31. The non-transitory computer-readable storage medium of claim 30 , wherein the puzzle layout further includes at least one central clue region surrounded by at least three or more mystery number regions, wherein the same pair of mystery number values corresponding to the pair of mystery number regions interposing any pair clue region can appear more than once in the puzzle layout if 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 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, wherein the puzzle layout is also initially devoid of pair times clues and central plus clues, wherein the graphical user interface further receives missing mystery number values based on the central plus clues and the central times clues, and wherein one or more of the pair plus clues, pair times clues, central plus clues or central times clues contain one or more prepopulated clues.
32. The non-transitory computer-readable storage medium of claim 31 , wherein a prepopulated pair clue is based on a central clue region that has a shared mystery number region with the pair clue region.