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.

*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.

*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.