algorithms

Sudoku Is a 3×3 Crossword!

First, we have nine symbols: 1 2 3 4 5 6 7 8 9.

Then, we have an alphabet of 9 factorial letters made of those symbols. The first letter of this alphabet is 123456789 and the last letter is 987654321.

Legal words generated from this alphabet are three letters long. “123456789 456789123 789123456” is an example.

A crossword of three such legal words horizontally and three such legal words vertically is a solved Sudoku puzzle!

An unsolved Sudoku puzzle is a subset of symbols with the property, that no two solved puzzles share this subset.

Perhaps I’m going to create ALL possible Sudokus. In the form of a small self-extracting executable, of course.

Currently I have no incentive for such a flooding, but that might change.

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algorithms

Crosswording Mona Lisa

Imagine every pixel of a picture as a letter. Every image is then a solved crossword. Which are the questions that would form a crossword  depicting the likeness of Mona Lisa?

Well, instead of queries you could have instructions for where to write what. At 1,1 just write “SEAR”. And so on.

You can have a dictionary of answers and then just a number N. The Nth giant crossword in alphabetical order of all possible crosswords made from this dictionary – looks like Mona Lisa!

N is a big number. But much smaller than Mona Lisa’s (uncompressed) number.

Then, you can divide Mona Lisa into a grid of smaller square images. Each square uniquely represented by its index number in the list of all possible small crosswords made out of the dictionary.

And why would one want to do such a thing?

Just for encryption. Not only for images but for any binary string as well. We still don’t have the computer power required to do this, though.

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