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.
- 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.
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.