The Sudoku Ripeto Puzzle

Sudoku Ripeto is a Frequency Puzzle played on a square board with nine rows, nine columns, and four 3 x 3 sub-squares as regions. The difference with classical Sudoku is that numbers may repeat: this requires new solving strategies, and provides players with new solving experiences.

The Custom Sudoku Puzzle

Custom Sudoku is a Frequency Puzzle played on a square board with nine rows, nine columns, and four 3 x 3 sub-squares as regions. The difference with classical Sudoku is that it is played with letters that may repeat: this requires new solving strategies, and provides players with new solving experiences. Additionally, letters may form a word in the starting board, like in the example.

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.

The Custom Win Puzzle

Custom Win is a Frequency Puzzle played on a square board with nine rows, nine columns, and four square sectors as regions.

The Custom Wave Puzzle

Custom Wave is a Frequency Puzzle played on a square board with seven rows, seven columns, and seven sectors as regions.

The Custom Steps Puzzle

Custom Steps is a Frequency Puzzle played on a square board with ten rows, ten columns, and ten sectors as regions.

The Custom Star Puzzle

Custom Star is a Frequency Puzzle played on fourteen lines as regions.

The Custom Quadoku Puzzle

Custom Quadoku is a Frequency Puzzle played on a square board with nine rows, nine columns, and thirteen 3 x 3 sub-squares regions.

The Custom Frequency Square Puzzle

Custom Frequency Square is a Frequency Puzzle played on a square board with rows and columns as regions.

The Custom Focus Puzzle

Custom Focus is a Frequency Puzzle played on a square board with eleven rows, eleven columns, and four sectors as regions.

The Quadoku Ripeto Puzzle

Quadoku Ripeto is a Frequency Puzzle played on a square board with nine rows, nine columns, and thirteen 3 x3 square sectors as regions.

The Custom Dantly Puzzle

Custom Dantly is a Frequency Puzzle played on a square board with eleven rows, eleven columns, and six sectors as regions.

The Custom Lotus Puzzle

Custom Lotus is a Frequency Puzzle played on a lotus-shaped board with seven wreaths and fourteen spiral arms as regions.

The Orb Ripeto Puzzle

Orb Ripeto is a Frequency Puzzle played on a spherical board with eight meridinas, eight parallels, and eight curved rectangular sectors as regions.

The Custom Choc Puzzle

Custom Choc is a Frequency Puzzle played on a square board with eight rows, eight columns, and eight rectangular sectors as regions.

The Custom Life Puzzle

Custom Life is a Frequency Puzzle played on a circular board with circles as regions.

The Custom Orb Puzzle

Custom Orb is a Frequency Puzzle played on a circular board with eight meridians, eight parallels, and eight curved sectors as regions.