7. The system of claim 6 , the computing device further configured at least to: while the puzzle has more than one possible solution, add one or more central plus clues or central times clues to one or more selected central clue regions of the partial puzzle layout, the one or more central plus clues or central times clues conforming to the set of hidden number values identify one or more pair plus clues or pair times clues associated with one or more pair clue regions and one or more central plus clues or central times clues associated with one or more central clue regions, each of the one or more pair plus clues or pair times clues associated with at least one pair of mystery number regions having a plurality of potential hidden values, the identifying based at least in part on attempting to solve the puzzle using a deterministic search of potential solutions; select a first clue from the one or more pair plus clues or pair times clues based at least in part on the one or more pair plus clues or pair times clues being associated with a pair of mystery number regions having a least number of potential hidden values; and assign a pair of candidate hidden values to the pair of mystery number regions associated with the first clue.
7. The system of claim 6 , the computing device further configured at least to: while the puzzle has more than one possible solution, add one or more central plus clues or central times clues to one or more selected central clue regions of the partial puzzle layout, the one or more central plus clues or central times clues conforming to the set of hidden number values identify one or more pair plus clues or pair times clues associated with one or more pair clue regions and one or more central plus clues or central times clues associated with one or more central clue regions, each of the one or more pair plus clues or pair times clues associated with at least one pair of mystery number regions having a plurality of potential hidden values, the identifying based at least in part on attempting to solve the puzzle using a deterministic search of potential solutions; select a first clue from the one or more pair plus clues or pair times clues based at least in part on the one or more pair plus clues or pair times clues being associated with a pair of mystery number regions having a least number of potential hidden values; and assign a pair of candidate hidden values to the pair of mystery number regions associated with the first clue. 8. The system of claim 7 , the computing device further configured at least to: choose between adding the pair plus clue, the pair time clues, the central plus clue and the central times clue based at least in part on which addition will lead to a larger reduction in a total number of complete solutions or partial solutions for the puzzle.