Month: October 2007

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Unary Sudoku T

Unary Sudoku T

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.

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Audio-Visual Sudoku

Audio-Visual Sudoku

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.

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Unary Sudoku

Unary Sudoku

The most rudimentary (prior to computers) number system is the Unary number system, consisting purely of 1s or strokes, usually representing tallies. It is described as a base 1 number system.

I studied it in my Computer Science classes (way back when) in a course about Computability, Turing Machines and Automata Theory. In particular, the Turing Machine example described a machine readable tape containing groups of 1s each separated by a single 0.

I used it as a child/teenager to count up physical items in several categories (popularity counts) and for keeping score in pool. Remember that this was *before* computers existed. Also, not all pool halls had an overhead Abacus. I was much more intimate with the physical world then.

The problem, as I see it, in this variant of Sudoku is that there’s absolutely no space to insert candidate (little) numbers based on which logic is performed. One possibly impractical solution is to do this on a classroom size whiteboard. But I warn you: Don’t have a stroke!

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Binary Sudoku 10

Binary Sudoku 10

Underneath it all, binary numbers are the numerical lingua franca of all computers! In mathematics, most rational numbers can be represented as binary numbers, provided that their binary places (bits) do not exceed the computer word length (or some multiple of it).

For this puzzle, I’ve translated the first 9 integers to their equivalent values written as binary numbers. Since most human beings lock onto the first number system they ever learned (decimal or base 10 numbers), they entertain other number systems only with painful difficulty, unless paid (as computer programmers/developers) not to do so.