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To solve the puzzle you must make sure that every column, row and 3x3 box in each larger 9x9 grid contains the numbers 1 through to 9. The colours on the puzzle are the cages which all contain a small number which is the sum total of all the squares in that caged area. (The puzzles is basically a combination of a Samurai Sudoku puzzle and a Killer Sudoku Puzzle.)
Almost all of the puzzles can be solved using logic alone and there is no need to guess. A puzzle can take from 1 hour to almost a day to complete depending on its level and your experience. More on the rules and tips for quick solving can be found here.
The puzzles along with their solutions can be found on this site.
The Creator of Killer Samurai Sudoku is Melvyn Lawes. Read the short interview here.