Category: Sudoku Variants

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.

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.

This is a Unary Number System variation that is popular in China, Japan and Korea. The full Character (Cheng) means honesty or correct according to the Wikipedia Tally marks article.

Something I neglected to mention in the first Unary Sudoku Cartoon is the Encyclopedia of Integer Sequences which contains within it the table of the first 1000 Unary Numbers! This table was created by David Wasserman. While this is something of a non-computational table, it turns out to be really handy when you need to copy and paste the Unary number elsewhere, rather than count the strokes yourself.

For this week, I am indebted to a notice by Peter (of Belfast) from Sudokuworld Yahoo Group whose reference tosudoku.xls site has directions for standard text files useful for the visually impaired and blind. In Peter’s link, there are not only ordinary Sudoku puzzles but also Sudoku Tanto (Odd and Even clues) and 6×6 Mini-San Puzzles which overlap in the last/first block of cells.

A search of the key phrase “Blind Sudoku” yields Sudoku-Swicki which is a list of links related to “Braille Sudoku”. Also, Google Groups has The Blind Sudoku Discussion group. Fred’s Head Companion with the American Printing House For The Blind, is another site specializing in tips, resources, and a general database for and by blind and visually impaired people.

Continuing the general theme of limitation, here’s a variant that I have devised where a blank cell plays the role of a digit, to be placed so that there is exactly one blank cell in each row, column and 3×3 block. What makes the rule amusing is that you cannot distinguish blank cells that have to be filled in with 8 of the digits and the special blank cells representing the ninth digit. I’ve not seen it in any other Sudoku variant sites, so you may be seeing it here first.

It’s abtractly identical to many of the Sudoku variants where other symbols are mapped to the digits 1-9. In this case, only one digit is mapped to blank, while the rest of the digits stay as they are.