Definition of Frequency Puzzles

The ideas regarding boards, regions, and multisets of symbols are condensed in the Frequency 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 Frequency 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 Frequency 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 Frequency Puzzle may have an inscription: a set of pairs (symbol, cell) present in all its derived puzzles.

4. The Frequency 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, Sudoku Ripeto –which includes classical Sudoku– and Custom Sudoku are both Frequency Puzzles.

Latin Puzzles are then a type of Frequency Puzzles.