Arabic to Roman Number Converter, using associative arrays of all the possible symbols as a preferred solution technique. It exercised many language aspects and involved arrays and pointers.

In this Sudoku variant, there is also no room for “small candidate” roman numbers, unless you use a classroom sized whiteboard. Reading clocks with Roman Numerals discloses that IV = IIII and that V, VI, VII and VIII are read while (they or you are) upside down. IV = IIII is done so that IV won’t be confused with an upside down VI, or so they say.

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Barcode Sudoku

Barcode Sudoku

The ubiquity of Barcodes! They’ve come upon the scene suddenly in 1973 and for a while barcodes showed themselves in many inappropriate places (tattoos, cartoons, human foreheads, etc.), they became invisible because they were everywhere. Indeed, they are significantly missing from the educational curriculum. Mathematics ignores them. Ironically, the initial outcry was that human beings should not be treated merely as numbers!

New tagging inventions, particularly the Radio Frequency Identification (RFID) tagging technology were born invisible. The furor against this has been minimal, despite that an RFID tag can be applied to or incorporated into a product, animal, or person for the purpose of identification using radiowaves. Perhaps the mantra for humans could be: I am not a signal tag!

But I digress. I have taught Unix Shell Programming with a Final exam question that was 3 pages of Barcode introductory description and one paragraph of question, involving computing the check digit on bonafide and illegal barcodes.

In the case of this Sudoku variant, it’s clear that the usual solving methods won’t work as well since the graphic representation of the number takes up nearly the entire cell. Perhaps a parallel Sudoku must be solved with ordinary numbers and then the barcode transcription be made.

In any event, I thought this was a cool way to solve a Sudoku puzzle. I hope you enjoy the sight or the struggle.