26. A non-transitory computer-readable storage medium having stored thereon information indicative of a puzzle, the information indicative of a puzzle generated by a method comprising: receiving information indicative of a mathematical puzzle configuration; generating a puzzle layout conforming to the information indicative of the puzzle configuration, the puzzle layout 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; associating a mystery number value with each mystery number region in the puzzle layout; adding, while the puzzle has more than one possible solution, one or more pair plus clues or pair times clues to one or more selected pair clue regions to create the puzzle layout, the one or more pair plus clues or pair times clues conforming to the mystery number values associated with the mystery number regions in the puzzle layout; for each pair plus clue or pair times clues added to the puzzle layout, attempting to solve the puzzle to determine if the puzzle layout has only one solution; repeating adding and attempting to solve the puzzle until the puzzle layout has only one solution; and storing a representation of the puzzle layout having only one solution on the non-transitory computer-readable storage medium.
26. A non-transitory computer-readable storage medium having stored thereon information indicative of a puzzle, the information indicative of a puzzle generated by a method comprising: receiving information indicative of a mathematical puzzle configuration; generating a puzzle layout conforming to the information indicative of the puzzle configuration, the puzzle layout 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; associating a mystery number value with each mystery number region in the puzzle layout; adding, while the puzzle has more than one possible solution, one or more pair plus clues or pair times clues to one or more selected pair clue regions to create the puzzle layout, the one or more pair plus clues or pair times clues conforming to the mystery number values associated with the mystery number regions in the puzzle layout; for each pair plus clue or pair times clues added to the puzzle layout, attempting to solve the puzzle to determine if the puzzle layout has only one solution; repeating adding and attempting to solve the puzzle until the puzzle layout has only one solution; and storing a representation of the puzzle layout having only one solution on the non-transitory computer-readable storage medium. 27. The non-transitory computer-readable storage medium of claim 26 , wherein the method further comprises: adding, while the puzzle has more than one possible solution, one or more central plus clues or central times clues to one or more selected central clue regions to create the puzzle layout, the one or more central plus clues or central times clues conforming to the mystery number values associated with the mystery number regions in the puzzle layout; and choosing between adding central plus clue or the central times clue based at least in part on which central plus clue or central times clue will lead to a larger reduction in a total number of complete solutions or partial solutions.