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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.

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“Undextrous” Sudoku

Most of us only use our least-used hand when we are kids or if we damage our favored hand. This feature of our species, called handedness is studied at a research institute called Handedness Research Institute. The intitute’s purpose is to reduce social and educational discrimination because of the existence of left-handers.

At Indiana University, the connection between Handedness and Brain Lateralization is decribed. It turns out that Language skills are in the opposite hemisphere from the dominant hand, but not always. It seems that some left-handers can and do screw it up and have language specialization on the left side also.

As a left-hander myself, I was able to overcome the design decisions, such as of: right handed chair-desks, scizzors, Guitar string order and other presumptive creations. Chair-desks not nailed in place I rotated 45 degrees; scizzors, I flipped over and Guitar strings I restrung in the opposite order.

I delighted in getting ink, pencil lead on the outside of my left hand and ignored the smudging as I traversed the lines of the page. I tried to say the most important things on the right side of the page. Basically, I ignored the difficulties. With the advent of keyboards and typing, this inequity has been significantly reduced.

It’s a handicap in solving Sudoku this way, because you are constrained to write legibly in your unpracticed hand, slowing you down and adding to the stress of solving the puzzle. Other people might, on the other hand (no pun intended), enjoy a calming effect that concentrated focus brings.

I use my ability to solve sudoku puzzles in a timely fashion as an indicator of how mentally adept and insightful I am. When I am ill, my mental acuity drops like a rock and solving a sudoku puzzle can take days. What other method can detect that you are getting better without taking your temperature?

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Liquified Sudoku

Liquified Sudoku

This is Part 2 of Sudoku Media testing. (See the Will it Blend? Cartoon on August 5, 2007). Perhaps because I have acquired a bad cold does this particularly appeal to me. It’s hard to maintain the clarity to do a sudoku puzzle. Frustration abounds. Ergo, the ultimate solution.

My thanks to Vlad Balan who runs free-sudoku-games.net, which provides daily puzzles of varying difficulty along with Sudoku related news and a community page, which shows the twisted sudoku picture encircled.

I’m going to rest my cold now and look for a better day tomorrow.

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Blank Sudoku

Blank Sudoku

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.

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Crossword Sudoku

Crossword Sudoku

I wanted to do a mash-up of Crossword and Sudoku Puzzles. Here is my contribution. It takes a while to think of interesting, non-obvious clues. Alas, these clues will probably have to suffice for all future mash-ups like this. There are just not so many synonyms for the first 9 digits! I tried not to do Fill-in clues, to minimize space. This crossword can be considered a diagramless puzzle, except the starting clues, once entered, are superceded by Sudoku logic.

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Sudoku In The Dark

Sudoku In The Dark

It occurred to me that this theme could benefit from a change in the point of view (no pun intended) closer to that of participant. While anyone can put on a blindfold, it is similarly possible to suffer from a power failure at night, with minimal (candle, flash) light available, or to be at a campsite at night in a remote location.

In these cases, mind maps are a way to making a changing scenario, like a puzzle persist and progress to its completion. Human nature being as it is, not many practice this technique when vision and light are plentiful, unless there is no alternative. It does offer another strong challenge to try to solve puzzles (like math problems, chess games) in your head. Blindfold Chess Tournaments have become a popular chess variation. The Math Forum at Drexel University has an archive of mental math techniques that compete or beat a calculator to the answer.

What’s the benefit? You become more portable and have less need for “stuff”.

For those in the United States, enjoy your Labor Day Weekend safely.

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Braille Sudoku

Braille Sudoku

This weekend, my daughter fell off a ladder and broke her ankle in two places. The emergency room in the hospital awarded her a splint along with crutches. As a newly handicapped person, she is learning the ease and inconvenience of this method of transportation.

And so it is with low and no vision (which my mother suffered from). Braille seems to be the standard way of writing things down that is accessible to the visually impaired. This kinesthetic language was created in 1821 by Louis Braille for non-linear reading and writing. It is the first binary encoding of the characters of various languages. See Wikipedia for more information.

I thought it interesting to see how Sudoku puzzles could be adapted for use in Braille. Obviously a board is not the best medium for this. Paper or parchment may allow one-time use. There do exist refreshable Braille Displays, which can serve the same purpose as erasable white boards. Unfortunately, the current models are limited to 80 cells at a maximum and are expensive to buy.

I feel strongly, that the mind and the active senses are quite adaptable. I hope Sudoku arrives in the world of the blind to offer mental exercise and logical satisfaction. Consider this my push in that direction.

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Illicit Sudoku = Proper Hitori

Illicit Sudoku = Proper Hitori
I discovered this distant cousin of Sudoku in the newsgroup rec.puzzles a couple of weeks ago. Kevin Stone has provided an enhanced user interface with notes for doing daily Hitori puzzles on his website brainbashers.com. His site provides 3 sizes: 5×5, 7×7 and 9×9. These puzzles change daily. Previous Puzzles revert to Neil Berget’s beta website hitoriconquest.com. An archive is not yet available. Hitoriconquest.com offers 5×5, 8×8 and 12×12 size puzzles, as well as a tutorial on how to play.

Hitori is Japanese for “Let Me Alone”. More information is in the Wikipedia Article. The Nicoli Company Website has an animated (flash) tutorial.

The rules are straightforward. Shaded cells cannot be contiguous. They are either separated by a non-shaded (‘white’) cell or touch at their corners. Non-shaded cells, on the other hand, must be contiguous (e.g. at least one side must touch another ‘white’ cell’s side.) The result is that when a puzzle is solved, one can travel a connected path of ‘white’ cells. Puzzles provided by these web sites lead logically to unique solutions.

Hitori exercises your brain differently than in Sudoku. It’s almost as if your luggage is too full to close and you must toss expendable articles so that it fits. I found it necessary to go down each row, making the numbers unique, then going across each column. When this is done, I checked that I didn’t isolate any ‘white’ cells. That seemed to be sufficient to form a correct answer.

Both websites have a (partial) solution checker and it can show any mistakes that are evident as well as if it is all correct. I definitely enjoy this variation on a Sudoku board.