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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.

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Sudoku Goes Postal /
Sudoku By Mail

Sudoku Goes Postal

Since you can play Chess by mail (See FAQ) or use a Chess Correspondence Server, I wondered how it would be possible to solve Sudoku by mail. In this case, it requires $4.50 for the 9 denominations of 1 cent through 9 cent stamps. Do not use rare stamps. You won’t be thanked. For those of you that like to solve Sudoku puzzles quickly, I believe that this variant will slow you down. The puzzle is considered neither easy nor hard.

While there are sites that claim the ability to do Sudoku by mail, this simply means that the site is willing to send you email (daily) with one or more Sudoku puzzles for you to solve on your own computer. This is convenient, but no way will a puzzle take days, weeks or months, iteratively, to complete.

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Planet Sudoku

Planet Sudoku

This variant is a consequence of another hobby I used to do involving Astrology. The planetary symbols are called glyphs which I dutifully memorized and matched to the planets and (and asteroids) in our solar system. They are listed above for your convenience. I used the Hamburg Symbols (True Type) Font to produce the glyphs.

Although it is arguable as to whether Pluto can be considered a major planet, I have no wish to diminish its importance to astrological interpretation. Scientists seem to have a consistent track record of saying one thing and subsequently changing or contradicting their original statement. There’s always a reason. I’m just waiting for the next reason (in 2015) to reinstate the planet.

As usual in these kinds of Sudoku variations, each symbol represents one of the non-zero units digits. You can first transcribe it to numbers or further flex your mind and solve it as is.

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Sudoku Buildings

Sudoku Buildings
This variant comes from the 2nd Annual World Sudoku Championship instruction booklet (pdf). This competition was held In Prague earlier this year. The idea is to consider the sudoku puzzle also as heights of buildings as seen from the top down. The total counts on each edge (side) represent how many buildings are viewable from that location. Note that taller buildings (higher numbers) hide shorter buildings (lower numbers). Once again the starting numbers are sparse due to the edge clues.

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Sudoku Y

Sudoku Y
Sudoku X has been an alternative to regular Sudoku puzzles, when I wanted some minimal relief. Having a vest pocket pair of constraints when I was otherwise reduced to guessing was nice. The site: easton.me.uk provides a downloadable (Windows) Puzzle Generator for Sudoku X (Nothing on this variant, though).

Because this variation is not one that Sudoku Solvers solve programmatically, I had to reverse engineer the solution by specifying a proper set of values for the Y and then solving by adding one number at a time and insuring that the result did not produce a conflict with the other cells. I stopped when there was a single unique solution. (I used the Web Based: Sudoku Solver By Logic.) I’m not sure if I could have provided fewer clues, but feel free to erase as many as you want and see if you can solve it that way.

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Sudoku Wraps

Sudoku Wraps
This Sudoku variant offers the ability of Blocks of 9 to be non-contiguous as well as non-square on the grid. Other versions of this kind of puzzle do not offer the gift of colorization, but merely the outline of the misshapen blocks. This is reminiscent of the Jigsaw Sudoku Puzzle Cartoon of a month ago, which also offered non-square block shapes, but were contiguous. These variants have also been known as Geometric (or Latin Square) Sudoku by Ed Pegg writing for the Mathematical Association of America.

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Subset Sudoku

Subset Sudoku

This Sudoku variant supplies the correct triad locations of the numbers of the solved puzzle, but offers far fewer starting numbers. Even so, the puzzle is solvable when considering the subset of candidates that can be in a particular cell.

I found a math site called cut-the-knot.org that shows how you can intersperse only plus or minus signs to the fixed sequence of digits 1 2 3 4 5 6 7 8 9 so that the resulting arithmetic expression, when simplified, is 100. It’s both harder and easier than you think! Likewise, the sequence 9 8 7 6 5 4 3 2 1 is also considered for expressions results simplifying to 100.  There’s more than one, but not many.

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Odd Sudoku

Odd Sudoku

I had to skip a week due to superceding short term tasks to complete involving a Linux workshop I conducted last week.

This Sudoku variant supplies the correct odd/even location of the numbers of the solved puzzle, but offers fewer starting numbers. This encourages constraining logic when considering the possibilities of each cell.

A discussion of Odd and Even Numbers is offered in Wikipedia.

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Jigsaw Sudoku

Jigsaw Sudoku

Jigsaw Sudoku relaxes the requirement of square blocks as in regular Sudoku puzzles. Instead, non-square rectilinear shapes made out of contiguous cells are used instead. The requirement that rows and columns each have unique digits is still true, however.

Some sites that offer Jigsaw Sudoku puzzles include: Puzzle Club, Competition Jigsaw Sudoku and a site offering Sudoku Variants And Other Number Placements.