23. A system for generating puzzles, the system comprising: a computing device comprising one or more processors communicatively coupled to one or more memories and a storage device, the computing device configured at least to: receive information indicative of a mathematical puzzle configuration; generate a puzzle layout conforming to the information indicative of the puzzle configuration, the puzzle layout including first areas of the puzzle including a plurality of clue regions and second areas of the puzzle including a plurality of mystery number regions, wherein the first areas of the puzzle and the second areas of the puzzle are in separate locations, wherein the plurality of clue regions include either a pair clue region interposed between a pair of mystery number regions, a central clue region surrounded by three or more mystery number regions, or both the pair clue region and the central clue region, wherein each of the mystery number regions corresponds to a mystery number value with no limitation on an amount of times a single mystery number value between 1-R appears in the puzzle when the puzzle is solved except that a same pair of mystery number values corresponding to the pair of mystery number regions interposing any pair clue region can only appear once in the puzzle unless the pairs of mystery number regions interposing three or more pair clue regions also form the three or more mystery number regions surrounding a single central clue, in which case the same mystery number value is utilized for all mystery number regions among the pairs of mystery number regions, wherein R is a whole number within a range of whole number values, wherein the puzzle can only have one solution when each mystery number value associated with each mystery number region among the plurality of mystery numbers regions are solved, wherein the pair clue region corresponds to a pair plus clue representing an arithmetic sum of mystery number values of the mystery number regions interposing the pair clue region or a pair times clue representing an arithmetic product of mystery number values of the mystery number regions interposing the pair clue region, wherein the central clue region corresponds to a central plus clue representing an arithmetic sum of mystery number values of the mystery number regions surrounding the central clue region or a central times clue representing an arithmetic product of mystery number values of the mystery number regions surrounding the central clue region, and wherein the puzzle layout is initially devoid of pair plus clues, pair times clues, central plus clues, central times clues, and mystery number values; generate a set of hidden number values, each hidden number value associated with a mystery number region in the puzzle layout; while the puzzle has more than one possible solution, add one or more central times clues to one or more selected central clue regions to create a partial puzzle layout, the one or more central times clues based at least in part on one or more hidden values of the set of hidden values, or add one or more pair plus clues to one or more pair clue regions to further create the partial puzzle layout, the one or more pair plus clues based at least in part on one or more hidden values of the set of hidden values, or add both one or more central times clues and one or more pair plus clues to create the partial puzzle layout; for each pair plus clue added to the partial puzzle layout, or for each central times clue added to the partial puzzle layout, or for each pair plus clue and central times clue added to the partial puzzle layout, attempt to solve the puzzle to determine if the puzzle has only one solution; and store a representation of at least the partial puzzle layout on the storage device.
23. A system for generating puzzles, the system comprising: a computing device comprising one or more processors communicatively coupled to one or more memories and a storage device, the computing device configured at least to: receive information indicative of a mathematical puzzle configuration; generate a puzzle layout conforming to the information indicative of the puzzle configuration, the puzzle layout including first areas of the puzzle including a plurality of clue regions and second areas of the puzzle including a plurality of mystery number regions, wherein the first areas of the puzzle and the second areas of the puzzle are in separate locations, wherein the plurality of clue regions include either a pair clue region interposed between a pair of mystery number regions, a central clue region surrounded by three or more mystery number regions, or both the pair clue region and the central clue region, wherein each of the mystery number regions corresponds to a mystery number value with no limitation on an amount of times a single mystery number value between 1-R appears in the puzzle when the puzzle is solved except that a same pair of mystery number values corresponding to the pair of mystery number regions interposing any pair clue region can only appear once in the puzzle unless the pairs of mystery number regions interposing three or more pair clue regions also form the three or more mystery number regions surrounding a single central clue, in which case the same mystery number value is utilized for all mystery number regions among the pairs of mystery number regions, wherein R is a whole number within a range of whole number values, wherein the puzzle can only have one solution when each mystery number value associated with each mystery number region among the plurality of mystery numbers regions are solved, wherein the pair clue region corresponds to a pair plus clue representing an arithmetic sum of mystery number values of the mystery number regions interposing the pair clue region or a pair times clue representing an arithmetic product of mystery number values of the mystery number regions interposing the pair clue region, wherein the central clue region corresponds to a central plus clue representing an arithmetic sum of mystery number values of the mystery number regions surrounding the central clue region or a central times clue representing an arithmetic product of mystery number values of the mystery number regions surrounding the central clue region, and wherein the puzzle layout is initially devoid of pair plus clues, pair times clues, central plus clues, central times clues, and mystery number values; generate a set of hidden number values, each hidden number value associated with a mystery number region in the puzzle layout; while the puzzle has more than one possible solution, add one or more central times clues to one or more selected central clue regions to create a partial puzzle layout, the one or more central times clues based at least in part on one or more hidden values of the set of hidden values, or add one or more pair plus clues to one or more pair clue regions to further create the partial puzzle layout, the one or more pair plus clues based at least in part on one or more hidden values of the set of hidden values, or add both one or more central times clues and one or more pair plus clues to create the partial puzzle layout; for each pair plus clue added to the partial puzzle layout, or for each central times clue added to the partial puzzle layout, or for each pair plus clue and central times clue added to the partial puzzle layout, attempt to solve the puzzle to determine if the puzzle has only one solution; and store a representation of at least the partial puzzle layout on the storage device. 24. The system of claim 23 wherein the addition of the one or more central times clues or the one or more pair plus clues is based on which of the one or more central times clues and the one or more pair plus clues leads to a larger reduction in possible solutions for the puzzle.