The puzzle known as "Al Escargot" (the snail) is currently considered the hardest Sudoku puzzle. It was created by a Finnish mathematician called Arto Inkala.
One of the hardest Sudoku books available is "Extreme Sudoku" by Antoine Alary, not to be confused with "X-TREME Sudoku" by Nikoli & Co. or "Sudoku Xtreme" by Christopher Monckton, which are both an order of magnitude easier.
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Sudoku
Its basically a math puzzle, so a type of puzzle.
Because 9*9 = 81 which is a square number or a perfect square.
One could visit SudokuProfessor or SudokuDragon to find strategies on how to complete a Sudoku Puzzle. Also, if one happens to have a Sudoku Puzzle Book, at the front page is usually a guide to how to complete a Sudoku puzzle. Once you know how to, they are really fun and good for keeping the mind active.
They were first published in 1979 by Dell Magazines, known as Number Place (the earliest known examples of modern Sudoku), probably contributed by Howard Garns. They were introduced to Japan in 1984 and eventually became known there as "sudoku".
Sudoku
You need more information.
It depends on the puzzle.
a Sudoku puzzle is a test of logic while a crossword puzzle is a test of how like a thesaurus you are or a test of general knowledge. which one if better is a matter of opinion, but i suppose one might stimulate the brain than the other, if that is what you mean by better.
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Its literally sudoku