Tuesday, 2 September 2014

Definition of Latin Puzzles

The ideas regarding boards, regions, and symbols mentioned in the post Latin Puzzles are condensed in the Latin Puzzle definition:

1. A board has:
  • any set of placeholders called cells
  • any set of cells called regions, each with the same size
  • every cell at least in one region
2. A Latin puzzle (lower-case p) has:
  • a board
  • a multiset of symbols with the same size as the regions
  • the instruction: Write one symbol on each empty cell so that every region has all symbols in the multiset
  • a set of clues: a particular set of pairs (symbol, cell) for some cells
  • a solution: the only set of pairs (symbol, cell) amongst those that fulfill the instruction to have the clues as a subset
3. A Latin Puzzle (upper-case p) is the set of puzzles that results when we render variable the multiset of symbols and the set of clues in a given puzzle. A Latin Puzzle may have an inscription: a set of pairs (symbol, cell) present in all its derived puzzles

4. The Latin Puzzle (upper-case p) is the set of puzzles that results when we render variable the board, the multiset of symbols and the clues in a given puzzle

With this definition, the Latin square Puzzle, Sudoku Ripeto –which includes classical Sudoku– and Custom Sudoku are all Latin Puzzles.

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