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.

Sudoku Ripeto: Power Mix (Volume 2)

Sudoku Ripeto: Power Mix (Volume 2) contains 60 Sudoku Ripeto puzzles with assorted difficulties and repetition patterns.

Sudoku Ripeto is the first Sudoku variant with repeated numbers. It presents new challenges to players and requires new solving techniques

Custom Sudoku: Countries & Territories (Volume 1)

Custom Sudoku: Countries & Territories (Volume 1) contains 252 puzzles in assorted difficulties, each featuring the name of a country or territory.

 

Custom Sudoku is the first Sudoku variant with repeated letters. It presents new challenges to players and requires new solving techniques

The Sudoku Ripeto Family

Presentation at the 13th Gathering 4 Gardner Conference in Atlanta.

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 Math behind Sudoku Ripeto

Mathematically, solving a Sudoku Ripeto or Custom Sudoku puzzle can be formulated as a problem of hypergraph coloring. As with classical Sudoku, finding puzzles and solutions can be performed with techniques like constraint programming or dancing links.
Of interest are questions of existence, enumeration and minimality. For example: what is the minimum number of clues that a Sudoku Ripeto puzzle played with numbers 111222333 may have? The answer for classical Sudoku is 17.
Many interesting decision questions about Sudoku Ripeto may well be NP-complete. In this case there could be no worst-case polynomial time algorithm able to answer them. One of these questions is: given a partially filled board, does it have a solution? For partially filled Latin squares the problem is known to be NP-complete indeed.

Definition of Latin Puzzles

The ideas regarding boards, regions, and sets of symbols 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 set 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 set.
• 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 set 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 set of symbols and the clues in a given puzzle.

With this definition, the Latin square Puzzle, classical Sudoku and other are all Latin Puzzles.

Latin Puzzles are then a type of Frequency Puzzles.